STEMscopes Georgia Math Teacher Guide Grade 4 by acceleratelearning

4 Georgia Math Teacher Guide

Grade 4 Teacher Guide

STEMscopes.com ISBN: 979-8-88826-716-5

ISBN: 979-8-88826-663-2

4 GEORGIA

MATH G4

GEORGIA

Teacher Guide: Grade 4 ISBN: 979-8-88826-663-2 Published by Accelerate Learning Inc., 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2023, by Accelerate Learning Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. To learn more, visit us at www. www.stemscopes stemscopes.com.

USING THE TEACHER GUIDE

Using the Teacher Guide Plan and Strategize In the Teacher Guide,, you’ll ﬁnd details about each element in our curriculum. Use these summaries to guide what you’ll integrate into your lessons based on the needs of your students and your teaching style. Throughout each scope, facilitation focuses primarily on understanding Vertical Alignment along with core Engage and Explore elements. Please note that all other elements are still available online.

Discover and Facilitate As you move through each scope, find STEMscopes Tips that explain how to use and where to find many of the aligned resources that are included throughout the curriculum. In each Explore lesson, you’ll also find Facilitation Tips to assist you in this critical part of the learning process.

Journal and Record The Teacher Guide includes areas throughout its pages for you to write notes about lessons, your students, and more. There are also areas to sketch out long-range plans, make observations, and coordinate smallgroup sessions.

Reﬂect and Enhance Trying to remember what you did last year when teaching a lesson? Use the notes and plans you write here to remind you. Find out what works, what doesn’t, and how to do it better from year to year with our product to help you along the way. When it’s time for a new year, it’s also time for a new Teacher Guide. Guide. Keep them to reference or share them with a colleague.

Using STEMscopes ............................................................................................... 4 SCOPE 1

Place Value of Whole Numbers............................................................................ 20

SCOPE 2

Compare and Order Numbers .............................................................................. 34

SCOPE 3

Rounding ........................................................................................................... 54

SCOPE 4

Addition and Subtraction Algorithms ................................................................... 70

SCOPE 5

Prime and Composite Numbers ........................................................................... 90

SCOPE 6

Multiplicative Comparisons ............................................................................... 108

SCOPE 7

Multiplication Models and Strategies ................................................................. 126

SCOPE 8

Division Models and Strategies ......................................................................... 150

SCOPE 9

Generate Patterns ............................................................................................ 176

TABLE OF CONTENTS

Table of Contents

SCOPE 10 Problem Solve Using the Four Operations .......................................................... 192 SCOPE 11 Compare Fractions ........................................................................................... 210 SCOPE 12 Equivalent Fractions ......................................................................................... 232 SCOPE 13 Compose and Decompose Fractions and Mixed Numbers ................................... 254 SCOPE 14 Add and Subtract Fractions and Mixed Numbers ................................................ 270 SCOPE 15 Represent and Compare Decimals ..................................................................... 294 SCOPE 16 Area and Perimeter........................................................................................... 312 SCOPE 17 Angles ............................................................................................................. 330 SCOPE 18 Points, Lines, and Angles .................................................................................. 352 SCOPE 19 Properties of Two-Dimensional Figures ............................................................. 372 SCOPE 20 Measurement ................................................................................................... 390 SCOPE 21 Represent Measurement with Line Plots ............................................................ 416 © Accelerate Learning Inc. - All Rights Reserved

YEAR AT A GLANCE 2

Year at a Glance JULY

AUGUST

SEPTEMBER

OCTOBER

NOVEMBER

DECEMBER

JANUARY

FEBRUARY

MARCH

APRIL

MAY

JUNE

YEAR AT A GLANCE

Year at a Glance

USING STEMSCOPES

Using STEMscopes Utilizing the Home Section In the Home section, build your own content knowledge, analyze the standards, and gain an understanding of everything the scope has to offer. This is where you will ﬁnd all your lesson-planning materials so you can facilitate fun, purposeful experiences for your students. CONTENT SUPPORT • The standard(s) being addressed in the scope • The mathematical thinking and reasoning standards addressed in the scope • An overview of related concepts students have learned in pre-kindergarten • Student misconceptions and obstacles teachers may face • Detailed description of the content • Extensive list of terms and deﬁnitions students should know • Sample student responses to example questions • An overview of related concepts students will learn in future grades

Use Content Support to gain background knowledge to fully support the students’ understanding. • Includes the reasons a concept is being taught a certain way, examples that can be used to help teach the concepts, and sample student questions and answers • Explains what the students have already learned and gives insight to the concepts students will learn next • Provides known misconceptions students have about the content and obstacles teachers may face when teaching the content • Includes vocabulary and deﬁnitions students should learn throughout the scope Ideas for using this element: • Use it as a resource to understand why math concepts are taught a certain way and how the concepts should be taught. • Use it to understand what students should know before you teach the content, what they should learn, and what they will need to know to be successful in future grades.

STANDARDS EXPLAINED • The standard(s) being addressed in the scope • The verbs used in the standard that highlight what students should be doing • Concrete words and deﬁnitions students should know • A brief summary of the implications for instruction, including what students should understand by the end of the scope

Use the Standards Explained to fully understand the standard(s) that are being addressed in the scope. • Includes what students should be doing and what words they should know • Explains what the students must know to meet the standard • Shows the vertical alignment of relevant standards throughout the grade levels Ideas for using this element: • Use it to become familiar with the standard(s) being addressed and fully understand the concepts students need to know.

• A vertical alignment of related standards 4

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MATERIALS LIST • The ability to generate the total quantity of materials needed based on your class • A list of all the supplies that are needed for the Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration sections • A breakdown of each material, including the quantity per use; the item; whether the item is used per student, per pair, per group, or per class; whether the item is printed, reusable, or consumable; and the total quantity needed

Use the Materials List to plan for the materials that will be needed throughout the scope.

USING STEMSCOPES

Home

• Includes the ability to individualize the number of materials needed based on the total number of students, number of groups and stations, maximum class size, and total number of classes • Lists the materials needed for all the activities throughout the scope Ideas for using this element: • Use it to plan the materials you will need throughout the scope.

SCOPE OVERVIEW Use the Scope Overview to see every component of the scope. • Provides an easy-to-read, color-coded graphic showing the activities included in each element • Shows the sequential path students will take as they move throughout the scope • Includes the standard(s) and suggestions of how to use certain elements Ideas for using this element:

• The standard(s) addressed in the scope • Each element in the scope • The title of each part of an element • The order in which the scope should be taught

• Use it to quickly see the parts of the scope and how they interconnect. • Use it to plan how you will move through the scope.

PARENT LETTER • A description of the content of the Parent Letter • Procedure and facilitation points that provide a time frame for distributing the Parent Letter and suggestions for encouraging parent participation in the at-home activity

Use the Parent Letter to explain math concepts to parents. • Has a brief overview of the concepts being taught • Includes vocabulary terms and deﬁnitions students need to know • Provides resources and activities students and parents can do together to practice the concepts Ideas for using this element: • Use it to keep parents informed about what their children are studying in math. • Send home a copy of the Parent Letter the week before to notify parents of upcoming concepts and ways to help at home. • Be prepared to explain activities as questions arise from parents.

USING STEMSCOPES

Using STEMscopes Introducing Content with the Engage Section The Engage section is all about laying the foundation for learning. You begin this section by pre-assessing students using the APK (Accessing Prior Knowledge) and ﬁlling knowledge gaps using the Foundation Builder. The Hook then lays out a storyline narrative to establish a purpose for learning and captures students’ attention with real-world connections. ACCESSING PRIOR KNOWLEDGE • A general description of the activity and how it relates to what is being taught in the scope • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Sample student responses to embedded discussion prompts • A handout students use to complete the activity, if needed

Use the APK activity to help determine what students already know about the content as well as any misconceptions they have before beginning the scope. • Activates students’ thinking about the concept and how it’s been presented to them previously • Gives students opportunities to display what they know • Identifies the need to use the Foundation Builder to fill any knowledge gaps • Reveals possible misconceptions Ideas for using this element: • Due to the nature of this element, it is suggested that you complete this activity before the Hook activity. • Students typically complete and discuss the activities in small groups. • Student misconceptions identified here can be addressed and corrected as students progress through the scope.

FOUNDATION BUILDER • A general description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Sample student responses to embedded discussion prompts • Handouts, slideshows, and any other printed materials students will use to complete the activity

Use the Foundation Builder to help ﬁll learning gaps and review and reinforce previously taught content before beginning the scope. • Reteaches content previously taught • Uses concrete materials students can manipulate to explore mathematical concepts and develop proﬁciency • Addresses vocabulary with multiple meanings to eliminate confusion Ideas for using this element: • This activity is intended to be a short teacher-guided intervention for use in small groups. • Student preconceptions are addressed and corrected during this activity. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

HOOK • A general description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Pre- and Post-Explore sections • A video showing a real-world situation • Sample student responses to embedded discussion prompts • Handouts, videos, and any other printed materials students will use to complete the activity

Use the Hook to engage students using real-world contexts where speciﬁc math skills are needed. Here, students have their ﬁrst experience with the new content.

USING STEMSCOPES

Home

• Introduces a real-world problem that requires use of the skills that will be taught in the scope • Uses media to show the real-world situation in action • Gives students the opportunity to see how math is used in a real-world situation • Is revisited and the problem is solved after students complete the Explore activities from the next section Ideas for using this element: • Explain the real-world situation while showing the video. • Facilitate a discussion about how the scope’s math concepts are used in the situation. • Return to the Post-Explore section to solve the problem after completing the Explore activities. • Students typically complete and discuss the Post-Explore activities in pairs or small groups.

USING STEMSCOPES

Using STEMscopes Student Learning Using the Explore Section This is where students dig into the meat of the content. The Explore section provides scaffolded hands-on activities that build toward mastery of the standards. Each Explore supplies prompts for rich discussion and student reasoning, a Student Journal, and an Exit Ticket. The Explore section also gives students access to Virtual Manipulatives and teachers access to Skill Basics lessons designed to reinforce basic concepts before introducing the Explores. EXPLORES • A suggestion of which Skill Basics to use before completing the Explore, if applicable • A general description of the activity • The Mathematical Thinking and Reasoning Standards addressed in the Explores • A brief setup video showing the materials and preparation needed and explaining the activity • Materials and preparation needed to complete the Explores • Procedure and facilitation points that take you step by step through the activity • A scenario involving a realworld situation students need to solve • Sample student responses to embedded discussion prompts • Math Chat questions at the end of each Explore

Use the Explores to focus on developing students’ conceptual understanding of speciﬁc math skills using relevant situations and manipulatives. As students work through the activities, they will develop more abstract thinking and better number sense. • Provides real-world problems to motivate students to ﬁnd solutions using the math skills covered in the scope • Involves hands-on learning, rich discussions, and collaboration that encourage students to use thinking and reasoning skills • Reduces dependence on manipulatives as students progress through the activities • Helps students acquire new mathematical vocabulary through academic language embedded in the activities Ideas for using this element: • Read and discuss the real-world situations. • Provide an opportunity for students to work through the activities with partners or in small groups. • As students collaborate, monitor and assess their understanding by asking guiding questions. • Guide and correct students through any misconceptions noted during discussions or on their Student Journals. • Provide a Math Chat time at the end of the activity for students to share their observations and learning. • Have students complete the Exit Ticket to formatively assess their understanding of the concepts. • Use students’ responses from the discussions, Student Journals, and Exit Tickets to guide future instruction. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

VIRTUAL MANIPULATIVES • The Virtual Manipulatives include components such as these: • Place Value Disks • Base Ten Blocks • Number Lines • Pattern Blocks • Fraction Circles • Fraction Tiles • Two-Color Counters • Color Tiles • Linking Cubes • Geoboard • Clock • XY Coordinate Board

Use the Virtual Manipulatives to provide each student with a limitless supply of manipulatives.

USING STEMSCOPES

Home

• Helps students explore mathematical concepts • Makes learning engaging and meaningful • Leads to more complex understanding of math concepts • Allows students to make visual connections between math concepts and the virtual manipulatives • Helps students develop mental models and abstract thinking Ideas for using this element: • Use the Virtual Manipulatives in the classroom or remotely in place of concrete objects. • Encourage students to use the Virtual Manipulatives to develop proﬁciency in math concepts. • Differentiate instruction by using the Virtual Manipulatives for Englishlanguage learners and for students who are struggling with the concepts. Students can also beneﬁt from visual models when learning new concepts. • Use the Virtual Manipulatives to help address and clarify student misconceptions.

USING STEMSCOPES

Using STEMscopes Guiding Students Using the Explain Section The Explain section offers a variety of resources that help connect the experiences of the Explore activities to the academic content students need to know. These resources include Anchor Charts, Picture Vocabulary, My Math Thoughts, Show What You Know, and, in some scopes, an Interactive Notebook that can be used to support the Explore activities and solidify student learning. ANCHOR CHARTS • A general description of each activity • An Anchor Chart for each Explore • Sample student responses to embedded discussion prompts • A printable sample Anchor Chart

Use the Anchor Charts during or after the Explore activities as a tool to anchor student learning of the concepts addressed in the scopes. • Provides large, poster-sized visuals of the most important content strategies • Helps students achieve mastery of skills and reinforce concepts throughout the year • Gives students access to the charts to use as resources when needed Ideas for using this element: • Create Anchor Charts during instruction or after the Explore activities. • Ask students guiding questions while interacting with the Anchor Chart to help reinforce students’ understanding of concepts. • Display Anchor Charts during instruction or throughout the year to review learning.

PICTURE VOCABULARY • A slideshow of each relevant vocabulary word • Starting in Grade 2, a ﬂash card option with either the picture and word or the picture and deﬁnition for each word • A printable copy

The Picture Vocabulary presents new vocabulary with pictures and studentfriendly definitions. • Includes a slideshow with a picture and written or visual definition for each vocabulary word • Clarifies the meaning of words used throughout the scopes • Gives students access to the vocabulary words to use as a resource when needed Ideas for using this element: • Directly teach math vocabulary using the Picture Vocabulary. • Refer to the Picture Vocabulary throughout the scope to reinforce students’ understanding of vocabulary terms. • If available, encourage students to use the flash card feature to learn relevant math vocabulary. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MY MATH THOUGHTS • A general description of the activity • Preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • A printable Student Handout and Answer Key

Use My Math Thoughts to allow students to write out their mathematical thoughts and ideas using several different avenues to ensure that a balanced approach to writing in mathematics is attained.

USING STEMSCOPES

Home

• Focuses students’ writing on problem solving, strategies, and procedures • Allows students to identify how they feel they are progressing in attaining targeted math skills Ideas for using this element: • Allow students to discuss their thinking with their neighbors before writing their thoughts on paper. • Encourage students to persevere through their thinking and to use mathematical tools and models as necessary.

SHOW WHAT YOU KNOW Use the Show What You Know to allow students to independently demonstrate their understanding and practice new skills after exploring concepts.

• A different Show What You Know activity to correspond with each Explore

• Allows students to apply the knowledge and skills they learned in the Explore activities to new situations

• A general description of the activity

• Correlates each activity piece with the same-number Explore. For example, Show What You Know – Part 1 allows students to practice the skills they developed in Explore 1.

• Materials and preparation needed to complete the activity

Ideas for using this element: • Assign the activity for students to complete independently after ﬁnishing the corresponding Explore. • Provide reading assistance if needed.

• Procedure and facilitation points that identify how to use the activity • A printable Student Handout and Answer Key

• Provide manipulatives, especially those used in the Explore, as needed. • Identify whether instruction needs to be adjusted based on student misconceptions before proceeding to the next Explore.

INTERACTIVE NOTEBOOK • A general description of the Interactive Notebook

Use the Interactive Notebook to allow students to take notes, express ideas,

• Materials and preparation needed to complete the activity

and/or process the information presented in class.

• Procedure and facilitation points that identify how to use the activity

Ideas for using this element:

• A printable Student Handout

• Provides students with the opportunity to solidify their learning

• Prepare an Interactive Notebook using a spiral or composition notebook for each student. • Precut or allow students to cut the pieces for each Student Handout according to the instructions. • Allow time for students to complete the activity and then glue the pieces in their Interactive Notebook.

USING STEMSCOPES

Using STEMscopes Extending Learning with the Elaborate Section Workstations are a go! The Elaborate section makes differentiation a cinch with readymade activities—digital and paper-based games, Spiraled Review, Career Connections, literacy connections, and more—that are perfect for rotations! These activities allow students to continue learning while you make time for small-group interventions, reteaching, and independent projects to help both struggling and advanced learners. FLUENCY BUILDER • A description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Printable Instruction Sheets and game materials

Use the Fluency Builder games to give students the opportunity to practice the skills they learned during the Explore activities. • Involves games designed to be motivating and entertaining • Increases focus and collaboration skills as students play with partners or in small groups • Allows students to continue to practice skills throughout the year using the games • Develops ﬂuency as students become more eﬃcient and accurate when using their math skills during game play Ideas for using this element: • Place students with partners or in small groups. • Read the game directions, and model the game if needed. • While students are playing the game, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

SPIRALED REVIEW • A general description of a Spiraled Review • Preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Multiple real-world questions that cover previously taught math concepts • Printable Student Handout and Answer Key

Use the Spiraled Review to allow students to continue to practice skills throughout the year. • Motivates students to use the math skills to find solutions for real-world problems • Allows students to review previous or current grade-level content based on the focal points set for each grade • Gives students the flexibility to use different processes and strategies to reach solutions • Develops fluency as the students become more efficient and accurate in solving problems Ideas for using this element: • Read the story to engage student interest before moving on to the questions. • Use the Spiraled Review as a warm-up in class or send it home for homework, but be sure to discuss answers and strategies with the class as a whole group. • Refer to the standard in the lower right-hand corner of each question box to assess the students’ content knowledge or need for further intervention.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MATH STORY • A Lexile reading level for each passage, starting in Grade 2

Use the Math Story to give students an opportunity to practice ﬁnding the information they need to solve a problem while performing a new skill.

• A real-world story students can relate to

• Uses real-world engaging stories to support real-world application of math skills and concepts

• Multiple real-world questions that cover not only math concepts taught in the scope but also reading comprehension

• Offers questions covering both math concepts and reading comprehension

• Printable story in Kindergarten and Grade 1; Student Handout and Answer Key starting in Grade 2

USING STEMSCOPES

Home

• Develops ﬂuency as the students become more eﬃcient and accurate in solving problems • Allows students to improve reading comprehension skills and use reading strategies to answer questions Ideas for using this element: • Use the Math Story as a workstation activity, or assign it as homework. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects. Notes

USING STEMSCOPES

Using STEMscopes Extending Learning with the Elaborate Section PROBLEM-BASED TASK • A general description of a Problem-Based Task • Procedure and facilitation points that provide details on how to use the activity • Multiple real-world problems with multiple solutions or responses • Printable Student Handout and Rubric

Use the Problem-Based Task to provide a more rigorous opportunity for students to practice within a real-world context. • Allows students to work collaboratively to apply the knowledge and skills they have learned to an open-ended, real-world challenge • Engages students throughout the learning process in relevant situations where the math skill is needed • Enables students to use different processes and strategies to reach a solution • Allows students to communicate their understanding and evaluate others’ reasoning • Develops ﬂuency as the students become more eﬃcient and accurate in solving problems Ideas for using this element: • Allow students to work in groups. • Encourage students to look back at their Student Journals from the Explore activities if they need to review the skills they have learned. • If students are stuck, use guiding questions to help them think through the issue without telling them what steps to take next. • Allow each group to share its solution with the class. • Discuss how different groups tackled the challenge in different ways. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

CAREER CONNECTIONS • A short description of the focus of the Career Connections • Materials and preparation needed to complete the activity • Procedure and facilitation points that provide details on how to use the activity

Use the Career Connections to introduce students to STEM careers and the 21st Century Skills needed to succeed in those ﬁelds.

USING STEMSCOPES

Home

• Includes creativity and innovation, critical thinking, problem-solving, and technology skills • Gives students the opportunity to learn about people who have made an impact in the ﬁeld of mathematics or careers that highlight professions where math is used Ideas for using this element: • Group the students for rich collaboration and discourse. • Project the slideshow or play the video, if included. • Use the provided in-depth guiding questions to help students think about the topic from multiple angles.

INTERACTIVE PRACTICE Use the Interactive Practice to engage students in practice using technology. • Increases student participation and focus through graphics, sound, point accumulation, and engaging content • Develops ﬂuency as the students become more eﬃcient and accurate in solving problems

• An interactive online game • A “Show Answer” button • A feature that reads the questions • Sound and music that can be muted

Ideas for using this element: • Use the Interactive Practice as a workstation activity, or assign it as homework. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

USING STEMSCOPES

Using STEMscopes Assessing Using the Evaluate Section Get the data you need from the assessment tools provided in the Evaluate section. From performance-based assessments to Skills Quizzes and Observation Checklists, there are multiple evaluations to ensure students have mastered the standards. DECIDE AND DEFEND • A real-world prompt • Printable Student Handout and Answer Key

Use the Decide and Defend reasoning assessment to evaluate students’ ability to use mathematical evidence and reasoning. • Allows students to write out an argument in response to a relatable real-world prompt and provide support for their response • Focuses on real-world applications in new situations where complex reasoning and planning are necessary • Enhances critical thinking involved in problem solving and heightens students’ ability to make connections among mathematical ideas Ideas for using this element: • Review students’ responses to determine student mastery of math concepts. • Use students’ responses to determine whether students would beneﬁt from Intervention or Acceleration activities. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

SKILLS QUIZ • Multiple skills-based questions • Printable Student Handout and Answer Key

Use the Skills Quiz to identify which skills addressed throughout the scope students have mastered.

USING STEMSCOPES

Home

• Focuses on facts, details, deﬁnitions, and procedures with one correct answer Ideas for using this element: • Review students’ responses to determine student mastery of math skills. • Use students’ responses to determine whether students would beneﬁt from Intervention or Acceleration activities.

STANDARDS-BASED ASSESSMENT Use the Standards-Based Assessment to identify which concepts and skills presented throughout the scope students have mastered. • Focuses on applying skills and concepts in addition to answering how or why with one correct answer

• Multiple skills- and reasoning-based questions • Printable Student Handout and Answer Key

Ideas for using this element: • Review students’ responses to determine student mastery of math skills and concepts. • Use students’ responses to determine whether students would beneﬁt from Intervention or Acceleration activities.

USING STEMSCOPES

Using STEMscopes Using the Intervention and Acceleration Sections Useful during Elaborate or as an after-school support, Intervention contains a small handson activity designed to target students’ conceptual misunderstanding while building their math skills. The Intervention activities can also be used as a reteach or test-prep tool. In addition, the Intervention section includes information about how Supplemental Aids like base ten grids and number lines can be used during instruction. SMALL-GROUP INTERVENTION • A general description of the activity • Materials and preparation needed to complete the activity

Use the Small-Group Intervention to revisit concepts to build student understanding. • Allows small groups of students to meet for 20–30 minutes to complete activities focused on the concepts and skills addressed in the scopes

• Procedure and facilitation points that take you step by step through the activity

• Provides more hands-on experience with concrete objects

• Sample student responses to embedded discussion prompts

• Reinforces mathematical vocabulary through academic language embedded in the activities

• Teacher Checklist to monitor students’ mastery • Depending on the scope, a Checkup and Answer Key, Student Handout, and other printed materials students will use to complete the activity

• Gives students the opportunity to use thinking and reasoning skills during rich discussions and collaboration

• Provides an opportunity to take notes about each student’s progress during the activity Ideas for using this element: • Select small groups of students who need more support to develop mastery of math skills and concepts. • Provide ample opportunities for students to use manipulatives to explore mathematical concepts. • Ask guiding questions throughout the activity to assess students’ understanding and address misconceptions. • Take notes on the Teacher Checklist for each student to monitor his or her progress toward mastery of the skills. • If provided, have students complete the Checkup to formatively assess their mastery of math skills and concepts. • Use students’ responses from the discussions, notes on the Teacher Checklist, and the Checkup to guide future instruction.

SUPPLEMENTAL AIDS • A general description of the activity • Grade levels where the Supplemental Aids would typically be used • Materials needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Printable Supplemental Aids 18

Use the Supplemental Aids to help students become familiar with the tools they can use during classroom instruction and assessments. • Provides paper resources to help students, particularly those with disabilities, comprehend content Ideas for using this element: • Provide Supplemental Aids to students who meet eligibility criteria for their use during assessments. • Model how to use the Supplemental Aids. • Consistently incorporate the use of Supplemental Aids into your instruction and student activities. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Are your students ready to go above and beyond what they’ve just learned? In the Acceleration section, students connect the mathematical concepts to either science or engineering or relate what they’re learning to current events around the world. These activities prompt them to think more deeply about the content and its applications.

USING STEMSCOPES

Home

MATH TODAY • A general description of Math Today

Use Math Today to connect mathematical content to real-world events.

• Media provided by the Associated Press

• Allows students to explore connections and applications of math and other cross-curricular content through interactions with authentic, real-world media

• Procedure and facilitation points that take you step by step through the activity

• Focuses on real-world applications in new situations where complex reasoning is necessary

• Sample student responses to embedded discussion prompts

• Uses media to engage students and motivate them to understand how math is involved in various events around the world Ideas for using this element:

• Problems that connect the media with math concepts

• Provide opportunities for students who have mastered the content to complete the Math Today activity.

• Printable Student Handout and Answer Key

• Encourage students to discuss how mathematical concepts are used in the real world.

CREATE YOUR OWN Use Create Your Own as an enriching activity for students to create their own math-related products.

• A general description of Create Your Own

• Allows students to create their own inventions, plays, songs, technology apps, and more based on a real-world scenario

• Materials and preparation needed to complete the activity

• Focuses on real-world applications in new situations where complex reasoning is necessary

• General procedure and facilitation points

• Engages and motivates students to use their creativity in a unique way

• Real-world scenario

• Provides an opportunity for students to communicate their ideas with their peers and teachers using academic language

• Printable Student Handout and Rubric

Ideas for using this element: • Provide opportunities for students who have mastered the content to complete the Create Your Own. • Allow students to complete the activities individually or in groups. • Allow time for students to be as creative as possible! There is no boundary to their creativity in this activity. • Invite each student to present or perform his or her creative product to the class or small group. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

SCOPE 1

Place Value of Whole Numbers Scope Introduction SCOPE SUMMARY

Student Expectations

Students extend their understanding and application of place value concepts in the baseten system. Students read and write numbers to the hundred thousands place by using standard, expanded, and word forms. They solidify the concept that in the base-ten system, recognizing and showing that a digit in one place has a value ten times greater than what it represents in the place to its right, and they extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division.

4.NR.1.1 Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form. 4.NR.1.2 Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students extend their understanding of base-ten numbers through the hundreds place as they become proﬁcient in using the structure of the base-ten system. Secondgrade students read, write, and compare numbers to 1,000 using base-ten numbers, number names, and expanded form. Second-grade students also reason about even and odd numbers. In third grade, students read and write numbers up to 10,000 by using standard, expanded, and word forms, and they compose and decompose ﬁve-digit numbers in multiple ways by using thousands, hundreds, tens, and ones.

In ﬁfth grade, students apply their place value understanding to reason about decimals. Fifthgrade students read and write decimals up to the thousandths place by using standard, expanded, and word forms, and they compose and decompose the digits in multiple ways. They reason about how the value of each digit changes in a multi-digit decimal number when moving from left to right or vice versa.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

read and write multi-digit whole numbers up to 10,000 using baseten numerals and expanded form.

Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope. If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

recognize how the value of a digit in a multi-digit whole number changes based on its position in a number.

•

recognize that the value of a digit is either ten times or one-tenth of the value of the digit on either side, depending on its place.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Place Value Relationships In this exploration, students will ﬁnd the place value relationships for each day of donations for disaster relief Students will:

Explore 2

Explore 1

EXPLORE ACTIVITIES Read and Write Multi-Digit Whole Numbers In this exploration, students will convert information on numbers of discovered jewels, up to the hundred thousands place, into various forms. Students will:

use the place value disks to build the donation amount and place it on their Place Value Charts.

•

write numbers in base-ten numerals, expanded form, and word form.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

•

and represent the numbers with a model using place value disks.

•

PLACE VALUE OF WHOLE NUMBERS

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After completion of the activity, students share their learning, complete an Exit Ticket; then, revisit the Hook to solve. Notes

PLACE VALUE OF WHOLE NUMBERS

Place Value of Whole Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students decide which of the statements made about the place value of three-digit numbers is correct. This activity is intended to assess mastery of the following standard(s): 3.NR.1.1 Read and write multi-digit whole numbers up to 10,000 using base-ten numerals and expanded form.

Materials

Preparation

Printed • •

•

1 Slideshow (per class or per group) 1 Set of Student Response Cards (per class)

•

Prepare to project the Slideshow for the class, or print a Slideshow for each group. Print one set of Student Response Cards, and hang them in different locations around the classroom.

PLACE VALUE OF WHOLE NUMBERS

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Reusable •

1 Projector or document camera (per class, optional)

Procedure and Facilitation Points 1. 2. 3. 4. 5.

Project the Slideshow for the class, or distribute a Slideshow to each group. Read the statements to the class. Instruct students to discuss each statement with partners or in groups. Have students decide whether they agree with Julian’s statement, Jasmine’s statement, or Jessica’s statement. Ask students to stand next to the image of the student with whom they agree. They should be prepared to justify their reasons to the class. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Discuss the following question with the class: a.

What would Julian’s answer look like if it were drawn out using place value blocks? 3 hundreds blocks and 8 tens blocks

How do you write Jessica’s number in standard form? 308

If we added 1 tens block to the model, how would that change Jasmine’s answer? It would make the answer 300 + 10 + 8.

Which blocks did Jessica look at incorrectly? She identiﬁed the hundreds blocks as tens blocks.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Have base ten blocks available for students who are not ready to make the transition from using concrete objects to a pictorial representation. These students may beneﬁt from the Foundation Builder.

FACILITATION TIP Draw a place value chart (showing ones, tens, and hundreds) to help bridge students’ understanding of how numbers are decomposed by place value.

PLACE VALUE OF WHOLE NUMBERS

Place Value of Whole Numbers Hook – City Traﬃc ACTIVITY PREPARATION Students recognize how the value of a digit in a multi-digit whole number changes based on its position in a number. Students recognize that the value of a digit is either ten times or one-tenth of the value of the digit on either side, depending on its place.

Materials

Preparation

Reusable • • • •

• •

1 Phenomena Video (per class) 1 Projector (per class) 1 Whiteboard (per student) 1 Dry-erase marker (per student)

Plan to show the Phenomena Video. Prepare to write the data for the amount of traﬃc present for four days in a metropolitan city on the board for the students.

Part II •

Gather enough whiteboards and dry-erase markers for each student to have one of each.

PROCEDURE AND FACILITATION POINTS Part 1: Pre-Explore 1.

FACILITATION TIP

Introduce this activity toward the beginning of the scope. The class revisits the activity and solves the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: This is a very busy part of a city. There are lots of cars passing through the area every day. You are given data showing how many cars pass through on some given days. You want to see which days have the most traﬃc and which have the least, given this data.

Write the given data below on the board:

Have students discuss the title of the columns. To assess students’ prior knowledge, ask, “Which day has the highest number of cars? Which day has the lowest number of cars?”

Days of the Week

Number of Cars in the City

Thursday

936,430

Friday

93,692

Saturday

304,596

Sunday

79,865

STEMscopes Tip The Standards list is located along the menu bar. Here, a keyword can be entered to locate each standard. The search will result in a list of standards and direct links to the scopes where those standards appear. The standards are organized by grade level as well. Clicking on a standard within a grade level will also provide direct links to the scopes.

Discuss the following questions:

DOK-2 What are some things that you could do to help you compare the number of cars in the city on different days? I think I could put each of the numbers in a place value chart. I think that would help me compare the places easily, and I will be able to tell which day had a greater or least number of cars.

DOK-3 Is there another way you could rewrite the numbers to help you compare the number of cars? I think if I wrote each number in expanded form, I would be able to compare them easily.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 24

2. 3.

4. 5.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Rewrite the data on the board for the students to see. Discuss the following questions: a.

DOK-3 Is there another way you could rewrite the numbers to help you compare the number of cars? I think if I wrote each number in expanded form, I would be able to compare them easily.

Give each student a whiteboard and a dry-erase marker. Discuss the following questions: a.

FACILITATION TIP

DOK-2 Compare Thursday’s traﬃc to Friday’s. Which day has the greater amount? How do you know? 936,430 > 93,692, so Thursday had more cars on the road than Friday. I knew because I put both numbers in a place value chart like this. hundred thousands

ten thousands

thousands

hundreds

tens

ones

DOK-2 Both Thursday’s and Friday’s numbers of cars start with the same digits. How does the value of the 9s in both numbers differ? The 9 in 936,430 is 10 times greater than the 9 in 93,692. The value of the 9 in the hundred thousands place is 900,000, and the value of the 9 in the ten thousands place is 90,000. 90,000 × 10 = 900,000, so it is 10 times greater in the hundred thousands place.

DOK-2 How does the 30,000 in Friday’s number of cars compare to the 3,000 in Thursday’s? The 3 in 93,692 is one-tenth of or 10 times less than the 3 in 936,430 because 30,000 ÷ 10 = 3,000. That means 3,000 is one-tenth of 30,000.

DOK-3 Compare Saturday’s and Thursday’s traﬃc. What strategy did you use to compare them? I wrote both numbers in expanded form. That made it easier for me to see which number was greater. It looked like this: 300,000 + 4,000 + 500 + 90 + 69 900,000 + 30,000 + 6,000 + 400 + 30 300,00 is less than 900,000, so Saturday < Thursday since 300,000 < 900,000.

In the Engage section, the Foundation Builder is a graphic organizer in which students can write any number using the standard form, base-ten model, word form, and expanded form.

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FACILITATION TIP A Place Value Chart is found in the Intervention Section as a Supplemental Aid. STEMscopes Tip Career Connections is found in the Elaborate section of Grades 3–5. This element features a STEM career video or slideshow to showcase how the math concepts students are learning are applied in real-world work settings and what 21st century skills are needed to be successful. A followup activity related to the career that highlights the math concepts from the scope is also included. FACILITATION TIP Call on students to write their expanded forms on the board. This is an opportunity for students to check their own work.

e. DOK-1 Did Sunday or Friday have less traﬃc? Sunday had fewer cars on the road because 93,692 > 79,865.

PLACE VALUE OF WHOLE NUMBERS

Place Value of Whole Numbers Explore 1 – Place Value Relationships ACTIVITY PREPARATION Students collect donations for a disaster relief organization for 8 days and ﬁnd the place value relationships for each day based on a company’s donation match. Amounts will build up to one million.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Place Value Chart (per group) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • • •

2 Sheet protectors (per group, unless chart is laminated) 1 Dry-erase marker (per group) 1 Set of place value disks (per group)

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Place Value Chart for each group, and laminate it, if desired. Otherwise, place the different pages in clear sheet protectors. Print a set of Scenario Cards for each group, and cut them out. For students who need more support in recalling information, please see our Place Value Chart and Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP Have students sort the place value disks and place them on the Place Value Chart. Give students a few examples to build using both the disks and the chart. FACILITATION TIP Project this scenario for students to read it along with you. FACILITATION TIP Demonstrate with an example of a donation and how to calculate the amount the Money Matchers Company is matching.

1. 2.

3. 4.

5. 6.

8. 26

Give a Student Journal to each student. Give a set of place value disks to each group, along with a Place Value Chart. Students should place the charts side by side so the ones period is on their right and the thousands period is on their left. Allow students to open the bag, sort the place value disks, and place them above their Place Value Charts. Read the following scenario to the class: A local disaster relief organization is having its annual Penny Palooza! The Penny Palooza is an 8-day fundraiser in which donors give different amounts of money in the form of pennies to support disaster relief. The Money Matchers Company has graciously agreed to match the donation amount by also donating ten times the amount of pennies that Penny Palooza receives daily. Give a set of Scenario Cards to each group. Have students read the information on each Scenario Card for each day and work with their groups to solve what the match amount from the Money Matchers Company should be. Students should use the place value disks to build the donation amount and place it on their Place Value Charts. They should then use the place value disks (as needed) to build ten times that amount (matched by the Money Matchers Company) and ﬁgure out how to write that number at the bottom of each place value to see how the value changes for each digit. Students should record the amount of the donation they received for that day on their Student Journals, as well as the donation from the Money Matchers © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Company. For each day, they should write one multiplication equation and one division equation showing the relationship between the amount collected and the donation from the Money Matchers Company. a.

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

10. 11.

If students begin to notice the pattern of what happens to the digits when multiplying by ten, they may no longer need to build the model. Just make sure they can explain their thinking.

DOK-1 What do you notice about the digits in the number when you multiply it by ten? The new amount has the same digits; they just moved one place value to the left. It’s like the number shifted with another zero at the end.

DOK-2 If you have the same number of disks in the next value, what is the same between the two numbers, and what is different? The digit is the same, but the value is different.

DOK-2 If you were moving from a higher place value to a lower place value, what operation would you use? What would this do to the value? You would use division; the value would decrease by ten times the amount. It would be one-tenth the value.

FACILITATION TIP Remind students that multiplication increases a number and division is dividing the number into smaller parts.

PLACE VALUE OF WHOLE NUMBERS

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FACILITATION TIP

Allow students to work in their groups at their own pace to complete the 8 Scenario Cards and ﬁll out their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

This Student Journal is 3 pages. Consider completing the third page together as a class. Students can complete the other 6 Scenario Cards at their own pace.

Math Chat DOK-2 What connections did you make between a digit moving to a larger place value and the movement of the disks? It seemed like the digits moved one place value to the left. There was now another zero in the ones place. Each digit became ten times its original value. • DOK-1 What did you notice about the number when you multiplied it by ten? It seemed like the digits moved one place value to the left. There was now another zero in the ones place. Each digit became ten times its original value. • DOK-2 If 70 × 10 = 700, is there another equation you can write that uses the same numbers? What is it? 700 ÷ 70 = 10 or 700 ÷ 10 = 70 or 10 × 70 = 700 •

•

DOK-2 What would happen if we had a company that taxed (or took away) ___ of 10 1 the amount donated? It would decrease by ___ , ten times less than the original 10

amount.

STEMscopes Tip Each scope includes a Home section accessed along the scope’s menu bar. Here you will see student expectations as well as key concepts and fundamental questions. Each Home tab includes drop-down options to access the Scope Overview, Content Support, Content Unwrapped, Materials List, and Parent Letter pages.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP For the written answers on this Exit Ticket, clarify your criteria for success before students complete it independently.

PLACE VALUE OF WHOLE NUMBERS

Place Value of Whole Numbers Explore 2 – Read and Write Multi-Digit Whole Numbers ACTIVITY PREPARATION Students convert information on numbers of discovered jewels, up to the hundred thousands place, into various forms. Students will practice writing numbers in base-ten numerals, expanded form, and word form and represent them with a model using place value disks.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • •

1 Student Journal (per student) 1 Place Value Chart (per group) 1 Set of Gemstone Discovery Cards (per group) 1 Exit Ticket (per student)

Reusable • • • •

• • • • •

1 Dry-erase marker (per group) 1 Set of place value disks (per group) 2 Sheet protectors (per group, unless chart is laminated) 1 Resealable bag (per group)

•

Plan to divide the class into groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Place Value Chart for each group, and laminate it, if desired. Otherwise, place the different pages in clear sheet protectors. Print a set of Gemstone Discovery Cards for each group. Cut out and place them in a resealable bag. For students who need more support in recalling information, please see our Place Value Chart and Base Tens Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1. 2.

FACILITATION TIP

Project this scenario for students to read it along with you. Consider reading it more than once and guide students to ﬁnd the important information. FACILITATION TIP Project examples of the word form, expanded form, and standard form on the board. Students can refer to the Foundation Builder.

Give a Student Journal to every student. Give a set of Gemstone Discovery Cards, a Place Value Chart, a set of place value disks, and a dry-erase marker to every group. Students should place the charts side by side so that the ones period is on their right and the thousands period is on their left. Read the following scenario to the class: BREAKING NEWS! There has been a discovery of a massive variety of precious gemstones found underground—the biggest ﬁnding in history! You are a media manager, and you can’t wait to report this new discovery to the world. Different media outlets come with their own forms of communication, though. You will receive either the number of each place value or the amount in standard form. However, the websites and news reporters take in information in different forms. The news website uses a coding system, so it will need the number converted to expanded form to input the values into the site. The news reporter reads from a teleprompter, so they will need the number in word form to read it in the news report. Your challenge is to convert the information you’re given into a form that can be used by other news outlets so you can share in the excitement of this discovery and update the world! Have students read the gemstone type and number on each Gemstone Discovery Card and work with their groups to build the number on the Place Value Chart with place value disks. © Accelerate Learning Inc. - All Rights Reserved

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

•

• •

•

DOK-2 How does building the number with disks help you convert the number into a certain form? It helps us convert the number into expanded form since it shows us the values.

DOK-1 If there is a zero for a place value, do we have to write that into expanded form? No, we just write the numbers that have values.

Students should take one card from the bag, build the number on their Place Value Charts, and then convert it into standard form, expanded form, and word form on their Student Journals. Misconceptions with writing in word form usually occur when there is a zero in a place value. For example, when students see 1,002 and put it in word form, they will usually write, “One thousand and two.” Monitor groups to address this if it arises. Allow students to work until most groups have completed their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-1 When the number is written using digits, what do you call that? Base-ten numerals; standard form DOK-1 How do you read a number written in base-ten numerals? Read the number before the comma, and then say the period. Read the number in the thousands period, and say “thousand” when you get to that comma, and then read the number in the ones period. DOK-2 What is similar about the value of a digit and the expanded form? You just add all the values to create the expanded form. DOK-1 When writing the number name, what should be included? Every word you say when you read it out loud. It must include the period name when you get to the comma. DOK-1 If a number has a zero for a place value, what should you write in that place value when writing it in word form? You shouldn’t write anything—only numbers that have values. DOK-1 When reading and writing whole numbers, do you ever use the word and? No

Post-Explore 1. 2. 3. 4.

Acceleration

Encourage students to label the place values on their Place Value Charts to help distinguish in what place value the digits belong. They should use the charts as work mats to help guide their thinking. Discuss the following questions:

Math Chat •

Intervention

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Return to the Hook and instruct students to use their newly acquired skills to successfully complete the activity.

FACILITATION TIP Be sure students understand how the value of the digit zero by itself is different from the value of zeros after a digit.

FACILITATION TIP

PLACE VALUE OF WHOLE NUMBERS

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Direct students’ attention to the importance of zeros in a given number. Use an example such as allowance and how $4 is different from $40 and $400. Use the Virtual Manipulatives to demonstrate the difference.

STEMscopes Tip The Engage section, located along the scope menu, is designed to activate student interest in the learning topic. Within the Engage section, activities to access students’ prior knowledge about the topic, to build a strong foundation to bridge any gaps in understanding before diving into the new content, and to set the purpose for learning a new skill are included.

PLACE VALUE OF WHOLE NUMBERS

Place Value of Whole Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Place Value Relationships Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Read and Write Multi-Digit Whole Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Color Compromise

Jan Tinbergen

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Texas: A Leader in Ranching

Whole Numbers within 1,000,000 – Position and Place Value

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

PhET Interactive Simulation

Concert Tour Time

Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

PLACE VALUE OF WHOLE NUMBERS

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Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.) Resources

Students who are still acquiring the concept and need remediation

PLACE VALUE OF WHOLE NUMBERS

Place Value of Whole Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can read and write multi-digit whole numbers using base-ten numerals and expanded form.

What prompts will be used?

What does mastery look like?

PLACE VALUE OF WHOLE NUMBERS

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I can use concrete materials and numerical reasoning to represent and explain the relationships between the numbers 1, 10, 100, and 1,000.

I can recognize the relationship of same digits located in different places in a whole number.

I can recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right.

I can determine the value of a digit if it is shifted to the left or right using the relationship between multiplication and division.

SCOPE 1

Compare and Order Numbers Scope Introduction SCOPE SUMMARY Students build on their prior knowledge of comparing and ordering whole numbers to compare whole numbers through the hundred thousands place. Students use place value and scaled number lines to make comparisons. They use comparative language (greater than, less than, or equal to) and symbols (>, <, or =) to make comparisons. Students also order numbers within this range from greatest to least and from least to greatest. Student Expectations

4.NR.1.3 Use place value reasoning to represent, compare, and order multi-digit numbers, using >, =, and < symbols to record the results of comparisons.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Between ﬁrst and third grades, students use their understanding of place value, and they work with concrete models and/or number lines to plot, order, and compare whole numbers by using both comparative language (greater than, less than, or equal to) and symbols (>, <, or =). First graders make comparisons up to 100, second graders make comparisons up to 1,000, and third graders make comparisons up to 10,000.

In ﬁfth grade, students compare and order decimals to the thousandths place. Fifth-grade students round decimals to the nearest hundredth, tenth, and whole number. They add and subtract decimals to the hundredths.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

compare multi-digit numbers up to 10,000, using >, =, and < symbols

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. Notes _____________________________________________________________________________________________________________ _____________________________________________________________________________________________________________ _____________________________________________________________________________________________________________

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Compare Numbers In this exploration, students will compare whole numbers using place values and number lines and represent these comparisons using the symbols >, <, and =. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

total the box oﬃce sales for the top two movies of the year.

Order Numbers In this exploration, students will order whole numbers through the hundred thousands place.Students will: •

to order numbers on the Place Value Mat

•

can place the numbers on the number line

After completion of the activity, students share their learning, complete an Exit Ticket; then, revisit the hook to solve.

After students have had time to explore and solve the scenario, they will discuss their learning and complete with an Exit Ticket for assessment.

COMPARE AND ORDER NUMBERS

Home

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students read the story provided about insect species in Florida cities. They choose the correct ordering of the number of species from greatest to least. This activity is intended to assess mastery of the following standard(s): 3.NR.1.2 Use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols to record the results of comparisons.

Materials

Preparation

Printed •

•

1 Slideshow (per class, student, pair, or group)

Print the Slideshow maps, and post them around the classroom. If needed, print a Slideshow for individual students, pairs, or groups.

COMPARE AND ORDER NUMBERS

Home

PROCEDURE AND FACILITATION POINTS 1.

2. 3. 4.

Read the following scenario to the class: Florida is known for its wildlife. Insects are one of the most diverse species. Help the Entomology Association compare and order the number of insect species found in each of the following cities: Doral, Daytona, Delray, and Jupiter. Direct students’ attention to the Slideshow pages posted around the classroom, or distribute the Slideshow to individual students, pairs, or groups. Have students examine each map and stand next to the one they think represents the number of insect species from greatest to least. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Write this phrase on the board for student reference so that they can keep track of which way they are being asked to order the numbers. Students (especially those with tracking issues) may benefit from using scrap paper and a pencil or a whiteboard to record the individual numbers vertically before making comparisons. FACILITATION TIP Emphasize the direction of the comparison symbols. Explain that the greater than symbol indicates that the first number in the inequality is to the right of the second number when they are plotted on a number line. The less than symbol indicates that the first number in the inequality is to the left of the second number when they are plotted on a number line.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Hook – Sales Comparisons ACTIVITY PREPARATION Students compare and order whole numbers through the hundred thousands place using the symbols >, <, and =.

Materials

Preparation

Printed •

Part I

Reusable • • • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Ruler (per student) 1 Marker (per student) 1 Magnet (per student)

Gather enough markers and sheets of paper for each student to have one of each.

Part II • • •

Consumable • • •

Plan to show the Phenomena Video.

•

1 Student Handout (per student)

1 Sheet of paper (per student) 1 Sticky note (per student) 1 Piece of tape (per student, optional)

Be prepared to hand back the papers that students wrote numbers on from Part I. Print a Student Handout for each student. Gather enough sticky notes, rulers, and pieces of tape or magnets for each student to have one of each.

PROCEDURE AND FACILITATION POINTS STEMscopes Tip Located along the scope menu is the Elaborate section, where engaging activities that extend student learning and solidify their understanding of math concepts are found. Included are hands-on and virtual games; a math review and math story; a problembased task; proﬁles of careers and everyday life situations where math is used, and in the primary grades, a discussion of a data set. FACILITATION TIP

2. 3.

Have students show their numbers, and ask, “Which number is the largest? Which number is the smallest?” 6.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Distribute blank sheets of paper and markers to students. Ask students to hold the paper in a landscape (long) direction and to write down a number that is less than 1,000,000 on their paper. Have them each write the number using large digits across the center of the page and record their name along the bottom of the page. Collect their papers. The students use these papers again in Part II. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You are a team of sales representatives. The number you just wrote down represents the number of sales you have made so far this year. The boss wants to analyze the sales in this class. To help with the process, we are going to order the class sale amounts from least to greatest. We also need to determine the top 3 sales. Then, to reason about the magnitude between these 3 values, we will plot each value along a scaled number line. Discuss the following questions: a.

DOK-2 Which concepts and skills will we need to apply when ordering the numbers? We will need to apply our knowledge of place value to compare and order numbers.

DOK-2 When comparing two numbers, which place value do you look at ﬁrst? You should look at the place value farthest to the left. This is the digit with the greatest value. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What do you do if two digits in the same place value are the same? You look at the next place value to the right. (It is OK if students do not remember this from third grade. It will be addressed in the Explore activities.)

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2. 3.

4. 5. 6.

After students have completed all the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Place students in groups of 5. Redistribute the papers on which the students wrote their numbers. Discuss the following questions: a.

DOK-2 Which concepts and skills will we need to apply when ordering the numbers? We will need to apply our knowledge of place value to compare and order numbers.

DOK-2 When comparing two numbers, which place value do you look at ﬁrst? You should look at the place value farthest to the left. This is the digit with the greatest value.

DOK-2 What do you do if two digits in the same place value are the same? You look at the next place value to the right.

Ask students to place their papers in order from the least to the greatest numbers. Ask students to identify the top 3 sales. Discuss the following questions: a.

DOK-1 Which symbols are used to compare numbers? Conﬁrm responses, and record them on the board. > (Greater than), < (less than), and = (equal to)

DOK-1 Are the top 3 values each one number apart? Answers will vary, but chances are that they are not.

DOK-3 What will we need to consider when setting up the number line? We will need to determine what range of values to include, and we will need to determine a scale or how to skip count between values. Note: a common misconception is that students think only the numbers in the data set are to be included on the number line. However, unless the numbers are one apart, they will need to be placed below their speciﬁc corresponding increments.

DOK-4 Ask students to turn and talk about what range of values to include on their number lines, what number to skip count by when marking the increments, and whether there will be smaller increments between the larger ones. For example, if each main increment represents 5, then 4 smaller increments could be used between the main ones.

Intervention

Acceleration

FACILITATION TIP Choose a few of the numbers students wrote down in the Pre-Explore. Challenge students to organize the numbers in order from least to greatest. This is an opportunity to assess students’ prior knowledge.

COMPARE AND ORDER NUMBERS

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STEMscopes Tip The Evaluate section, found along the scope menu, contains assessment tools designed to help teachers gather the data they need to determine whether intervention or acceleration is warranted. From standards-based assessments to an open-ended reasoning prompt, there is an evaluation for every student’s learning style.

FACILITATION TIP If the student’s sequence is not correct, have other students explain why to provide assistance.

FACILITATION TIP Explain that the range is the lowest and highest numbers in a set of data.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Hook – Sales Comparisons 7.

FACILITATION TIP Model for students how to use the ruler to create evenly spaced increments for the number line.

Provide each student with a Student Handout and ruler. Explain that they are to reference their group’s sale values as they record comparisons and then plot the top 3 values. If none of the group’s sales values are the same number, they are to leave the equal sign row blank. Then, they are to plot the top 3 sales from least to greatest on the number line. Remind students to use a ruler when marking evenly spaced scaled increments. As students work, check their work for accuracy, and assist as needed. Discuss the following questions:

FACILITATION TIP

Place students in pairs and have them compare their numbers using the appropriate symbol.

DOK-2 Give an example of a greater-than comparison. Answers will vary.

DOK-2 Give an example of a less-than comparison. Answers will vary.

DOK-2 Were any sales of equal value? If so, which ones? Answers will vary.

DOK-3 Which scale did you use to mark the increments? Answers will vary.

STEMscopes Tip The Intervention section of each scope is found along the scope menu. If the assessments revealed that some students have not reached mastery of the content, the Intervention section has Small-Group Intervention and Supplemental Aid resources to help those students who need reteaching and additional support.

e. DOK-4 How does a number line show comparisons between numbers? A number farther to the left is less than a number farther to the right, a number farther to the right is greater than a number farther to the left, and numbers that are in the same position are equal to one another. f.

DOK-4 How does a number line help us see the magnitude between numbers? If the numbers are close together, they are close in size. The farther apart the numbers are, the greater the magnitude is between their values.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE AND ORDER NUMBERS

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COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 1 – Compare Numbers ACTIVITY PREPARATION Students compare whole numbers using place values and number lines and represent these comparisons using the symbols >, <, and =.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Place Value Mat (per group) 1 Set of Movie Ticket Sales (per group) 1 Exit Ticket (per student)

• •

Reusable • • • •

1 Set of place value disks (per class, to be used only if students are struggling) 1 Sheet protector (per group, optional) 1 Dry-erase marker (per group) 1 Dry eraser or tissue (per group)

• •

Consumable • •

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Place Value Mat for each group. Place each Place Value Mat in a clear sheet protector. Alternatively, Place Value Mats can be printed on card stock and laminated. Students can use dry-erase markers on the charts and erase them with the dry eraser or tissue. Print a set of Movie Ticket Sales for each group. Write the following two numbers on the index cards; each index card should have one digit. Draw a place value chart on the board, and use the index cards to build both numbers by taping them into the chart with the digits facing the board. Students should not be able to see the digits. Label the numbers in the place value chart:

12 Index cards (per class) 1 Roll of tape (per class)

•

Backyard Adventures: $369,241 Fish Tales: $273,506

For students who need more support in recalling information, please see our Place Value Chart and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used for support in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks and Number Lines)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP Reveal the numbers of sales (Backyard Adventures: 369,241, and Fish Tales: 273,506) on the board from right to left. Have students write the numbers on their Student Journals.

Part I: The Big Reveal! 1. 2.

3. 42

Read the following scenario to the class: It’s the ﬁnal tally for box oﬃce sales for the top two movies of the year! Who will win? Who will have the most sales? Reveal the digits in one place value at a time, starting with the far right (ones place). a.

DOK-1 What do you notice? There is a 1 and a 6.

DOK-1 Which number do you think is greater? The number with the 6, Fish Tales.

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What do you notice? There is a 4 and a 0 in the tens place. Now it looks like 41 and 6.

DOK-1 Which number do you think is greater? Backyard Adventures looks greater now!

•

• • •

Acceleration

Erase the check mark by Fish Tales,, and place a new check mark by Backyard Adventures.. Reveal the next-highest place value (hundreds place). a.

DOK-1 What do you notice? There is a 2 and a 5! Now it looks like 241 and 506!

DOK-1 Which number do you think is greater? Now it looks like Fish Tales has more again!

Change the check mark again, and continue until all the digits are revealed. On their Student Journals, students should record the two numbers, use the number lines to compare the two ticket sales, and write two comparison statements using symbols. After Part I, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

Intervention

DOK-1 How many digits are in each of these numbers? Each number has 6 digits. DOK-1 What did you notice when we were comparing the smaller place values? We went back and forth on which number we thought was greater. Every time we uncovered a new place value, it made us change our minds on which one was greater. DOK-2 Which place values are more helpful when comparing two numbers? The higher place values are more helpful for figuring out which number is greater or less. In these numbers, the hundred thousands place helped us find which number was greater. DOK-2 What did you notice when you placed the numbers on the number line? I could quickly see which number was the greatest. DOK-1 How could you write your findings using symbols? 369,241 > 273,506 DOK-1 How would you read this statement? The number 369,241 is greater than 273,506.

COMPARE AND ORDER NUMBERS

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FACILITATION TIP Have students share their number lines and comparison statements with partners. Each pair can then develop an explanation about comparing two numbers.

STEMscopes Tip The Acceleration section of each scope, located along the scope menu, provides resources for students who have mastered the concepts from the scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.

Part II: Movie Ticket Sales! 1. 2. 3. 4.

Distribute a Place Value Mat, a set of Movie Ticket Sales, place value disks, and a dry-erase marker to each group, as well as a Student Journal to each student. Give students a few moments to look over the materials and discuss what they notice. Explain to students that they are going to be comparing all-time movie ticket sales. They will compare two at a time until they ﬁnd the movie that earned the most! Have students collaborate to look at each pair of movies indicated on their Student Journals. Using their dry-erase markers, students should write both numbers, one right under the other, on their Place Value Mats. Students should also place each number on a number line and compare those results with what they found when they used the place value chart using symbols >, <, and = on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What do you notice about these numbers? They are different.

DOK-1 What is similar about these amounts? They are both in the hundred thousands.

DOK-1 How do you know they are different? They have different digits. There is a 5 in the thousands place in one number and a 6 in the thousands place in the other number.

FACILITATION TIP Students can take turns reading the table to ﬁnd the movie ticket sales and writing the numbers on their Place Value Mats.

FACILITATION TIP Provide students with a reference chart of place value names as they discuss the movie ticket sales. 43

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 1 – Compare Numbers d.

DOK-1 Which movie made the most money? Math Marvels made the most money.

e. DOK-2 How do you know? Students should explain that they can tell the ﬁrst two digits reading left to right are equal. The highest place value where the digits are different is the thousands place. One is a 5, and one is a 6. The number 6 is greater than 5; therefore, Math Marvels made more money. When they place the numbers on the number lines, students see that Math Marvels is greater than The Fourth-Grade Genius.

FACILITATION TIP Use other visual aids for students who are struggling with place values and comparison. 7.

After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP Use some total physical responses to review and reinforce the meanings of these inequality symbols. Fluency with these symbols will help students’ success when they compare decimals, fractions, and integers later.

• • • • • • •

DOK-1 What does the > symbol mean? (Point to it.) It means “greater than.” It means a number is greater than another number. DOK-1 What does the < symbol mean? (Point to it.) It means “less than.” It means a number is less than another number. DOK-1 What does the = symbol mean? (Point to it.) It means “equal to.” It means two numbers are equal. DOK-1 Which symbol would we write between movies 1 and 2 to show their comparison? We would write a < symbol. DOK-1 How would we read the relationship between these numbers? We would read it as “$305,485 is less than $306,490.” DOK-1 What is another statement we could use to show this? We could say, “$306,490 is greater than $305,485.” DOK-2 What helped you determine which movie made the greatest amount of money? Looking at the digits in the highest place values helped. The values of the digits helped me determine which movie made more money. The number line also helped me because I could quickly see which number was greatest and which number was least.

Post-Explore FACILITATION TIP

This Exit Ticket can be also be used as a Pre-Explore assessment to inform your instruction.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE AND ORDER NUMBERS

Home

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 2 – Order Numbers ACTIVITY PREPARATION Students order whole numbers through the hundred thousands place.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials Printed • • • • •

Reusable

1 Student Journal (per student) 1 Place Value Mat (per group) 1 Set of Spacecrafts for Sale Posters (per class) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

• • • • •

1 Sheet protector (per student, optional) 1 Dry-erase marker (per group) 1 Pad of sticky notes (per class) 1 Dry eraser or tissue (per group) 1 Set of place value disks (per group)

Consumable •

3 Sentence strips (per class)

Preparation • •

Plan to have students work in groups of 4 to complete this activity. Print a set of Spacecrafts for Sale Posters, and attach them to the sentence strips that show their values (below). Cover each digit in each number with a sticky note, and display the posters and covered values on the board. It may be necessary to trim the width of the sticky note so all digits ﬁt on the sentence strip. • • •

• •

Print a Student Journal and an Exit Ticket for each student. Choose how to implement the activity in the classroom: • •

• • • •

Spacecraft 1: 433,199 Spacecraft 2: 433,907 Spacecraft 3: 433,102

Print a set of Scenario Cards for each group of students. Print two sets of Scenario Cards, and have groups rotate between each set, like stations.

Print a Place Value Mat for each group. Place the Place Value Mat in a clear sheet protector. Alternatively, Place Value Mats can be printed on card stock and laminated for future use. Gather a set of place value disks for each group of students. For students who need more support in recalling information, please see our Place Value Chart and Open Number Line Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used for support in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks and Number Lines)

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS Part I: Which Spacecraft to Buy? 1.

2. 3.

Read the following scenario to the class: Mateo loves video games! His favorite video game, Simulated Universe, allows him to create a galaxy that includes different worlds, people, and buildings. He earns credits when everything in his universe is healthy and thriving, but he loses credits when there are problems in his universe. He recently noticed that he is losing credits because he has no way to transport people from one world to the other. Mateo wants to purchase a spacecraft that will take people from one planet to another, but he can’t decide which one to buy. He thinks the spacecraft that costs the most credits might be the best spacecraft, but he is not sure. We need to list the spacecrafts in order from greatest to least to help Mateo make his decision. Under the posters, draw three horizontal lines side by side. Label the far-left one “greatest” and the far-right one “least.” Allow students to come up with a plan for how they would order the numbers. a.

DOK-1 What would we need to do? We need to see what the digits in the numbers are.

DOK-1 You can only uncover one place value at a time. Where should we start? We should start with the highest place value, the hundred thousands place!

Uncover the hundred thousands place. a.

DOK-1 What do you notice? The digits are all the same; we need to uncover the ten thousands place to see if those digits are the same or different.

Uncover the ten thousands place. a. DOK-1 What do you notice? The digits are all the same; we need to uncover the thousands place to see if those digits are the same or different.

Uncover the thousands place. a. DOK-1 What do you notice? The digits are all the same; we need to uncover the hundreds place to see if those digits are the same or different.

Uncover the hundreds place. a.

DOK-2 What do you notice? Spacecraft 2 has a 9 in the hundreds place, while the other values have 1s. Spacecraft 2 is the most expensive spacecraft.

DOK-1 Do we need to keep uncovering digits for this number? No, we already know it’s the greatest.

DOK-1 If we were listing our numbers from greatest to least, where would this number go? It would go ﬁrst; it is the greatest.

The STEMscopes Teacher Toolbox, located under the Scopes tab on the menu bar, features a variety of resources and tools to help teachers get the get most out of their STEMscopes experience, including essentials like lesson-planning documents, intervention strategies, monitoring tools, mathematical discourse strategies, and data resources.

FACILITATION TIP Students will sequence, in order, the costs of the 3 rockets. Spacecraft 1: 433,199 Spacecraft 2: 433,907 Spacecraft 3: 433,102 To do this, they should begin with the largest place value and move to the smallest place value.

FACILITATION TIP Ask students the names of each place value. Ensure that students are saying the place value numbers. For example, a student might say, “The four is in the hundred thousands place, and the value is four hundred thousand.”

Move the poster and sentence strip for spacecraft 2, and retape it above the “greatest” line on the board. a.

STEMscopes Tip

COMPARE AND ORDER NUMBERS

Home

DOK-1 What should we do next? We should keep uncovering one place value at a time until we see digits that are different in the other two numbers.

Uncover the tens place. a.

DOK-1 What do you notice? Spacecraft 1 has a 9 in the tens place, while spacecraft 3 has a 0 in the tens place.

DOK-2 What does this tell you about the order we are trying to place our numbers in? Spacecraft 2 is the most expensive spacecraft; it is already ﬁrst in our list. Spacecraft 1 is the next greatest, so it is listed next, while spacecraft 3 is listed last because it is the least.

FACILITATION TIP Have students discuss their ordering in groups. Each group can then share their ordering with the class and give an explanation.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 2 – Order Numbers 10. 11.

FACILITATION TIP A number line will assist students in sequencing the numbers from least to greatest or vice versa.

12.

Move the posters and sentence strips so that spacecraft 3 is on the “least” line and spacecraft 1 is in the middle. Have students place the three numbers on the number line. a.

DOK-1 What do you notice about the numbers on the number line? They are in order from least to greatest.

DOK-2 Should we record these numbers in this order? We can, but we need to make sure we use the less than symbol between the numbers. We can also record them from greatest to least as long as we use the greater than symbol.

DOK-3 Describe how placing numbers on a number line can help you when ordering numbers. It is very easy to see the order of the numbers; you don’t have to line up the numbers by place value.

Students should record the values and the order on their Student Journals.

Part II: Explore the New Universe 1. FACILITATION TIP

Monitor groups and clarify as needed. Guide students with questions as needed. 3. 4.

Distribute a set of Scenario Cards, a Place Value Mat, place value disks, and a dry-erase marker to each group, as well as a Student Journal to each student. Explain to students that they should work as a group to order their numbers on the group Place Value Mat ﬁrst. Then, students can place the numbers on the number line on their Student Journals and make sure the order of the numbers on the Place Value Mat is the same as the order of the numbers on the number line. Have students answer the corresponding questions and record how the numbers are ordered on their Student Journals. Discuss the following questions: a.

DOK-1 What is different about these numbers? One number has no digit in the hundred thousands place.

DOK-2 What does that tell you about the order of this number? This number has the least value since its highest digit is in the ten thousands place, and ten thousands has less value than hundred thousands.

DOK-2 What strategy helps you determine the order of numbers? Looking at the numbers by their place value helps me see which number is greatest, which number is least, and which numbers are between those two numbers. Using a number line helps me quickly see the order of the numbers.

DOK-2 What do you need to do when writing the symbols between these numbers? I need to make sure they are all either greater than or less than symbols and that they show that all the numbers are ordered from least to greatest or greatest to least.

STEMscopes Tip A link to the list of standards is located on the menu bar. Here, standards can be accessed using two methods: click on the expandable list to see standards organized by grade level, or locate speciﬁc standards using the key word search. Either method will result in locating standards with direct links to the scopes in which they appear.

e. DOK-2 Why did you choose to order these numbers from greatest to least instead of least to greatest? I needed to list the seasons in order from when the planet was the farthest from its sun to when it was the closest. If the planet was farthest from the sun, the number of miles between it and the sun would be greater than the number of miles when the planet was closest to the sun, so I needed to order the number of miles from greatest to least. f. 5.

DOK-1 What symbol do you use when numbers are the same? The equal symbol.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat •

DOK-2 How did you know how to order the numbers in the various scenarios? Describe the process you used. We used the Place Value Mat. We looked at the digits and considered their value in each number. We circled the ﬁrst digit from the left that was different from the other digits. We also used a number line. We placed the numbers on the number line and could easily see the order of the numbers.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP When you preview this Exit Ticket with students, encourage them to neatly use the limited space above the number line.

COMPARE AND ORDER NUMBERS

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COMPARE AND ORDER NUMBERS

Compare and Order Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Compare Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Order Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

National Donut Day

Meteorologist

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

The Perfect Day

Compare Numbers within 1,000,000

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

COMPARE AND ORDER NUMBERS

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Problem-Based Task College Trip Around Texas Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Students who are still acquiring the concept and need remediation

COMPARE AND ORDER NUMBERS

Compare and Order Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can use place value reasoning to represent, compare, and order multi-digit numbers.

What prompts will be used?

What does mastery look like?

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I can use symbols to compare multi-digit numbers.

SCOPE 1

Rounding Scope Introduction SCOPE SUMMARY

Student Expectations

4.NR.1.4 Use place value understanding to round multi-digit whole numbers.

Fourth-grade students continue to use number lines to round, but experience with place value and number sense allows them to generalize the process of rounding numbers. This leads to being able to round much larger numbers and to round to digits other than the leading digit. For example, to round 15,397 to the nearest 10, the tens place changes form 90 to 100, and this affects the resulting digits in the ones, tens, and hundreds places. Students begin to develop eﬃciency rules for rounding numbers by thinking about the proximity of a number in relation to a midpoint set between two benchmark numbers. Students recognize that rounding is a tool for estimation while solving problems. Fourthgrade students round multi-digit numbers eﬃciently and appropriately, both in and out of the context of a real-world problem.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Kindergarten students gain a foundation for the base-ten number system as they work with numbers up to 20. In ﬁrst grade, students begin to count, represent, and write numerals that represent a number of objects up to 120. First-grade students also begin to view 10 ones as a new unit called a ten, and they begin to engage in mental calculation to determine 10 more or 10 less than a given two-digit number. In second grade, students extend their understanding of base-ten numbers up to 1,000. Second-grade students become proﬁcient in using the structure of the base-ten system by repeated bundling in groups of 10 or 100, with each unit being ten times as much as the unit to the right. Third-grade students use place value to round numbers up to 1,000 to the nearest 10 or 100. Third graders begin to see that rounding is valuable when estimating and for predicting and justifying the reasonableness of solutions while problem solving.

Fifth-grade students extend their understanding of place value by working with decimals to the thousandths place. They round decimals to the nearest whole, tenth, and hundredths place. Students in this grade have a deep understanding of place value and number sense, so they can explain and reason about rounded answers. It is important to know that the procedure for rounding is not taught after ﬁfth grade. Students are expected to apply rounding while estimating an approximation and to determine the reasonableness of an answer.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to:

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to:

•

round whole numbers up to 1,000.

•

round to the nearest 10 and 100.

•

analyze multiple-choice statements that identify rounded values.

organize guesses into a number line using three numbers at a time.

•

change a rounded numbers’ place value by 10, 100, or 1,000.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ROUNDING

Home

Round Using a Number Line In this exploration, students will place a number on a number line between intervals of 1,000, 10,000, or 100,000. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

use relative language to describe the position of the number between two intervals in order to round whole numbers.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Round Using Reasoning In this exploration, groups of students will round to different place values to estimate the number of miles traveled in a month using mental calculations. Through solving the scenario, students will: •

use mental calculations.

•

explain their mental calculation strategy.

After completion of the activity, students share their learning, complete an Exit Ticket; then, revisit the Hook to solve.

ROUNDING

Rounding Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ROUNDING

Home

ACCESSING PRIOR KNOWLEDGE Students determine which whole number is correctly rounded to the nearest ten or hundred. This activity is intended to assess mastery of the following standard(s): 3.NR.1.3 Use place value understanding to round whole numbers up to 1000 to the nearest 10 or 100.

Materials

Preparation

Printed •

•

1 Set of Task Cards (per class or per group)1 ABCD Answer Card (per student)

•

Reusable •

Prepare to project the Task Cards for students, or print a copy for each group. Print an ABCD Answer Card for each student. Cards may be laminated for future use.

1 Projector or document camera (per class)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5.

6. 7.

Project the Task Cards one at a time for the class, or distribute the cards to each group. Distribute an ABCD Answer Card to each student in the class. Give students time to read each card, and then ask them to hold up their ABCD Answer Cards with the answer they think is correct at the top. Scan the classroom to see which students answered correctly or incorrectly. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Continue this process for the other three task cards. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Pair up students who have different answers, and ask them to explain their thinking to one another. Provide an opportunity to change their answers. FACILITATION TIP Draw an open number line on the board. Students can justify their thinking by plotting a featured number and the related benchmark numbers. Have them then describe their position to one another on the number line.

ROUNDING

Rounding Hook – Jelly Bean Estimation ACTIVITY PREPARATION Students use place value understanding to round multi-digit whole numbers to any place.

Materials

Preparation

Printed •

• •

1 Jelly Bean Estimation (per class)

Reusable • • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Piece of yarn or string, 8 ft. long (per class)

•

Plan to show the Phenomena Video. Print one Jelly Bean Estimation per class. Cut out the cards along the dotted lines. You will have one large card with the total jelly bean number on it. You will have 3 cards for rounding to each place value. Cut a piece of yarn or string 8 ft. long for each class.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

3. FACILITATION TIP The Foundation Builder activity provides a review of rounding using a number line. Consider providing several examples for students to practice rounding. 4.

STEMscopes Tip Within the Engage section, Accessing Prior Knowledge is designed to determine what students have learned in the past about a concept before moving on. Activities are designed to assess students’ proﬁciency levels and ﬁnd learning gaps, which can be addressed using the Foundation Builder, also found in the Engage section.

Students will use this number line they are creating to see how the jelly bean number can be rounded to different places. 58

DOK-3 Why do you think rounding would help you make a closer guess? If we think of how the number would round, we can think of the two numbers it would be between when it is rounded.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following question: a.

3. FACILITATION TIP

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: At a carnival you are attending, there are several jars of jelly beans. Everyone is allowed guesses for the total number of jelly beans in all the jars. You made a guess as to how many jelly beans there are in all the jars. You did not guess correctly, but you think using approximate numbers could have helped you guess correctly. You learn there were 384,752 jelly beans in all the jars. You want to know what the number of jelly beans would be rounded to in different ways. You want to know how that may have helped you guess correctly. Discuss the following question:

DOK-3 Why do you think rounding would help you make a closer guess? If we think of how the number would round, we can think of the two numbers it would be between when it is rounded.

Use the cards from Jelly Bean Estimation, the yarn or string, and 4 students to create a number line at the front of the room. Give 3 student helpers 3 cards at a time. There are 3 cards for rounding to each place. Have another student hold the total jelly bean card the whole time and stand at the appropriate point along the number line with the help of their classmates. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Explain to students that the smaller number goes on the left, and the larger number goes on the right. There is a third number that is the midpoint benchmark. Have the 3 students hold the yarn or string to create the number line. Have the class help the student with the total jelly bean card choose the correct place to stand near the number line. Have students determine what the total number of jelly beans would be when rounded to different places, changing the cards each time it is rounded to a different place. Discuss the following questions: a.

DOK-2 How did you determine where the student with the total jelly bean card would go on the number line? I looked at the number that was halfway and placed the student before or after that number. If the student was after that midpoint, I knew that we needed to round up. If the student was before that midpoint, I knew we needed to round down.

DOK-2 Did the number get less or more precise, or closer to the actual number of jelly beans as we rounded to smaller place values? The smaller the place value we rounded was, the more precise and closer it got to the actual number of jelly beans in the jars.

DOK-3 Why would thinking of approximate or estimated numbers be helpful? This may help you get a result that is close to the actual number or solution. This may be helpful when determining whether we have enough money to purchase different items or when determining travel distance between places.

Intervention

Acceleration

ROUNDING

Home

STEMscopes Tip The Math Chat provides a forum for students to collaboratively discuss the concepts taught in the Explore lesson. This rich discussion helps students develop their number sense, mathematical vocabulary, and math thinking skills. A Math Chat is located at the end of each part of the Explore lesson and is also available in printable form.

FACILITATION TIP Demonstrate the difference between estimation and precision with a few examples. For example, say that there are about 300 students in the school (estimation) but that there are exactly 335 students (precision).

ROUNDING

Rounding Explore 1 – Round Using a Number Line ACTIVITY PREPARATION Students place a number on a number line between intervals of 1,000, 10,000, or 100,000. Students will then use relative language to describe the position of the number between two intervals in order to round whole numbers.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • •

Reusable

1 Student Journal (per student) 1 Set of Savings Signs (per class) 1 Exit Ticket (per student)

• •

4 Resealable bags (per group) 4 Cups of beans (lima, pinto, etc., per group)

Consumable • • • • • •

1 Roll of painter’s tape (per class) 1 Roll of clear tape (per class) 6 Sheets of white card stock (per class) 1 Black permanent marker (per class) 1 Red permanent marker (per class) 1 Pad of sticky notes (per class)

Preparation • • • • • • • •

Plan to have students work in groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Savings Signs on card stock. To make a beanbag, pour 1 cup of beans in each bag and close the bag. You may want to secure the closure with tape to ensure the bag does not come open. Create 4 beanbags for each group. Label each group’s bags A, B, C, and D. Find an area with enough room to tape down six lengths of painter’s tape. Each tape strip should be approximately 10 feet long. Mark intervals on each tape strip at each foot, using the Savings Signs. Number lines should show the following numbers: • • • • • • •

• • • 60

Multiples of 1,000 (1,000; 2,000; 3,000; 4,000; 5,000...) Multiples of 10,000 with numbers in the two hundred thousands (210,000; 220,000; 230,000; 240,000; 250,000; 260,000...) Multiples of 10,000 (10,000; 20,000; 30,000; 40,000; 50,000...) Multiples of 1,000 with numbers in the ten thousands (10,000; 11,000; 12,000; 13,000; 14,000; 15,000...) Multiples of 100,000 (100,000; 200,000; 300,000; 400,000; 500,000...) Multiples of 1,000 with numbers in the hundred thousands (100,000; 101,000; 102,000; 103,000; 104,000; 105,000...) See the example below:

Duplicate number lines if necessary. For students who need more support in recalling information, please see our Assorted Number Lines and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Number Lines) © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ROUNDING

Home

PROCEDURE AND FACILITATION POINTS Part I 1.

Have students gather around the number line with multiples of 1,000. Ask the following question: a.

4. 5.

6. 7. 8.

10.

DOK-1 What multiples does this number line show? It shows multiples of 1,000.

Read the following scenario to the class: You and your group have started a toy business. The number on which your beanbag lands is the amount you will report as your estimated savings each week from the sales of your toys. You need an estimate of your business’s proﬁt—how much money you are able to save each week—in order to be able to buy more materials to make new toys. Discuss the following questions: a.

DOK-2 When we want an estimate, what can we do? We can round the number to the closest multiple of 10; 100; 1,000; etc.

DOK-2 When is rounding numbers useful? Rounding makes numbers easier to add, subtract, multiply, or divide, especially when doing math in your head. A rounded number is not the exact amount, but it is picked strategically to be close.

Choose one student from each group to demonstrate how to toss the beanbag onto the 1,000s number line. Demonstrate how to toss the beanbag between the numbers on the number line. Students should take turns standing at the 0 mark and tossing the beanbag so it lands somewhere along the number line (proﬁt). Have students determine the number that shows the location of the beanbag their teammates tossed. Students will then determine which amount is closest to that location and record it on their Student Journals as their estimated savings. Next, repeat by asking students to take turns in their groups at the multiples of 1,000 number line. They will record their experience on Part I of their Student Journals and discuss the questions with their groups. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Describe the location of the beanbag along the number line. My beanbag is in the middle of the number line.

DOK-1 Which numbers is your beanbag between? My beanbag is between 2,000 and 3,000.

DOK-1 Is your beanbag closer to _____ or _____? (Fill in the blanks with the numbers the student’s beanbags were between.) My beanbag is closer to 2,000.

FACILITATION TIP Secure an area that is large enough for the different number lines. Each number line will have beanbags being tossed to determine the proﬁt.

STEMscopes Tip The Show What You Know activities, located in the Explain section, allow students to independently demonstrate understanding and practice new skills after exploring the concepts presented in each Explore lesson. These assignments provide insight into student learning and help guide teachers’ future instruction.

Encourage students to use language that helps them understand the relative distance, such as the words closer closer, nearer nearer, almost, and farther.

Part II 1.

Have students rotate to the other ﬁve number lines with their groups. They will write down their estimated numbers on their tables and begin rounding in their groups. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What number is directly in the middle of two multiples on your number line? The number 275,000 is between 270,000 and 280,000.

FACILITATION TIP After students complete all of the number lines, have them compare each number line. Ask students, “Which number line is more precise? Which number line is less precise? Why?” 61

ROUNDING

Rounding Explore 1 – Round Using a Number Line b.

DOK-2 How does knowing the middle number help you? It can help you ﬁgure out which multiple of 1,000s; 10,000s; or 100,000s you are closest to.

DOK-1 Describe the actual location of the beanbag along the number line. Answers will vary. My beanbag looks to have landed on 272,000.

DOK-1 Which numbers is your beanbag between? Answers will vary. My beanbag is between 270,000 and 280,000.

e. DOK-1 Is your beanbag closer to _____ or _____? (Fill in the blanks with the numbers the student’s beanbags were between.) My beanbag is closer to _______. 3.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat STEMscopes Tip

•

Fluency Builders are hands-on games that motivate students to practice the concepts from the scope. Located in the Elaborate section, these studentled games include printable studentfriendly instruction sheets detailing how the games are played as well as all the materials needed for game play.

•

• •

FACILITATION TIP Be prepared to follow up with some additional relevant real-world examples. In addition, challenge students by asking “When can rounding be misleading or unhelpful?” FACILITATION TIP On this Exit Ticket, have students draw a line from the values to their location on the number line.

•

DOK-2 How can a number line help you determine how to round a number? A number line can help us round a number because it gives us a visual model to see what multiples an actual number falls between and which multiple that number is closest to. The multiple it is closest to will help us determine what 1,000; 10,000; or 100,000 to round to. DOK-2 How does knowing the middle number help you? It can help you figure out which multiple of 1,000s; 10,000s; or 100,000s you are closest to. If the actual number is more than the middle number, then we will round up to the nearest multiple. If the actual number is less than the middle number, then we will round down to the nearest multiple. Using the first number line, write a number of your choice on a sticky note. For example, write 4,628 on a sticky note, and show it to the class. Explain the following to the class: Overall, your answers should reflect your understanding of looking at the digit in the place value your number line is counting by. Then, you should look at the digit to the right to see which multiple it is closest to. DOK-1 I’ve written 4,628 on a sticky note. Using the first number line that counts by multiples of 1,000, where would this number go on your number line? It would go between 4,000 and 5,000, but closer to 5,000. DOK-1 What multiple of 1,000 does it round to? It rounds to 5,000. DOK-2 How do you know what multiple of 1,000 it rounds to? I was rounding to the thousands place, and there was a 4 in the thousands place and a 6 in the hundreds place, so it had to be between 4,000 and 5,000. Since there is a 6 in the hundreds place, we know the number will be more than the midpoint of 500. This means the number is closer to 5,000 than 4,000. DOK-2 How is rounding a number useful? Rounding helps us when we are trying to estimate an answer. We can round the numbers first to see what number the actual answer is close to. We can round the price of items to see if we have enough money to buy them, etc.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes

ROUNDING

Home

ROUNDING

Rounding Explore 2 – Round Using Reasoning ACTIVITY PREPARATION Students reason through the situation to choose which place value it makes more sense to round to.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Monthly Delivery Posters (per class) 1 Exit Ticket (per student)

Preparation • • • •

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Monthly Delivery Posters, and hang them around the room. For students who need more support in recalling information, please see our Assorted Number Lines and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

2. FACILITATION TIP

Challenge students to estimate the sum of two different numbers using only a mental calculation. Consider informally assessing students’ prior knowledge.

3. 4. 5.

Read following scenario to the class: You’re the manager of a semitruck driving company that has hired truck drivers to deliver shipments all over the United States. As a delivery service, your company delivers packages to commercial businesses and residential homes. You have documented the miles traveled for commercial businesses and residential homes for different months of the year. It is important to track about how many total miles your semi-truck drivers are traveling for these different deliveries, as well as determining about how many more miles the drivers had to travel for the different types of deliveries. Discuss the following question: DOK-2 What can we consider when choosing which place value to round to? Answers will vary. Based on the situation, sometimes rounding to the greatest place value doesn’t always give you a very accurate answer. We can also consider what place value both numbers have. If one has up to the ten-thousands place and one to the tens, it doesn’t make a lot of sense to round to the ten thousands; the answer wouldn’t be as accurate as it could be. In this case, it would make most sense to round both numbers to the tens because both have numbers in that place value.

Give a Student Journal to each student. Assign each group to a poster. Students should stand next to the poster they are assigned to. Explain that each sign tells them the distance the truck drivers drove for commercial business deliveries as well as residential home deliveries. They will discuss and decide which place value to round to and then round the total number of miles as well as the difference between the distances traveled each month. © Accelerate Learning Inc. - All Rights Reserved

6. 7. 8.

9. 10. 11. 12.

Engage

Explore

Explain

Elaborate

Evaluate

Challenge students to try to do the calculations mentally. Tell students they don’t need to ﬁnd the exact amount. It is okay to calculate the total by strategically choosing numbers that are close. Allow students to share their strategies and solutions with their group members. Students should then record their mental calculation strategy on their Student Journals. Encourage students to repeat the same process and try to mentally calculate the difference between the distances traveled. Students should share their strategies and solutions with their groups and record them on their Student Journals. Students should rotate to the next month and repeat the same process on your cue. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-1 What do you have to do to ﬁnd the estimated solution? We have to ﬁgure out whether we have to add or subtract. Then, we round the numbers to make it easier to mentally add or subtract. DOK-2 How did you round the numbers quickly in your head? We looked at the numbers and considered which place value would give us a number close to the exact answer but can be easily added and subtracted. Sometimes, depending on the number of digits in each number, that was to the nearest thousand, ten thousand, or hundred thousand. These numbers were close to the exact number but easier to add or subtract. DOK-3 Why is it useful to be able to estimate the solution to a problem? It helps us know what the actual answer is going to be close to. It gives us an idea of what the solution will be.

Post-Explore 1. 2. 3. 4.

Intervention

Acceleration

FACILITATION TIP

ROUNDING

Home

Some students are very hesitant to estimate or round. A common practice is for students to ﬁnd an exact sum or difference and then round. Reassure students that being able to estimate solutions by rounding will help them become more proﬁcient mathematicians. FACILITATION TIP Groups will choose different place values to round. Monitor groups, and challenge each group to be the most accurate. FACILITATION TIP Have a group share with the class for their mental calculation for the distance traveled in a month. FACILITATION TIP Consider showing students how to do an equal sign that shows approximation (two wavy lines).

FACILITATION TIP Provide some real-world examples of when older students or adults need to be able to quickly round. For example, purchasing construction or landscaping supplies, ordering pizzas for a crowd, or budgeting for a birthday party.

ROUNDING

Rounding Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Round Using a Number Line Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Round Using Reasoning Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ROUNDING

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Blueberry-Picking Season

Elevator Installer

A quick story to engage student interest along with four problems covering previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Great State Fairs

Round Numbers within 1,000,000

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task We’re Moving In! Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

ROUNDING

Rounding Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ROUNDING

Home

What prompts will be used?

What does mastery look like?

I can use place value understanding to round multidigit whole numbers.

I can use tools (number line and hundred chart) to round numbers.

I can eﬃciently use rounding to get an estimate and to check the reasonableness of an answer.

SCOPE 1

Addition and Subtraction Algorithms Scope Introduction SCOPE SUMMARY Students fluently add and subtract multi-digit whole numbers using an efficient algorithm based on place value and the properties of operations. As students evaluate and solve problems, they determine the most efficient strategy to use. Students must understand and be able to explain the strategy chosen. Possible strategies include partial sums and differences algorithms and the standard algorithm. Student Expectations

4.NR.2.1 Fluently add and subtract multidigit numbers to solve practical, mathematical problems using place value understanding, properties of operations, and relationships between operations.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

By third grade, students are able to ﬂuently add and subtract numbers up to 1,000 using various strategies, such as base-ten models and a number line, as well as the standard algorithm with procedural ﬂuency. Third graders also use diagrams and number lines to model and solve addition and subtraction problems up to 10,000, and they represent these problems with an equation with a letter standing for an unknown quantity.

The goal in fourth grade is fluency with multi-digit addition and subtraction. Students must be able to work problems efficiently, flexibly, and accurately. Fifth grade expects students to be proficient in this area as their focus with addition and subtraction moves to decimals and fractions. Students add and subtract multi-digit numbers with decimals to the hundredths by using various strategies. Students use base ten blocks, place value disks, partial sums, and the standard algorithm to help them solve. The use of place value and properties of operations continues to be valuable in problem-solving situations.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses whether students’ ability to:

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to:

•

read word problems.

•

decide whether to add or subtract (numbers within 1,000).

discuss how to ﬂuently add and subtract multi-digit whole numbers.

•

use standard algorithm.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Students move on to the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 70

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Multi-Digit Addition With peers, students work to solve a scenario where they help determine the distances traveled for boarding passes and the total distance traveled for a lottery winner. In solving the scenario, students will: •

choose a strategy to solve before using the standard algorithm.

•

use open number lines and partial sums.

•

solve multi-digit addition problems.

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, groups of students will be presented with a scenario where they will be solving problems for a secret raﬄe for a carnival to win a prize. Through solving the scenario, students will: •

subtract multi-digit numbers using a variety of strategies, including the standard algorithm.

Students conclude the exploration after they have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 3

Multi-Ddigit Subtraction

ADDITION AND SUBTRACTION ALGORITHMS

Home

Adding and Subtracting Strategies In the last exploration, students will practice using various problem-solving strategies and the standard algorithm when adding and subtracting multi-digit numbers. In solving the scenario, students will: •

choose one of two statements to write an expression to represent the problem.

•

solve each problem using two strategies (open number line, partial sums of differences, or the standard algorithm).

•

write a solution statement with justiﬁcation.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students read word problems and decide whether to add or subtract (numbers within 1,000). This activity is intended to assess mastery of the following standard(s): 3.PAR.2.1 Fluently add and subtract within 1000 to solve problems.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Print a Student Handout for each student. Plan to have students work in pairs to complete this activity.

PROCEDURE AND FACILITATION POINTS 1. 2. 3.

Give a Student Handout to each student. Give students time to read each word problem and solve the problems using any strategy they choose. Instruct students to trade papers with their partners. Students should review the work of their partners, and the pair should discuss their responses to the following questions: a.

Did we solve the problem the same way?

Were any mistakes made?

After the students have had time to review their work with their partners, lead a class discussion about what strategies they used. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

ADDITION AND SUBTRACTION ALGORITHMS

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FACILITATION TIP After reading the ﬁrst word problem, this would be a good place to insert a review of key words in addition and subtraction problems. You could create an anchor chart listing key words by having students brainstorm words that indicate whether a word problem calls for addition or subtraction. FACILITATION TIP Look out for students struggling with the addition and subtraction versus struggling with the wording and determining which operation to use. Suggest using a place value chart to students who are struggling with the computation.

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Hook – Spaghetti, Spaghetti, and More Spaghetti ACTIVITY PREPARATION Students ﬂuently add and subtract multi-digit whole numbers using the standard algorithm.

Materials

Preparation

Reusable

Part I

• • • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Dry-erase marker (per student, optional) 1 Whiteboard (per student, optional)

•

Part II •

Consumable •

Plan to show the Phenomena Video.

•

1 Sheet of scratch paper (per student)

Have scratch paper or a whiteboard and dry-erase marker for each student. Plan to have students work in pairs or groups for this activity.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

3. FACILITATION TIP Depending on your students, consider challenging them by skipping writing the clues on the board. Focus on listening skills and repeat the clues two to three times each.

STEMscopes Tip In Grades 2–5, a Standards-Based Assessment can be found in the Evaluate section. This assessment is designed to allow students to demonstrate their mastery of the standards. Multiple-choice and gridded response questions reﬂect the formats found on state tests. The assessment can be administered and scored multiple ways: digitally, printed, or edited to meet students’ needs. 74

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Three brothers are building spaghetti monsters. You need to ﬁgure out how many spaghetti noodles each boy used and how many noodles they used altogether. Write the following three clues on the board: a.

The middle brother used 1,317 spaghetti noodles.

The older brother used 724 more noodles than the middle brother.

The youngest brother used 598 noodles less than the middle brother.

Discuss the following questions: a.

DOK-1 What do we know? We know the three brothers each have a different number of spaghetti noodles.

DOK-1 How many brothers are there and which brother’s spaghetti noodles do we know? There are 3 brothers. We know that the middle brother used 1,317 noodles. We have clues to help us ﬁgure out how many noodles the other two brothers used for their monsters.

DOK-2 How do you think we would ﬁnd out how many noodles the other two brothers used? There are some words in the clues for the older and younger brothers’ noodles used that sound like we will need to add or subtract to ﬁnd the numbers of noodles.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do we know? We know the three brothers each have a different number of spaghetti noodles.

DOK-1 How many brothers are there, and which brother’s spaghetti noodles do we know? There are 3 brothers. We know that the middle brother used 1,317 noodles. We have clues to help us ﬁgure out how many noodles the other two brothers used for their monsters.

Give each student scratch paper and a pencil or a whiteboard and a dry-erase marker. Have students work in pairs or small groups. Review the problem, and allow students to solve it. Gather students in a whole group, and discuss the following questions: a.

DOK-1 How many noodles did the middle brother use for his spaghetti monster? He used 1,317 noodles. This is the one brother we knew for sure. This is the information I used to help me ﬁnd how many noodles the other two brothers used.

DOK-2 What did you do to ﬁnd the number of noodles the older brother used for his spaghetti monster? I added 1,317 + 724 since the clue said that he used 724 MORE than the middle brother. I drew this tape diagram to help me know which operation to use. This is what my algorithm looked like: 1,317

FACILITATION TIP As students are working, prompt their discussions by asking how they know if they need to add or subtract to ﬁnd each boy’s number of spaghetti noodles.

ADDITION AND SUBTRACTION ALGORITHMS

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FACILITATION TIP As soon as one student answers, ask others if there are other models or other strategies that anyone else used to solve.

724 ? 1

1,317 + 724 2,041 c.

STEMscopes Tip

DOK-2 What operation did you use to ﬁnd the number of noodles used by the youngest brother? I subtracted to ﬁnd the number of noodles used by the youngest brother. I drew a tape diagram to help me decide what operation I needed to use. This is what my algorithm looked like: ?

598 2,041 9 13 1 10 3 11

2,041 – 598 1,443 d.

Small-Group Intervention is found in the Intervention section. This handson lesson is used to build student understanding of the concepts covered throughout the scope. The lesson includes Teacher Checklists to help monitor students’ progress and Student Handouts. A short assessment to determine whether students have attained mastery of the skills and concepts being retaught is available in Grades 2-5.

DOK-2 How many noodles did all three brothers use altogether? The oldest brother used 2,041, the middle brother used 1,317, and the youngest brother used 1,443. I added all three together. Altogether, the brothers used 4,801 spaghetti noodles.

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Explore 1 – Multi-Digit Addition ACTIVITY PREPARATION Students solve multi-digit addition problems. Students will choose a strategy to solve before using the standard algorithm. Strategies include open number lines and partial sums.

Standards for Mathematical Practice • • • •

MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • • •

1 Student Journal (per student) 1 Set of Boarding Passes (per group) 1 Set of Passport Pursuit Cards (per group) 1 Set of Addition Work Mats (per group) 1 Exit Ticket (per student)

• •

• • •

Reusable • • •

1 Set of place value disks (per group, as needed) 2 Dry-erase markers (per group) 3 Sheet protectors (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a set of Addition Work Mats for each group. The third page is intended to be used by students who need the support of place value disks as they complete the standard algorithm. Place all Addition Work Mats inside sheet protectors. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Boarding Passes and Passport Pursuit Cards, and laminate them for durability. If possible, print the Passport Pursuit Cards in color. For students who need more support in recalling information, please see our Base Tens, Open Number Line, and Place Value Mat Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

Locate the destinations on a map. Students could draw lines to show the ﬂight path on a printed map.

Read the following scenario to the class: You hit the lottery! You have decided to use your winnings to travel to new places around the world. Grab your passport, and get ready to see new sights! Invite students to look at the Passport Pursuit Cards so they can see the beautiful places they will be visiting over the next year. Have students pull out their Boarding Passes, and have them match up the connecting ﬂights for trip 1. The different trips are listed on their Student Journals. Once they have chosen the correct boarding passes for trip 1, have the students match the correct Passport Pursuit Cards for this trip to their Boarding Passes so they can get an idea of the locations they will be visiting. Students will then work in groups to take the distances traveled for each boarding pass and add them together to ﬁnd the total distance traveled for that trip. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Instruct students to work together using their Addition Work Mats to add their numbers using multiple strategies, including an open number line, partial sums, and the standard algorithm. Students can record subtraction strategies of their choice and the standard algorithm on their Student Journals. Their strategies do not have to be the same as everyone else in their groups. If students are struggling with the algorithm, allow them to use the Addition Work Mat and place value disks to model regrouping. After the students have completed solving for trip 1, discuss the following questions to check for understanding: a.

DOK-3 Which addition strategy did you find to be the most efficient way to solve this problem? Answers may vary. I found partial sums to be the most efficient way to solve because I found the same answer as with the standard algorithm, but I could more easily add my numbers using their place value.

DOK-1 How do you solve using the standard algorithm? First, we need to line up the numbers to make sure the place values are in line. Second, we add the numbers’ common place values together starting in the ones place, working toward the greatest place value. Third, we must regroup as we go if any place adds up to more than a group of ten of that place. We continue this pattern until all the place value digits have been added together.

DOK-1 How do we regroup in trip 1 using the standard algorithm? When I add the ones, I ﬁnd that I have 11 ones. We regroup the 11 ones and make a group of 1 ten and 1 one. The 1 ten gets carried over to the tens place, and the 1 one remains in the ones place. I can then add the 1 ten I carried over to the 9 tens and 3 tens that are in the tens place. This would give me 13 tens. I regroup the tens by making a group of 10 tens and 3 tens. The 10 tens is worth 1 hundred and gets carried over to the hundreds place, and the 3 tens remains in the tens place. I repeat this process as necessary with any place that requires regrouping or where we can make a group of ten.

d. DOK-2 Which addition strategy had a similar way of regrouping as the standard algorithm? Answers may vary. I found that regrouping while using the partial sums was similar to the standard algorithm because I could regroup my ones and make them a ten to carry over to the tens place. e. DOK-2 Did you ﬁnd that all of the strategies have regrouping? Not all the strategies show regrouping in the same way the standard algorithm represents regrouping. I did not see regrouping with my open number line, I just made hops of a certain amount. 8.

Instruct students to continue working together using the same steps and their Addition Work Mats to ﬁnd the answers for trips 2 and 3. On the last page of their Student Journals, encourage students to ﬁnd the total distance of all 3 trips on their own. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 Should we always use the same addition strategy for every problem? Explain. No, the addition strategy we use should depend on the numbers in the problem and whether any of those numbers will need to be regrouped or added based on place value or how far away they are from 10 or 100. • DOK-3 What makes a strategy the best choice? The best choice is the strategy you find to be the most efficient and that can help us solve the problem as quickly as possible while still understanding the value of the digits. • DOK-2 Is the standard algorithm always the most efficient method to solve an addition problem? Explain. No, the standard algorithm is not always the most efficient because being able to add using place value can sometimes be quicker. •

Intervention

Acceleration

FACILITATION TIP For groups who ﬁnish early, have them calculate the total mileage including the return trip. Assume the distances for the return trip are the same as the distances for the trip to the destination.

FACILITATION TIP List the addition strategies that students used. Add any strategies that were not shared by students. Some students may not have practice with several of the strategies.

ADDITION AND SUBTRACTION ALGORITHMS

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STEMscopes Tip Math Today, found in the Acceleration section, is designed to engage students using real-world videos, photos, or articles provided by the Associated Press in exploring the connections between the current events and math as well as other cross-curricular content. Used as a review or a formative assessment, this activity includes a printable Student Handout and Answer Key.

FACILITATION TIP Watch out for students who misalign the digits when adding. Remind students that the ones places should align, the tens places should align, and so on. FACILITATION TIP Include some more real-world applications for proﬁciency with different addition strategies. FACILITATION TIP Address calculators as a tool; explain the strengths and weaknesses. Remind students that even if they use a calculator they still need to understand different ways to solve problems. 77

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Explore 1 – Multi-Digit Addition DOK-1 When solving the standard algorithm, what do you do if you have more than ten in a place value? You have to regroup them: take 10 from one place value, and regroup them for one in the next place value. • DOK-2 What similarities did you ﬁnd between the strategy you used and the standard algorithm? I noticed that all my strategies add based on place value. As long as you add the correct place values together and regroup as necessary, you will ﬁnd the same sum. • FACILITATION TIP Before this Exit Ticket, use individual whiteboard practice to guide students through the standard algorithm with regrouping.

Post-Explore

FACILITATION TIP

When you preview this Exit Ticket with students, clarify your criteria for success. Consider that some students may only be proﬁcient in one strategy.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ADDITION AND SUBTRACTION ALGORITHMS

Home

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Explore 2 – Multi-Digit Subtraction ACTIVITY PREPARATION Students are able to subtract multi-digit numbers using a variety of strategies, including the standard algorithm.

Standards for Mathematical Practice • • • •

MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Raﬄe Ticket Scenario Cards (per group) 1 Set of Subtraction Work Mats (per group) 1 Exit Ticket (per student)

Reusable • • •

3 Sheet protectors (per group) 2 Dry-erase markers (per group) 1 Set of place value disks (per group)

Preparation • • • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Raﬄe Ticket Scenario Cards for each group. Laminate for durability (optional). Print a set of Subtraction Work Mats for each group, and put each page inside a clear sheet protector or laminate for reuse. The ﬁrst two pages can be used by all students. The third page is intended for students who need to use place value disks to support their understanding of the standard algorithm. For students who need more support in recalling information, please see our Base Tens, Open Number Line, and Place Value Mat Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1. 2.

FACILITATION TIP Discuss the strategies that students could use to solve the problem before they begin. Have students call out different strategies and explain how to use them to their peers.

Give each group their Raffle Ticket Scenario Cards, dry-erase markers, place value disks, and Subtraction Work Mats. Give each student a Student Journal. Read the following scenario to the class: The biggest carnival has arrived in our city. They are having a secret raffle so that visitors to the carnival can win a prize. Each game booth has a raffle ticket to give away if a visitor can solve their problem. There are 4 game booths. In order to collect all the raffle tickets and win the prize, you must solve the problem at each game booth. The answer for each game booth is the number for each raffle ticket. Once you’ve found the answer for each raffle ticket, you must let the headmaster of the carnival know, and they will reward you with your prize. Instruct students to work together using their Subtraction Work Mats to solve each game booth problem using multiple strategies, including the open number line, partial differences, and the standard algorithm. a.

Students can use place value disks to model the standard algorithm if needed. This can be done by having students build the minuend with place value disks and then removing the number of disks that need to be subtracted, regrouping as necessary. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

After the students have completed solving booth 1, discuss the following questions to check for understanding: a.

DOK-2 How can we use the open number line to ﬁnd the difference between our two numbers in this subtraction problem? I place the number with the smallest value on the left side of my number line and the number with the largest place value on the right side. I will then use place value to add on to the smallest-value number using various amounts from the ten thousands, thousands, hundreds, tens, and ones until I reach the largest place value. I will then add all the numbers from my hops together. This number will be the difference between the two numbers.

DOK-2 Explain how adding works when finding the difference of the numbers. Because subtracting is just finding the distance between two numbers on a number line, you can also add up the parts to find the distance from one point to the next on a number line.

DOK-1 How do you solve using the standard algorithm? First, we need to make sure we place the number we’re subtracting from on top and then line up the place values with the amount we are subtracting on the bottom. Second, we subtract the numbers that have the same place value starting in the ones place, working toward the greatest place value. Third, we must regroup as we go if the top digit is smaller than the bottom digit. We continue this pattern until all our place value digits have been subtracted.

STEMscopes Tip The Visual Glossary, located under the Scopes tab, provides a variety of instructional resources. Browse topics alphabetically in English or Spanish. Each topic includes a visual and/or video featuring key vocabulary and concepts. The visuals include text and a speech button with narration. The videos, featuring real-world examples, are 3–15 seconds in length.

ADDITION AND SUBTRACTION ALGORITHMS

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d. DOK-1 How do we regroup in booth 1 using the standard algorithm? There was no regrouping needed until I got to the thousands place. We can’t subtract 9 thousands from 5 thousands. We need to regroup a group of ten thousands from the ten thousands place. I then add the ten thousand I regrouped to the ﬁve thousand I already had, so we now have 15 thousand in the thousands place, and I’m left with 4 ten thousands in the ten thousands place. I can now subtract 9 thousands from 15 thousands. 5.

After the discussion, have students record the subtraction strategies of their choice and the standard algorithm on their Student Journals. Their strategies do not have to be the same as everyone else in their groups. Once they have recorded their work on their Student Journals, instruct students to continue working together using the same steps and their Subtraction Work Mats to ﬁnd their answers for the remaining game booths and then answer the reﬂection questions. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What observations did you make about these problems? I noticed that every problem required some regrouping. Some problems needed more regrouping than others. I noticed that the standard algorithm was not always the most efficient way to solve each problem because the amount of regrouping left more room for error. • DOK-3 Which subtraction strategy did you find to be the most efficient way to solve each problem? I found partial differences to be the most efficient way to solve because I found the same answer as with the standard algorithm, but I could more easily subtract the numbers using their place value. The open number line was easier for me because I like to use addition to find the difference between the two numbers. • DOK-2 When solving subtraction problems using the standard algorithm, how does place value play a role? You must line up place values to make sure you are subtracting the correct values. You must also use place value when regrouping and rearranging groups of ten as necessary. •

FACILITATION TIP Watch out for students who struggle with lining up the places in the standard algorithm. Remind them to line up the ones places in one column, the tens places in the next column, the hundreds places in the next column, and so on. FACILITATION TIP Invite early ﬁnishers to create their own booth and problem to solve. Once they have solved it themselves, they can trade with another group.

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Explore 2 – Multi-Digit Subtraction •

•

DOK-2 Which subtraction strategy had a similar way of regrouping as the standard algorithm? I found that the partial differences strategy was similar to the standard algorithm because I could regroup the place value positions in a similar way to the standard algorithm. DOK-1 Did you ﬁnd that all of the strategies have regrouping? Explain. No, the open number line doesn’t show regrouping like the other strategies do.

FACILITATION TIP

Post-Explore

When you preview this Exit Ticket with students, clarify your criteria for success. Consider that some students may only be proﬁcient in one strategy.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ADDITION AND SUBTRACTION ALGORITHMS

Home

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Explore 3 – Addition and Subtraction Strategies ACTIVITY PREPARATION Students are able to practice using various problem-solving strategies and the standard algorithm when adding and subtracting multi-digit numbers.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Task Cards (per group) 1 Exit Ticket (per student)

• • •

•

Reusable •

2 Dry-erase markers (per group)

Consumable •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Provide each group with sets of Addition and Subtraction Work Mats from prior Explore activities.

1 Resealable bag (per group)

• •

•

Do not include the place value disk pages, as the goal is for students to become ﬂuent in their problem solving.

Print and cut apart a set of Task Cards for each group, and place them in resealable bags. Optionally, laminate them for durability. For students who need more support in recalling information, please see our Base Tens, Open Number Line, and Place Value Mat Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1. STEMscopes Tip Fact Fluency activities, located in each grade level under the Scopes tab, help develop students’ addition and subtraction fact fluency in all grades and multiplication and division fact fluency in grades 3–5. Activities include mini-lessons, stations, games, and assessments to help address common fact-fluency groupings and strategies.

2. 3.

4. 5.

Invite the class to play a game. Ask how many people have heard of the game “Would You Rather?” If students have not heard of the game, explain that they are given 2 options, and they have to pick the one they would prefer. Play a couple of rounds with the students to get them excited. Questions can be individualized for each class, or use the following examples. Students can discuss with their groups. Invite a couple of students to share their answers and why they chose them. a.

Would you rather miss recess 1 day but get 10 extra minutes every other day that week or not miss recess but have to play inside?

Would you rather eat cafeteria food or your favorite vegetable for a week straight?

Would you rather have an entire day of math or an entire day of reading?

Would you rather have winter forever, including snow, or summer forever, with 100-degree heat?

Explain to students that there is no right or wrong answer but that they choose the answer based on what they like the most. Pass out the Student Journals, Addition and Subtraction Work Mats, dry-erase markers, and bags of Task Cards. Read through the directions, and have groups start working together to solve. © Accelerate Learning Inc. - All Rights Reserved

6. 7.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

Students will choose two strategies to solve each problem, justify their choice of strategies, and explain which strategy is the most eﬃcient. Allow students to work through each problem with their groups using their Addition and Subtraction Work Mats and then record their answers on their Student Journals. Monitor students as they work, looking for misconceptions. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-1 Did the strategies you used match the strategies of other people in your group? Explain. Yes, we all used the same strategies for each problem. No, not all of our strategies were the same, but we all still found the same answers. DOK-2 How did you determine whether to use addition or subtraction? If we were adding on to our starting number or joining together numbers, then we knew we needed to use addition. If we had to take away from our starting number or find the difference between two numbers, then it was subtraction. DOK-3 Why do you think there are multiple strategies we can choose from? Some strategies are more efficient for that specific problem, and people do not all learn or see things the same way. One strategy could be easier for some people than another. DOK-1 How are addition and subtraction related? Addition and subtraction are opposites. You can use addition to help solve a subtraction problem, like with the open number line. DOK-3 What does it mean to be efficient at solving a math problem? To be efficient means you can solve something while spending a small amount of time or effort on that problem. DOK-2 Is the standard algorithm always the most efficient way to solve a problem? Explain. No, because sometimes the regrouping needed in the standard algorithm takes more time to solve or allows for more errors to occur.

Intervention

Acceleration

FACILITATION TIP Review the strategies available that students have learned. Allow students to show an example of each strategy that is discussed on the board. FACILITATION TIP Watch out for students who do not correctly align the place values. Remind them that the ones places should line up, the tens places should line up, the hundreds places should line up, and so on. FACILITATION TIP Allow early ﬁnishers to create their own “Would You Rather?” questions and problems to go along with them. They can trade with a partner or another group once they have solved the problem themselves.

ADDITION AND SUBTRACTION ALGORITHMS

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FACILITATION TIP Follow up with the value of being eﬃcient at problem solving. Reassure students that being ﬂuent with these skills will support their future success as math students and in real life. Include some real-world examples.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP When you preview this Exit Ticket with students, allow time for questions and clarify what success looks like for the written explanations.

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Multi-Digit Addition Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Multi-Digit Subtraction Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Addition and Subtraction Strategies Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Garrett Goes to the Store

Dave Ramsey

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Raﬄing to State

Addition and Subtraction within 100,000

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

ADDITION AND SUBTRACTION ALGORITHMS

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Problem-Based Task Happy Birthday and Sayonara! Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Students who are still acquiring the concept and need remediation

ADDITION AND SUBTRACTION ALGORITHMS

Addition and Subtraction Algorithms

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can ﬂuently add and subtract multi-digit whole numbers using place value understanding to solve mathematical problems.

What prompts will be used?

What does mastery look like?

ADDITION AND SUBTRACTION ALGORITHMS

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I can ﬂuently add and subtract multi-digit whole numbers using properties of operations to solve mathematical problems.

I can ﬂuently add and subtract multi-digit whole numbers using the relationship between the operations to solve mathematical problems.

SCOPE 1

Prime and Composite Numbers Scope Introduction SCOPE SUMMARY Students utilize their knowledge of multiplication as arrays and its connection to the area of rectangles to figure out factor pairs. They use their knowledge of multiplication facts to define multiples of one-digit numbers. Students then use their knowledge of basic multiplication facts to decide if products are prime or composite by determining all possible factor combinations for specific products. Student Expectations

4.PAR.3.3 Find factor pairs in the range 1–100 and ﬁnd multiples of single-digit numbers up to 100. 4.PAR.3.4 Identify composite numbers and prime numbers and explain the relationship with the factor pairs.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

This is the ﬁrst grade level in which students describe numbers as either prime or composite. However, in previous grade levels, they experience factors and multiples. In third grade, students are introduced to multiplication. Third graders explore single-digit multiplication facts in various ways, including concrete objects to represent equal groups, repeated addition, arrays, area models, number lines, diagrams, and skip counting. They also understand the properties of multiplication and the relationship between multiplication and division. Third-grade students can multiply and divide within 100.

It is not until sixth grade that students will expand their application of ﬁnding factors and multiples. At this point, they will learn a variety of strategies to determine the greatest common factor and the least common multiple for whole numbers to make sense of applicable problems.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

show and explain the relationship between multiplication and division for numbers up to 100.

•

solve multiplication and division problems.

•

use related facts to write a corresponding problem.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

match factor pairs with the correct number to prevent hackers from hacking the software.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 90

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Find Factor Pairs In this exploration, groups of students will work together to create a garden plot using color tiles to ﬁnd factor pairs for whole numbers. In solving the scenario, students will: •

create a plot using color tiles.

•

ﬁnd factor pairs for whole numbers in the range of 1 to 100.

Explore 2

Explore 1

EXPLORE ACTIVITIES

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Determine Multiples In this exploration, students will learn how to determine whether a given whole number is a multiple of another given one-digit whole number through solving a scenario about ﬁlling different book orders with speciﬁc guidelines. In solving the scenario, students will: •

determine whether a given whole number is a multiple of another given one-digit whole number.

•

discuss strategies to solve scenarios.

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After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Prime and Composite Numbers In the ﬁnal exploration, students will build arrays to determine which numbers are prime and which are composite. In solving the scenario, students will: •

build arrays to determine which numbers are prime and which are composite.

•

use color tiles to arrange desks for a classroom.

•

determine the factors and identify number as composite, prime, or neither.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

PRIME AND COMPOSITE NUMBERS

Prime and Composite Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students work with partners to show the relationship between multiplication and division for numbers between 0 and 100. This activity is intended to assess mastery of the following standard(s): 3.PAR.3.2 Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.

Materials

Preparation

Printed •

• •

1 Student Handout (per pair)

Plan to have students work in pairs for this activity. Print a Student Handout for each pair of students.

PRIME AND COMPOSITE NUMBERS

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PROCEDURE AND FACILITATION POINTS 1. 2. 3.

6. 7.

Divide the class into pairs. Designate one student in each pair as Partner A, and designate the other student as Partner B. Give each student the Student Handout page that corresponds to which partner they are. Students should only answer the first problem on their sheets. After both students in the pair have finished their individual problems, they should trade sheets with their partner. Partner A will decide if they agree or disagree with the answer that was written by Partner B, and vice versa. Then, they will write another possible fact to go along with that problem. Students should then trade papers again so that the partners have their original sheets. Each student can read the new fact written by their partner and see if they agree. Partners will repeat steps 3–5 for the other three problems on the page. Facilitate a class discussion to see what patterns the students saw. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. If students are struggling to complete this task, do the Foundation Builder to fill this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Some students may benefit from using counters to form rectangular arrays to represent the problems. Others may benefit from accessing multiplication charts. Watch for students who rely on these supports, as they may further benefit from participating in the Foundation Builder. FACILITATION TIP For each example, record each possible related fact. Ask students whether the order of the factors matters in multiplication problems and division problems. Have students justify their reasoning with specific examples. Remind students of the commutative property of multiplication, which states that the order of the factors does not matter. Point out that this property works only for addition and multiplication, not for subtraction and division.

PRIME AND COMPOSITE NUMBERS

Prime and Composite Numbers Hook – Encrypt It! ACTIVITY PREPARATION Students ﬁnd factor pairs for whole numbers and determine whether a whole number is a multiple of a given one-digit number. Students determine whether a whole number is a prime number or a composite number.

Materials

Preparation

Printed

Part I

•

1 Encrypt It! (per group)

Reusable • • •

Plan to show the Phenomena Video.

•

Part II

1 Phenomena Video (per class) 1 Projector (per class) 1 Gallon-sized resealable bag (per group)

• • • •

Plan to have students work in groups of 3 or 4 to complete Part II of this activity. Print one Encrypt It! per group. Cut out the cards on the ﬁrst 2 pages. The third page is the answer key. Do not cut the third page. Place the cards and the answer key in the gallon-sized resealable bag.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

2. FACILITATION TIP To engage students about encrypting a message, create a message for the students using a code. For example, each letter of the alphabet is represented by a letter or shape.

STEMscopes Tip The Scope Overview, located in the Home section of each scope, provides a colorful ﬂowchart that maps out the overall ﬂow of the scope. Activities contained in each of the 5E lessons are included, as well as the path for students who need additional support and acceleration activities for those who mastered the content.

5. 6.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You are computer programmers and are encrypting some computer software to prevent hackers from getting into it. You must use your knowledge of factor pairs and multiples of whole numbers. You will also use your knowledge of prime and composite numbers to encrypt the software. Using your knowledge will block hackers and prevent them from getting into your program. Discuss the following questions and concepts: a.

DOK-1 What do we know? We know that we have to prevent hacking. We need to know factor pairs of whole numbers and multiples of single digits in order to do this.

DOK-1 Is there anything else needed to encrypt the software? We need to know which whole numbers are prime and which whole numbers are composite numbers. We have to ﬁnd out what makes a number prime or composite.

Explain that we need to solve problems like this. Computer programmers use prime and composite numbers to prevent hacking in software today. Move on to complete the Explore activities. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do we know? We know that we have to prevent hacking. We need to know factor pairs of whole numbers and multiples of single digits in order to do this.

DOK-1 Is there anything else needed to encrypt the software? We need to know what whole numbers are prime numbers and what whole numbers are composite numbers. We have to ﬁnd out what makes a number prime or composite.

Give each group a resealable bag with the cards and answer key. Explain that they will shuﬄe the cards and then lay them out in 5 rows and 6 columns. Have students lay the cards facedown with the blank side up. Have students turn over two cards at a time and determine whether they are a match. If they are a match, the student will keep the pair. If they are not a match, the student will ﬂip the cards back over in their spots. Have each group attempt to make a match for each card until all cards are paired. Set a timer for 8 minutes. See whether each group can prevent hacking (make matches) before the timer goes off. You can play multiple times. For the next game, you can set the timer for 6 minutes. Adjust the timer to meet your class needs. If the group completes the matches and checks to be sure they encrypted the software correctly (with the answer key), they have prevented the hackers. If the group does not get the cards matched in time, they have been hacked. Gather students in a whole group, and discuss the following questions: a.

DOK-2 How were you able to ﬁnd a match for the factor pair cards? I looked to see what factor pairs there were. I would multiply each pair on the card and then look for a whole number that matched all the pairs.

DOK-2 How were you able to determine whether a whole number was a multiple of a single digit? I looked at the single digit and tried to think of another digit I could multiply it by. If I could think of a multiplication sentence, I knew that the whole number was a multiple of that single digit.

DOK-3 Can you explain your thinking with a multiple card? I know that 6 × 6 = 36, so I know 36 is a multiple of 6. I could not think of anything to multiply 7 by to get 44, so I knew it could not be a multiple of 7.

DOK-3 How did you determine whether the whole numbers were prime or composite? I know a prime number has only two factors, 1 and itself. If I could not think of any other factor pairs, I knew it had to be a prime number. If I could think of other factor pairs for the whole number, I knew it was a composite number.

FACILITATION TIP Provide a few examples of prime and composite numbers and have students classify each.

PRIME AND COMPOSITE NUMBERS

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FACILITATION TIP Provide some scratch paper for students to work out some of the matches for the ﬁrst round.

FACILITATION TIP Listen to students’ explanations about multiple cards. This presents an opportunity to address misconceptions about multiples, prime numbers, and composite numbers. FACILITATION TIP Take time to solidify these deﬁnitions for students. Knowing how to factor and identify prime and composite numbers will be essential for future work with fractions and algebra.

PRIME AND COMPOSITE NUMBERS

Prime and Composite Numbers Explore 1 – Find Factor Pairs ACTIVITY PREPARATION Students work together using color tiles to ﬁnd factor pairs for whole numbers in the range of 1–100.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

•

Reusable • •

100 Color tiles (per station) 1 Resealable bag (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Scenario Cards for each group. Laminate the cards for durability, if desired. Place in a resealable bag for each group. For students who need more support in recalling information, please see our Grid Paper and Sharing Mats Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Color Tiles)

PROCEDURE AND FACILITATION POINTS 1. 2.

FACILITATION TIP If students are confused about why 4 by 6 and 6 by 4 are considered to be the same arrangement, have them focus on the rectangle itself. They can rotate the rectangle 90 degrees to see that the orientation does not affect the area of the shape. FACILITATION TIP Prompt students to list the factor pairs in order (listing the ﬁrst factor consecutively from least to greatest). This may help them account for all the pairs.

4. 5. 6.

Distribute the Scenario Cards and Student Journals. Read the tomatoes Scenario Card to the class: Alex decided to use her backyard to plant fruits and vegetables in rectangular sections. She wanted to start with her 24 tomato plants. Use color tiles to ﬁnd all the possible arrangements Alex could make. Invite students to use the color tiles to create as many rectangular arrangements of 24 tiles as they can. Each new arrangement must have new dimensions. For example, 4 by 6 and 6 by 4 would be considered the same arrangement. Students should record their models and list all of the factor pairs for 24 on their Student Journals. Circulate around the room, and monitor student work. When they ﬁnish, ask students to share all of the factor pairs they found. Record the pairs they share on the board or a sheet of chart paper until all of the pairs have been listed. Discuss the following questions: a.

DOK-2 What do all of these arrangements have in common? Each arrangement’s length and width can be multiplied together to equal 24.

Explain that the length and width of each arrangement are called “factor pairs.” When you ﬁnd factor pairs for a number, you are ﬁnding all the numbers that could be multiplied to equal that number.

DOK-1 Did you ﬁnd all the factor pairs the ﬁrst time? Were there any your group missed? Yes or no? We didn’t think of 1 and 24. We missed 3 and 8!

FACILITATION TIP Ask students to hold up the number of ﬁngers that represents the total number of factor pairs (4). Have them check to see whether they are all in agreement. List all 4 factor pairs on the board, and have students add any that they had not initially discovered. 96

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 What strategy could we use to make sure we ﬁnd all the factor pairs? Try each number in order starting with 1, then 2, then 3. We could check each consecutive number and see if it could be multiplied by something to equal the total number.

e. DOK-2 How would you know when you have found all the different possible arrangements? If you tried every number starting at 1, when you saw a reversal in the dimensions, you would know that all the rest would be reversals of the other factor pairs you had already written. f. 7. 8.

Have students begin to work on the remaining Scenario Cards. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

9. 10.

DOK-2 Is there any way you could organize the factors? Make a list, or use a T-chart.

DOK-2 How are you making sure your list of factor pairs is organized and you don’t miss a factor? We start with 1, which is a factor of every number, and then continue to test each consecutive number until we ﬁnd all the factor pairs. The T-chart keeps our work organized.

DOK-2 How are all the numbers in your list related to the number of plants? They are the numbers that can be multiplied to equal the total number of plants. They are all the factors of that number. They are ways to decompose the original number by multiplication.

DOK-2 What if you have a large number or product? How will you know if a number is a factor of it? We will have to divide it by that number. If there is a remainder, it is not a factor. If there is no remainder, it is a factor.

Have students record all of the arrangements and factor pairs they ﬁnd on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • •

• •

DOK-2 How did a T-chart help when decomposing numbers into their factors? It kept our work organized. DOK-1 How did the factors relate to the product? They are all the factors that can be multiplied together to make the product. DOK-1 How did you use the T-chart to check for factor pairs? We started with the factor of 1 and the number itself. Then, we checked to see if 2 was a factor, then 3, and so on until the factor pairs started to repeat. DOK-2 If factors started to repeat, what did that tell you? We knew when the factor was repeated, we had found all the factor pairs. DOK-2 When finding the factor pairs of larger numbers like 72 and 90, was it efficient to use the tiles to build a model? What could you do instead? No, it took a long time to count out all those tiles. Instead, we could just divide each product by different factors to see if they had a remainder or not. DOK-3 What measurement concept did you think of when you were finding all the dimensions of various gardens? Area DOK-2 How did the gardens relate to area? They were rectangles that had dimensions of length and width and were made of square units.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Students might beneﬁt from using a “factor rainbow” strategy. List the factors consecutively, and match them end to end with arcs. Another common strategy that helps many students is the “cake method.”

PRIME AND COMPOSITE NUMBERS

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FACILITATION TIP Recognizing that one is a factor of every number is an important concept. Challenge students to think of a number with only one factor and to identify what that factor is. (The number one has only one factor: itself.) FACILITATION TIP Demonstrate how to test factors using a calculator. When factors are divided into a number, they result in a whole number. If the answer is in the form of a decimal, then the number you divide by is not a factor of the original number.

STEMscopes Tip The Accessing Prior Knowledge activity, located in the Engage section, helps teachers determine students’ prior knowledge about a concept before engaging in the inquiry process. If students struggle with the task, the Foundation Builder, also found in the Engage section, helps to ﬁll the gaps in prior knowledge.

FACILITATION TIP Follow up this Math Chat with some quick real-world rectangular areas (interlocking brick toys, construction supplies (2 by 4s), sports ﬁelds). FACILITATION TIP For this Exit Ticket, consider asking students to show their factoring method (in addition to labeled sketches). 97

PRIME AND COMPOSITE NUMBERS

Prime and Composite Numbers Explore 2 – Determine Multiples ACTIVITY PREPARATION Students determine if a given whole number is a multiple of another given, one-digit whole number.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

• • • •

Plan to have students work in groups of 2 or 3 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Scenario Cards for each group. Laminate the cards for durability, if desired. For students who need more support in recalling information, please see our Grid Paper and Sharing Mats Supplemental Aids elements in the Intervention section.

PROCEDURE AND FACILITATION POINTS

STEMscopes Tip Each Explore activity includes a Student Journal that students complete collaboratively while participating in group work. Students use the journal to develop metacognitive skills by reﬂecting on how and what they are learning. Communicating mathematical thinking leads to a deeper conceptual understanding of the skills at hand.

FACILITATION TIP Show students how to generate multiples with a calculator. For example, press 4 + 4 equals, equals, equals . . . Each time you press the equal sign, the next consecutive multiple is generated and displayed.

Read the following scenario to the class: Mrs. Buckman is ordering books for the library. The book company ships fiction books in boxes of 4. She knew she could order 4, 8, or 12 books, but she was wondering if she could place a larger order of 96 books. How can she determine whether she can buy exactly 96 books if they are shipped in boxes of 4? Students will work in their groups to discuss the fiction books Scenario Card and record their thinking processes. As you monitor, decide which groups and in which order you would like them to present their solutions. If there are groups that draw a picture, you may wish to have one of them present first. If you have groups that skip count, you may want one of them to present next. If you have any students that use the associative property when decomposing, you may want them to present next. If you have groups that divide 96 by 4, you may want one of them to present last. If any group finishes early, challenge them to find a 3-digit number of books that would not be able to be shipped in boxes of 4. Instruct them to write out a way they could explain their process to the class. Allow groups to present. If some students drew pictures and some used skip counting, connect the two methods by pointing out how they show the same information in a different way. Discuss the following question: a.

DOK-1 Does anyone notice any patterns in the numbers? Answers may vary. They are all even numbers. In the ones place, the pattern 4, 8, 2, 6, 0 repeats. Notes

Engage

Explore

Explain

Elaborate

Evaluate

If anyone decomposed 96 using the associative property, discuss the following questions: a. DOK-1 How did you decompose 96 initially? Answers may vary. 12 × 8 = 96

DOK-1 How did you decompose it further? Answers may vary. (4 × 3) × 8 = 96

DOK-2 How did that help you determine that the books could be shipped in boxes of 4? If 4 is a factor of the number, it can be divided evenly by 4, or it could be put into equal groups of 4.

If some students used division, discuss the following question: a.

9. 10. 11.

DOK-2 How did you know to divide? If books were shipped in equal groups and we had a total of 96, we would have to see if 96 could be separated into equal groups of 4.

Discuss the following questions: a.

DOK-3 Which method seemed the most efficient? Why? Dividing was efficient because it could be done very quickly and in the fewest number of steps. Decomposing the number was also efficient if you know your facts like 8 × 12 = 96.

DOK-1 What can we say about the number 96 if it can be divided evenly by 4? It is a multiple of 4.

DOK-1 What is the relationship of 4 to 96? It is one of the factors of 96. 96 is a multiple of 4.

Intervention

Acceleration

FACILITATION TIP Using division to determine a multiple can be misleading. To avoid confusion, associate division with determining factors and repeated addition or skip counting with generating multiples. Point out that consecutive multiples increase in size and that the factors of a number are equal to or less than that number. FACILITATION TIP To help students differentiate between factors and multiples, have them play a counting game where they stand in a circle and count by ones. When the count gets to a multiple of 4, the person should say “Salt” instead of the number. When the count gets to a factor of 96, the person should say “Pepper” instead of the number. If a number is both a multiple of 4 and a factor of 96 (such as 4, 8, or 16), the person should say “Seasoning.” Try this with other multiples and factors. This game takes practice and may be challenging at ﬁrst, but continual practice leads to eﬃciency in identifying factors and multiples.

PRIME AND COMPOSITE NUMBERS

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Have students use the remaining space for fiction books to decide if Mrs. Buckman could order exactly 86 books and record their final solutions on their Student Journals. Allow students to continue working on the remaining Scenario Cards. Students can use a variety of strategies to approach each problem. Students should record their work and final solutions on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 How did you figure out if the order was possible? We skip counted by the package size to figure out if the order amount was a multiple of the package size. If it was a multiple, then we knew we could order that exact amount. We divided the total by the package size to see if we could order a certain number of whole packages to get that amount. • DOK-2 How is a multiple different from a factor? A multiple is a number you can find by combining equal groups of a number. A factor is a way you can decompose a number into equal groups. • DOK-2 Turn and talk to finish this sentence: A number is a multiple of another if _______ . ...you divide it by the number and get a 0 remainder. (or)…you count that number when skip counting by the other number. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Differentiating between multiples and factors is an essential math concept for students as they progress in math (especially fractions and algebra). Post the definitions on your word wall. Have students write the definitions in their own words, provide examples, respond orally to multiple prompts, and encourage them to use the specific vocabulary in your class discussions. FACILITATION TIP When you preview this Exit Ticket with students, highlight the words factor and multiple. Take time to be certain they understand the difference between these two terms before showing their proof.

PRIME AND COMPOSITE NUMBERS

Prime and Composite Numbers Explore 3 – Prime and Composite Numbers ACTIVITY PREPARATION Students build arrays to determine which numbers are prime and which are composite.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Graph Paper (per student, optional) 1 Exit Ticket (per student)

•

Reusable • •

•

75 1 in. color tiles (per group) 1 Thin marker (per student)

•

Plan to divide the class into 4 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Graph paper is provided on the Student Journal, but if students need additional space, print one Graph Paper for each student. Gather one thin marker for each student and 75 1 in. color tiles for each color group. For students who need more support in recalling information, please see our Grid Paper and Sharing Mats Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Color Tiles)

PROCEDURE AND FACILITATION POINTS Part I 1. 2.

Distribute materials to each group. Read the following scenario to the class: A teacher wants to ﬁnd all of the ways to arrange the desks in even rows for different numbers of students. You will need to help the teacher by showing all the possible arrays for each number of desks. Challenge students to arrange the desks for a class that has 12 students. Use the color tiles to show all the ways the desks can be arranged.

FACILITATION TIP Model this process using a smaller number, such as 4. As you form the arrays, show students how to keep track of and account for each factor by listing the factors consecutively from least to greatest.

a. 4.

Students will sketch their arrays on the Graph Paper using a thin marker. They can sketch them as rectangles to make it easier to visualize.

After Part I, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-1 Describe the arrays you made. We made 1 row of 12 desks, 2 rows of 6 desks, 3 rows of 4 desks, 4 rows of 3 desks, 6 rows of 2 desks, and 12 rows of 1 desk. • DOK-2 How are the rectangles the same, and how are they different? They all have an area of 12 square units. They are made of different numbers of rows and columns. • DOK-2 Does the orientation of the rectangles matter? Is a 2 × 6 rectangle the same as a 6 × 2 rectangle? The rectangles are different in that they show two distinct arrays, but they cover the same area. A 6 × 2 rectangle can be rotated to become a 2 × 6 rectangle. •

100

Engage

Explore

Explain

Elaborate

Evaluate

Explain the following to the class: For this activity, the dimensions of the rectangles are important (or the factors of the numbers), not their vertical or horizontal orientations. It is also important to note that 2 and 6 are both factors of 12. • DOK-1 What are the factors of 12? How do you know? The factors of 12 are 1, 2, 3, 4, 6, and 12. These are the dimensions of the rectangles that can be made with an area of 12. • DOK-1 What are the factor pairs of 12? The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4. • Explain the following to the class: When a number has factors other than one and itself, it is called a “composite number.”

Intervention

Acceleration

•

Part II 1.

2. 3.

Assign each group different numbers of desks to arrange. Explain that the whole class will create a master list of desk arrangements. Suggested assignments are as follows: a.

Group 1: 4, 7, 10, 11, 15, 22

Group 2: 2, 9, 13, 14, 18, 24

Group 3: 3, 6, 16, 17, 19, 20

Group 4: 1, 5, 8, 12, 21, 23, 25

STEMscopes Tip The Picture Vocabulary, located in the Explain section, can be made into a word wall that students reference throughout the scope. Add vocabulary to the wall during the Math Chat or an Explore lesson as a means of solidifying conceptual understanding and of modeling precision in language and mathematical communication.

PRIME AND COMPOSITE NUMBERS

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Students will use the color tiles to create rectangles and then draw the arrays or rectangles on the Graph Paper. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What do you notice about this number? It only has two factors. The only factors are one and the number.

DOK-1 Can the desks be arranged into any other array? No. The only way we can make even rows is by putting them all in the same row. i. Introduce that a number like this is called a “prime number.”

4. 5.

6. 7.

Students will fill in the rows they worked on on their Student Journals. Each group will share their findings with the class so that all students can record the factors for the numbers 1 through 25. If possible, allow groups to project their work on a document camera to prove their findings with evidence. Any groups who finish early can use the color tiles to create arrays for numbers greater than 25 to search for other prime numbers. After Part II, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Use these suggested challenges for early ﬁnishers: Observe and describe the conﬁguration for the 5 by 5 array and the list of corresponding factors. Explain that 25 is called a square number because it forms a square-shaped array; it has an odd number of factors because one of the factors pairs with itself. Ask students to think of another square number. Ask students whether or not 1 is a prime number, and have them explain why or why not. (One is neither prime nor composite; it has exactly 1 factor: itself.)

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Prime and Composite Numbers Explore 3 – Prime and Composite Numbers Math Chat •

• FACILITATION TIP Find a fun way to help students differentiate between these two terms. For example, hidden in the letters of the word PRIME is “ME,” and “I,” and prime numbers are all about “me, myself and I, and only look out for number 1.” Hidden in the word COMPOSITE is “comp” for “company.” Composite numbers have lots of friends and like lots of “company.”

• •

•

Have each group report their findings to the class. Students will need to listen to their classmates to hear what they need to fill in the table for each number of desks. Each group will need to tell the class how many desks there are, what the factors are for that number, and whether it is a prime or composite number. Students should fill in their Student Journals with the findings of all the groups. DOK-1 Is the number one prime or composite? Neither. A prime number has two factors—one and itself. Composite numbers have more than two factors. The number one only has one factor, so it doesn’t fit in either group. DOK-2 Are all even numbers composite numbers? No. The number two is even, but it is prime because it only has two factors—one and two. The number two is the only even prime number. DOK-2 What is the difference between a factor and a multiple? Factors are the numbers that we can multiply to get another number. Multiples are the numbers we get when we multiply a given number by any whole number. Multiples are what you say when you skip count by a number, and you can go on and on skip counting. You only have a certain number of factors in a number.

Post-Explore 1. 2. 3. 4.

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Prime and Composite Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Find Factor Pairs Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Determine Multiples Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Prime and Composite Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Summer at the Neighborhood Pool

Charlie Alfred Miller

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Autumn on the Farm

Match Multiples with Composite Numbers

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

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Problem-Based Task Artistic Arrays Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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Students who are still acquiring the concept and need remediation

PRIME AND COMPOSITE NUMBERS

Prime and Composite Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can use a variety of strategies and tools to ﬁnd all of the factor pairs of a number in the range of 1–100.

What prompts will be used?

What does mastery look like?

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I can recognize that a whole number is a multiple of each of its factors.

I can identify composite numbers and prime numbers and explain the relationship with the factor pairs.

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SCOPE 1

Multiplicative Comparisons Scope Introduction SCOPE SUMMARY

Student Expectations

Students distinguish between an additive comparison and a multiplicative comparison. Additive comparisons focus on the difference between two quantities, whereas multiplicative comparisons show that one quantity is a certain number of times larger or smaller than the other. Students use concrete and visual models (such as diagrams), multiplication and division as inverse operations, and equations with a letter to represent an unknown quantity to generate, represent, and solve multiplicative comparisons within a contextual situation.

4.NR.2.2 Interpret, model, and solve problems involving multiplicative comparison.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students gain an understanding of the meaning and properties of multiplication and division. Third-grade students use various strategies, including modeling multiplication with concrete objects, visual representations, expressions, and equations, to represent and solve multiplication problems. Students ﬁnd products by forming equal groups and arrays, and they use the distributive property to multiplicatively compose and decompose. They use the relationship between multiplication and division, properties of operations, and arithmetic patterns to ﬂuently multiply and divide within 100. These strategies lead to representing multiplication and division problems using equations with a letter standing for the unknown quantity and justifying their solutions.

In ﬁfth grade, students use parentheses, brackets, or braces to write and evaluate multistep numerical expressions. Students generate numerical patterns with the same starting number for two different rules and identify relationships between corresponding terms. Students examine these relationships within sequences of ordered pairs graphed on a coordinate plane. The resulting graphs are analyzed to determine the relationship between the two patterns. The graphs show how two quantities vary together.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

read a multiplication or division word problem that has been solved with different strategies.

•

decide if each response is correct or incorrect.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: multiply or divide to solve a problem involving multiplicative comparisons. •

use drawings and equations with a symbol for the unknown to solve problems.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 108

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Model Multiplicative Comparisons

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, students will work collaboratively to solve a real-world scenario about helping two farmers where they explore multiplication as comparisons and practice representing multiplication in a variety of ways. In solving the scenario, students will: •

record a multiplication sentence.

•

write descriptions and sketch models of comparisons.

•

solve problems about different comparisons by creating a model using colored counters.

In this exploration, students will help solve a scenario where they must help determine a drink, appetizer, main course, and dessert for a family dinner. As students solve the scenario, students will: •

use tape diagrams to distinguish between additive and multiplicative comparisons.

•

read task cards and use them to develop a tape diagram to model the problem.

•

read task cards to create equations.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 3

Additive and Multiplicative Comparisons

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Solve Problems with Multiplicative Comparisons In the ﬁnal exploration, students will solve a real-world scenario that involves comparing items from shopping catalogs for a wish list. In solving the scenario, students will: •

represent multiplicative comparisons as visual models, equations, and verbal statements.

•

collaborate with peers.

•

use money manipulatives and exploration resources.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

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Multiplicative Comparisons Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students read a multiplication or division problem and several different ways to solve the problem. Students decide if each response is correct or incorrect. This activity is intended to assess mastery of the following standard(s): 3.PAR.3.7 Use multiplication and division to solve problems involving whole numbers to 100. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.

Materials

Preparation

Printed •

• •

1 Slideshow (per class or per group)

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Prepare to project the Slideshow one slide at a time. Optionally, print a Slideshow for each group.

Reusable •

1 Projector or document camera (per class)

Consumable •

1 Piece of scratch paper

PROCEDURE AND FACILITATION POINTS 1. 2.

4. 5.

6. 7.

Project the problem on the ﬁrst slide of the Slideshow for the class, or distribute a Slideshow to each group. Allow time for the students to read the question and think about their answers. Students may try working the problem out on scratch paper using any method that they choose. Project the student 1 response on the second slide of the Slideshow for the class. Allow students time to read it and to determine if this student correctly or incorrectly answered the problem. Ask students to show a thumbs-up if they agree with the student’s response. Ask students to show a thumbs-down if they disagree with the student’s response. Facilitate a class discussion about their choices. Allow students to explain why they agree or disagree with the response. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Repeat steps 2–5 for the student 2 response on the third slide and the student 3 response on the fourth slide of the Slideshow. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Explain to students how there are different strategies to use to solve problems. They are going to “grade” other students’ responses.

FACILITATION TIP Have students discuss why the problem is not answered correctly and share with the class.

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Multiplicative Comparisons Hook – Bake Sale ACTIVITY PREPARATION Students multiply or divide to solve a problem involving multiplicative comparisons by using drawings and equations with a symbol for the unknown.

Materials

Preparation

Printed

Part I

•

1 Bake Sale (per class)

Reusable • •

Plan to show the Phenomena Video.

•

Part II

1 Phenomena Video (per class) 1 Projector (per class)

•

Print a Bake Sale to project for the class.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

2. FACILITATION TIP Students can write their ideas and questions about the bake sale to revisit after the Explore activities.

STEMscopes Tip Fluency Builders, located in the Elaborate section, are partner or smallgroup student-led games that engage students in practicing the skills and concepts addressed in the scope. These games come with studentfriendly instruction sheets. All the materials used in the games are found in the print ﬁles on the right side of the screen.

FACILITATION TIP Revisit students’ observations and questions before the Explore activities to address any missing information. 112

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Ethan, William, and Addison are baking cupcakes for a bake sale to raise money for their favorite charity. You want to know how many cupcakes each friend made for the bake sale. Discuss the following questions: a.

DOK-1 What do we need to know? We need to know how many cupcakes each friend baked for the bake sale.

DOK-1 What do we need in order to determine the number each friend baked? I think we need some information or clues in order to determine the number each friend baked.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do we need to know? We need to know how many cupcakes each friend baked for the bake sale.

DOK-1 What do we need in order to determine the number each friend baked? I think we need some information or clues in order to determine the number of cupcakes that each friend baked.

Project Bake Sale. Tell the class that William baked 32 cupcakes, and we want to ﬁnd out how many cupcakes Addison and Ethan baked. Have students use the diagrams to determine the other two’s cupcake totals. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Tell the class they will also use the two numbers and a letter for the unknown in the boxes to make the equations to ﬁnd Addison and Ethan’s cupcake totals. Have students turn and talk to solve the problem together. Gather students in a whole group, and discuss the following questions: a.

DOK-2 How did you determine how many cupcakes Addison made? I looked at the diagram and saw it was taking William’s 32 cupcakes and splitting it into 8 equal groups. I knew the equation would be 32 ÷ 8 = a. I know 32 ÷ 8 = 4, so Addison made 4 cupcakes.

DOK-2 How many times as many cupcakes as Addison did William make? William made 8 times as many cupcakes as Addison. I know that because 8 × 4 = 32. I could also see he made 8 times as many as Addison in the diagram since there are 8 equal parts with question marks in them.

DOK-2 How did you determine how many cupcakes Ethan made? I looked at the diagram and could see that he made 6 times as many as Addison. The equation is 4 × 6 = e. So, I know that Ethan made 24 cupcakes since 4 × 6 = 24.

DOK-3 If we wanted to know how many cupcakes were made by all three kids, how would we ﬁnd out? We could add each friend’s total number of cupcakes. William made 32, Addison made 4, and Ethan made 24. We add 32 + 4, which is 36. Then, we add 36 + 24 = 60 cupcakes altogether. They had 60 cupcakes to sell at the bake sale.

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FACILITATION TIP Listen to groups’ conversations about solving the Hook. At this point, students are applying their knowledge from the Explore activities in a new situation.

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Multiplicative Comparisons Explore 1 – Model Multiplicative Comparisons ACTIVITY PREPARATION Students explore multiplication as comparisons and practice representing multiplication in a variety of ways.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed

Part I: Farm Wars

• • • •

1 Student Journal (per student) 1 Set of Farm Wars (per group) 1 Set of Farm Scenario Cards (per class) 1 Exit Ticket (per student)

Reusable Part I: Farm Wars •

1 Set of counters (per group)

• • •

•

Part II: Farm Scenario Cards • •

Part II: Farm Scenario Cards •

1 Set of counters (per station)

Consumable •

1 Resealable bag (per group)

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal for each student. Print a set of Farm Wars cards for each group (print on card stock for durability if desired), and cut out each set. (It is suggested that you print each game set on a different color of card stock to keep the sets together.) Place the cards for each game set in a resealable bag.

•

Print and cut out the Farm Scenario Cards. Laminate them, if desired. Place the cards around the room as station cards, and place a set of counters with each station. For students who need more support in recalling information, please see our Sharing Mats, Multiplication Arrays, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Two-Color Counters)

PROCEDURE AND FACILITATION POINTS Part I: Farm Wars 1. 2.

FACILITATION TIP You can ask students: “How many pieces of candy could the brother share equally if there are 2 other siblings?” 114

3. 4. 5.

Give a set of counters to each group. Read the following scenario to the class: I remember that growing up, it seemed that my older siblings ALWAYS got the bigger share of something. One of the memories that has stayed with me was the time we broke a piñata at my older brother’s birthday party. As my older brother broke the piñata, all of the candy came ﬂying out of it and all of us kids rushed to pick up as many pieces as we could. Being the smallest kid there did not help me. I managed to pick up four pieces of candy. Have students count out four counters to represent the candy. Continue the scenario: My brother, on the other hand, picked up 12 pieces! Needless to say, I was so disappointed! Have students count out 12 counters to represent the candy gathered by the older brother. © Accelerate Learning Inc. - All Rights Reserved

7. 8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What is the relationship between the two amounts? We notice that your brother had a much greater amount of candy than you. We notice that you can make three groups of yours out of your brother’s. This means your brother picked up three times as much candy as you did.

DOK-1 How could we show this relationship using a number sentence? If your brother picked up 3 times the amount you did, that means we can express it as 4 × 3 = 12. That means that 12 is 3 times as much as 4.

Tell students that they will practice expressing the factors and product in relation to each other through a game of memory. Distribute Farm Wars cards and Student Journals. Explain the rules of the game, and allow students to play: a.

Shuﬄe the cards, and place them upside down in an array.

Each student gets a turn to turn over two cards.

Each of the cards will have an animal from a farm.

If the animals on both cards match, students must work together to build a comparison model (equal groups of, arrays, a diagram) to determine the number of animals each farmer has on their farm.

On their Student Journals, students will draw their models, write multiplication sentences, and write descriptions of the farmers’ farm animals using the phrase times as many. many

If the cards matched, the student may turn over two new cards.

h. If cards do not match, the student must turn the cards over again in their exact same position. The student’s turn is over, and play goes to the next student. i. If they don’t match, students should try to remember where those cards are—they may need them later!

11. 12.

Acceleration

Allow students to think and discuss what they notice about those two amounts:

e. Tell students they may use counters to help them understand their multiplication facts. They could also use scratch paper to draw models, as needed.

10.

Intervention

Once students have completed all of the matches, students will choose two of the farm animal matches and record their models, multiplication sentences, and descriptions on their Student Journals. Explain to students that each student will choose the 2 farm animals they want to model on their Student Journals. Discuss the following questions: a.

DOK-1 How many _____ does Farmer _____ have? Answers may vary. Farmer Joe has 7 chickens.

DOK-1 How many more _____ does Farmer ____ have? Answers may vary. Farmer Susan has 4 times as many chickens as Farmer Joe has.

DOK-2 What strategy did you use to ﬁgure out how many _____ Farmer _____ has? Answers may vary. I drew an array showing 4 rows with 7 in each row. I drew 4 equal groups of 7. I made a diagram with 7 written 4 times.

DOK-1 How did you show the relationship between ___ times as many as ___ using a number sentence? Answers may vary. I multiplied 4 × 7, which equaled 28.

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FACILITATION TIP Take time to preview any unique vocabulary from the Farm Wars cards, scenarios, and the Student Journal.

FACILITATION TIP Students are going to choose only 2 sets of cards to create a model, write a description, and write an equation. Then, have different partners share information with their groups.

STEMscopes Tip If students are not ready to move on to the next concept, use Small-Group Intervention, located in the Intervention section, to revisit the conceptual foundation of the scope’s concepts and to build student understanding. Here, you will ﬁnd a hands-on reteach activity, Teacher Checklists for monitoring student progress, and supplemental Student Handouts. A student Checkup is provided in Grades 2-5.

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Multiplicative Comparisons Explore 1 – Model Multiplicative Comparisons Part II: Farm Scenario Cards 1. FACILITATION TIP

Groups should circle the variables on the Scenario Cards. This information will be used to complete the statements and create the model.

4. 5. FACILITATION TIP

As you monitors the groups, determine if the students have the correct information or if they are challenged by creating the models.

Explain to students that there are different Farm Scenario Cards around the room. Place each group at a station. Their task is to read each scenario and solve by creating a model using colored counters and recording their work on their Student Journals. It is important to note to students that not every scenario may use multiplication to solve. Encourage students to read carefully and see if they can discover another operation that could be used to solve some of the scenarios. Students will begin working together in groups to model and solve their Farm Scenario Cards. Have groups rotate to each Farm Scenario Card after they have been given enough time to complete their work. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How many groups do we have? Answers may vary. Joe has 2 pens, or 2 groups. Susan has one pen, or 1 group.

DOK-1 How many are in each group? Answers may vary. There are 5 pigs in each group.

DOK-1 What is our total? Answers may vary. Joe has 10 pigs. Susan has 5 pigs.

DOK-2 What is the relationship between the two amounts? Answers may vary. Joe has 2 times as many pigs as Susan, so Joe will need two times as many pens, or groups, as Susan.

e. DOK-2 Do you think we are multiplying or dividing to solve? Explain your reasoning. Answers may vary. I think we are dividing because we are given the total number of pigs Joe and Susan have and how many pigs go in each pen, or group. We had to ﬁnd how many pens, or groups, Joe and Susan need. FACILITATION TIP Reassure students that being ﬂuent with these physical models will support their further success in math as the scenarios and problems become more complex. Even if they don’t feel that they need the model to solve today’s work, the models provide helpful thinking tools for later school work and life skills.

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DOK-1 What could the model look like? Answers may vary. I split 10 up into equal groups of 5. Then, I split 5 up into equal groups of 5.

DOK-1 How can we describe the model? Answers may vary. I made equal groups.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat

STEMscopes Tip Located in the Acceleration section, Math Today is an activity in which students in all grades explore connections and applications of mathematics and other crosscurricular content through interactions with videos, photos, or articles provided by the Associated Press. This engaging activity can be used as a review or as a formative assessment.

• •

•

DOK-2 Did every Farm Scenario Card use multiplication to solve? No, some scenarios needed to be solved using division. DOK-2 Why do you think some scenarios needed division to solve? I think some needed division to solve because we were given a total, and we had to find how many groups it was being split into, or we had to find how many were in each group. DOK-2 What scenarios needed multiplication to solve? I used multiplication when I knew the group size and how many groups I had, but I was looking for the total. DOK-2 Why do you think we call these scenarios “multiplicative comparisons”? I think we call them “multiplicative comparisons” because we are comparing numbers using multiplication. We are trying to find how many times greater or smaller one number is from another number. DOK-2 What are some strategies you used to solve multiplicative comparisons? We made models for both numbers in a scenario using the information given and compared how many times greater or smaller those numbers were to each other.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP When you preview this Exit Ticket, ensure that students understand the word acre.

Notes __________________________________________________________________________________________________________________________________________________

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Multiplicative Comparisons Explore 2 – Additive and Multiplicative Comparisons ACTIVITY PREPARATION Students are able to distinguish between additive comparisons and multiplicative comparisons. Students will represent additive comparisons and multiplicative comparisons with diagrams.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials Printed • • • •

1 Student Journal (per student) 1 Comparison Sort Mat (per group) 1 Set of Dinner Cards (per group) 1 Exit Ticket (per student)

Reusable • •

20 Play $1 bills (per group) 1 Resealable bag (per group)

Preparation • • • • • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for every student. Print a set of Dinner Cards and a Comparison Sort Mat for each group. Laminate them for durability, if desired. Cut out the Dinner Cards. Place 20 play $1 bills and a set of Dinner Cards into a resealable bag for each group. For students who need more support in recalling information, please see our Sharing Mats, Multiplication Arrays, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Two-Color Counters)

PROCEDURE AND FACILITATION POINTS 1. 2.

FACILITATION TIP

Have students circle the variables and the terms like much more and times. Discuss how the terms provide a clue to determine if this additive or multiplicative comparison.

FACILITATION TIP Use the Picture Vocabulary to introduce and explain the terms additive comparisons and multiplicative comparisons.

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Give each group a Comparison Sort Mat, a set of Dinner Cards, and a set of 20 play $1 bills. Give each student a Student Journal. Read the following scenario to the class: Your family decided to go out to eat for dinner. They are treating you to a drink, appetizer, main course, and dessert. You look at the prices and do a quick comparison of the items you would like for dinner. Encourage students to use their set of play $1 bills to represent each word problem, ﬁnd the cost of each dinner option, and then record their models and work on their Student Journals. Once they have solved one of the Dinner Cards, students should place the card on the Comparison Sort Mat based on whether it was an additive comparison or a multiplicative comparison. Discuss the following questions: a.

DOK-1 What is this question asking you to ﬁnd? Answers may vary. It is asking us how much more a milkshake costs than a glass of lemonade.

DOK-1 How can you solve this problem? Answers may vary. I can ﬁnd the difference between 6 and 4. I can count up from 4 until I get to 6.

DOK-1 What operation can you use to solve this problem? Answers may vary. Addition or subtraction.

DOK-2 How is this different from a multiplicative comparison? Answers may vary. I am ﬁnding the difference between two numbers, not the same number being repeated a number of times. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-1 What operations are being performed in an additive comparison? Addition and subtraction can be used when solving an additive comparison. An additive comparison discusses something being a little more or a little less than something else. • DOK-1 What operations are performed in a multiplicative comparison? Multiplication and division can be used when solving a multiplicative comparison. A multiplicative comparison discusses how many times more or less one thing is than something else. • DOK-2 How are the models for an additive comparison different from the model of a multiplicative comparison? A multiplicative comparison model shows the same quantity being repeated a given number of times, while an additive comparison shows the difference or combination of two numbers. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Intervention

Acceleration

STEMscopes Tip Depth of Knowledge (DoK) Levels are found on the Lesson Planning Resources page in the Essentials section of the Teacher Toolbox. A printable document lists the DoK levels for all elements of the scope. This resource gives teachers the ability to choose the appropriate DoK-leveled assignments to help students expand and deepen their mathematical thinking and reasoning.

MULTIPLICATIVE COMPARISONS

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FACILITATION TIP On this Exit Ticket, determine your criteria for success. Some students may be able to solve and write a solution statement, but still be unclear which comparison is being represented.

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Multiplicative Comparisons Explore 3 – Solve Problems with Multiplicative Comparisons ACTIVITY PREPARATION Students are able to represent multiplicative comparisons as visual models, equations, and verbal statements.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Shopping Cards (per group) 1 Set of Shopping Catalogs (per group) 1 Exit Ticket (per student)

• • •

Reusable • •

50 Play $1 bills (per group, optional) 1 Resealable bag (per group, optional)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for every student. Print a set of Shopping Cards and a set of Shopping Catalogs for each group. Laminate them for durability, if desired. Cut out the Shopping Cards. Optionally, place 50 play $1 bills in a resealable bag for each group. For students who need more support in recalling information, please see our Sharing Mats, Multiplication Arrays, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Two-Color Counters)

PROCEDURE AND FACILITATION POINTS 1. FACILITATION TIP

Engage students by letting them share what they would buy for their family if given $50. Depending on your students, be sensitive to different family economic situations. FACILITATION TIP Model how students need to read the Shopping Card then ﬁnd the item on the Shopping Catalog to complete the Student Journal.

3. 4.

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Give each group their set of Shopping Cards, Shopping Catalogs, and set of play $1 bills. Give each student a Student Journal. Read the following scenario to the class: You are preparing a wish list of presents and have gathered 2 shopping catalogs to find the best deals on products. For each purchase, you are comparing the prices of two items and will then make a decision on what present you would like. Some of the information in the catalogs is missing because rain blurred the numbers. Luckily, a family member called the store and got some helpful information on the prices. This information can be found on the Shopping Cards. Instruct students to find the card for purchase 1 and use their Shopping Catalogs and $1 bills to solve for what the question is asking. Students can create a multiplication model using their $1 bills, if they find this helpful, and then draw a diagram to represent that model along with an equation and solution statement on their Student Journals. Students should use a letter to represent the unknown value in their equation. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What information do we know in the problem? We know the cost of the hat and the helmet.

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 What strategy was most helpful in ﬁnding how many times more the helmet costs than the hat? Answers may vary. I found division to be the best strategy because I divided $32 by separating it into groups of $8. I found that I had 4 groups of $8, which meant the helmet costs 4 times more than the hat.

Have students record their models, equations, and solution statements on their Student Journals. Students can then decide which present they want and state their reason (it does not have to just be based on price). Students will continue working as a group to complete the problems for the remaining purchase options. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How do you determine whether to multiply or divide a problem? If I have an unknown product, then I multiply. If I have an unknown group size or amount in each group, then I divide. • DOK-2 How does a multiplicative comparison with a diagram help us compare the size of numbers? A multiplicative comparison model can show us how many times larger or smaller a number is than another number. • DOK-1 What do the numbers in a multiplication equation represent when solving a word problem? A multiplication equation represents how many groups there are times how many are in each group, which then equals my total or product. • DOK-1 What does the letter represent in the multiplication equation? The letter represents what is unknown about my word problem and what I am trying to ﬁnd. •

FACILITATION TIP Have groups discuss and reach a consensus about the present they would buy. The reason can be different for each student. FACILITATION TIP

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Purchase Six provides a great chance to guide students to ﬁnd the essential numerals in a scenario. Careful readers will notice that the number of propellers is not needed to ﬁnd the solution.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP This Exit Ticket includes critical information in the image. Remind students that standardized math tests use similar formats. Encourage careful reading and examination of all material included in all math problems.

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Multiplicative Comparisons Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Model Multiplicative Comparisons Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Additive and Multiplicative Comparisons Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Solve Problems with Multiplicative Comparisons Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Cleaning Great Aunt Priscilla’s Old House

Peyton Manning

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Adventures in Babysitting Times Three

Problem Solving with Multiplicative Comparisons

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

MULTIPLICATIVE COMPARISONS

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Problem-Based Task Settling the Moon Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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Students who are still acquiring the concept and need remediation

MULTIPLICATIVE COMPARISONS

Multiplicative Comparisons

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can interpret, model, and solve problems involving multiplicative comparisons.

What prompts will be used?

What does mastery look like?

MULTIPLICATIVE COMPARISONS

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I can distinguish multiplicative comparisons from additive comparisons.

I can demonstrate an understanding of simple multiplicative relationships by using concrete materials, drawings, and equations.

I can write and solve simple multiplicative equations that use symbols for the unknown numbers to represent the problem.

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SCOPE 1

Multiplication Models and Strategies Scope Introduction SCOPE SUMMARY Students extend their knowledge of multiplication by solving problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers. Students focus on illustrating and clearly explaining their calculations by using rectangular arrays, area models, and partial products.

Student Expectations

4.NR.2.3 Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Kindergarten and first grade form the foundation for our baseten number system, developing basic addition and subtraction concepts and skills. Second grade advances this progression; here, students work with equal groups and five-by-five arrays. In third grade, students develop an understanding of what multiplication of whole numbers is through problem solving and exercises that involve arrays, area models, repeated addition, number lines, and skip counting. Students discover that multiplication is finding an unknown product. They use properties of operations (commutative, associative, and distributive) to calculate these products. Students begin to use strategies that increase in sophistication based on these properties to solve multiplication problems within 100. Students are encouraged and expected to develop a variety of strategies for finding solutions so they can determine the relationship between multiplication and division.

In ﬁfth grade, students apply their knowledge of place value (baseten system) and the distributive property (properties of operations) of multiplication to compute partial products as they begin to multiply multidigit whole numbers. They then connect partial products to the standard algorithm for multiplication and use this to solve real-world and mathematical problems involving multi-digit whole numbers.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

represent and interpret multiplication facts.

•

analyze various strategies used to represent multiplication facts.

•

explain which representations are correct.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

create a model using manipulatives.

•

ﬁnd the area using a strategy.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 126

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Multiply up to Four-Digit by One-Digit Numbers: Arrays

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, students will work with groups to solve a scenario about calculating Field Day results. In solving the scenario, students will: •

multiply a 2-digit number by a 1-digit number.

•

build an array and area model.

•

decompose into tens and ones.

Multiply Two-Digit by Two-Digit Numbers – Arrays In this exploration, students will solve a real-world scenario about helping determine the areas of different ﬂower beds. In solving the scenario, students will: •

use arrays and area models.

•

multiply 2-digit numbers by 2-digit numbers.

•

decompose factors into tens and ones and write an equation.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 5

In this exploration, students will explore two more strategies to solve multiplying 2-digit by 1-digit numbers. Through completing this exploration, students will: •

create an area model to decompose numbers into tens and ones.

•

build partial product equations to complete the total product.

•

use the Partial Products Work Mat.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 4

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Multiply up to Four-Digit by One-Digit Numbers–Area Models

MULTIPLICATION MODELS AND STRATEGIES

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Multiply Two-Digit by Two-Digit Numbers – Area Models In this exploration, groups of students will determine the total area of different sizes of pizzas in order to ﬁgure out the amount of sauce and toppings to set a fair price for pizza. In solving the scenarios, students will: •

use base ten blocks to construct area models.

•

represent two-digit by two-digit multiplication realworld problems.

•

create an area model and write an equation.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Multiply Two-Digit by Two-Digit Numbers – Area Models and Partial Products In the ﬁnal exploration, students will solve the real-world problem of determining the area needed for different types of candy for the Sugar and Spice Candy Shop by multiplying 2-digit by 2-digit numbers. In solving the scenarios, students will: •

use the Area Model Template to multiply the numbers.

•

write their partial products for each part of their area models.

•

use another strategy of standard algorithms to solve scenarios.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

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Multiplication Models and Strategies Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students look at different models and equations using the distributive property of multiplication to ﬁnd the product of a multiplication fact and to decide which representations are incorrect. This activity is intended to assess mastery of the following standard(s): 3.PAR.3.3 Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100.

Materials

Preparation

Printed •

• •

1 Slideshow (per class or per group)

Prepare to project the Slideshow one slide at a time. Optionally, print a Slideshow per group.

Reusable •

1 Projector or document camera (per class)

MULTIPLICATION MODELS AND STRATEGIES

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Consumable •

1 Piece of scratch paper (per group)

PROCEDURE AND FACILITATION POINTS 1. 2. 3.

5. 6.

Project the scenario on the ﬁrst slide of the Slideshow for the class, or distribute a Slideshow to each group. Allow time for students to read the scenario. Students may try using the distributive property to solve the multiplication fact on scratch paper. Project Jack’s model on the second slide of the Slideshow for the class. Allow students time to determine whether this student correctly or incorrectly used the distributive property. Ask the students to show a thumbs-up sign if they believe the student’s representation is correct. Ask the students to show a thumbs-down sign if they believe the student’s representation is incorrect. Repeat steps 2–4 for Natalie’s and Rachel’s representations on the third slide and for William’s and Alexis’s representations on the fourth slide of the Slideshow. Facilitate a class discussion about their choices. Allow students to explain why they believe that some of the students’ representations of the distributive property are incorrect. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a. Rachel’s arrays are incorrect because she broke both numbers into smaller parts instead of just one number. William’s equation is incorrect because he added the smaller numbers together rather than multiplying them, and then he multiplied their sums together.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Create a list of each type of multiplication representation with an example: repeated addition, equal-sized groups, an array, an area model, equal jumps on a number line, and skip counting. Post it in the classroom for students to reference and add to throughout this scope. FACILITATION TIP Reassure students that ﬂuency with this model will be helpful when they work with more complex fraction and algebra scenarios. This model supports visual thinking which is an essential problem solving skill for math class and real life.

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Multiplication Models and Strategies Hook – Spot the Talent ACTIVITY PREPARATION Students multiply 2 two-digit numbers using strategies based on place value. They will illustrate and explain the calculations by using area models.

Materials

Preparation

Reusable

Part I

• • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Set of base ten blocks (per group)

Plan to show the Phenomena Video.

•

Part II • •

Plan to have students work in groups of 3 or 4 to complete this activity. Gather base ten blocks. Each group will need a maximum of 4 hundreds, 18 tens, and 81 ones.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP Explain that each base ten block represents 1 square foot. FACILITATION TIP

In the hallway or another large area, have the students predict the size of the stage.

STEMscopes Tip Located under the Scopes tab, the Visual Glossary is an alphabetical list that provides learners with visuals of the key vocabulary and concepts in English and Spanish. Each visual includes the term, a written deﬁnition, and a speech button with narration. Some vocabulary also includes a 3- to 15-second video featuring real-world examples.

DOK-1 What do you know about ﬁnding the area of a rectangle? We multiply the sides, the length by width. It is like an array.

DOK-2 The problem states that the stage needs to be between 12 and 20 feet in each direction. Would a stage that is 10 feet by 15 feet work? Explain. No, 10 by 15 won’t work, because 10 is less than 12. The sides have to be between 12 and 20 feet.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

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Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You’re helping build a stage for the school talent show. You are using ﬂoor pieces that are 1 square foot each. The stage needs to be between 12 and 20 feet in each direction. Make a model of the stage, and ﬁnd the area. Discuss the following questions:

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do you know about ﬁnding the area of a rectangle? We multiply the sides, the length by width. It is like an array.

DOK-2 The problem states that the stage needs to be between 12 and 20 feet in each direction. Would a stage that is 10 feet by 15 feet work? Explain. No, 10 by 15 wouldn’t work, because 10 is less than 12. The sides have to be between 12 and 20 feet.

4. 5. 6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Have each group decide what the dimensions of their stage will be. Remind them that the sides must be between 12 and 20 feet. Instruct groups to build their stage model with the base ten blocks. Walk around and check for understanding with each group. Look at their stage model to see if it matches the required dimensions. Gather students in a whole group, and discuss the following questions and concepts: a.

DOK-2 Once all the groups are done, have one representative from each group share their model and write a multiplication equation that represents the area of the stage modeled. For example, one student could write down 16 × 12 = 192. In the model, the student would represent 16 rows of 12 like this:

Intervention

Acceleration

STEMscopes Tip Housed in the Home section, the Content Unwrapped element provides a clariﬁcation of the instructional expectations. Each student expectation is dissected into what students should be doing and what they should know, as well as the implications for instruction. A vertical alignment shows how the topic progresses through applicable grade levels.

MULTIPLICATION MODELS AND STRATEGIES

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Placeholder AW

DOK-2 Once you had your model, how did you ﬁnd the product of the two dimensions? We added up all the base ten blocks we used. 1 hundreds block, 8 tens blocks, and 12 ones blocks (100 + 80 + 12 = 192). DOK-3 What strategy did you use to ﬁnd the total? We multiplied decomposed factors by place value, and then we added the partial products to get the total product. It looked like this. We then added the products 100 + 60 + 20 + 12 = 192. It is the same as our area model without the base ten blocks. 10

10 × 10 = 100

10 × 2 = 20

6 × 10 = 60

6 × 2 = 12

FACILITATION TIP Monitor the groups and have them present their stage dimensions. Have the other groups check the presenting group’s work.

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Multiplication Models and Strategies Explore 1 – Multiply up to Four-Digit by One-Digit Numbers – Arrays ACTIVITY PREPARATION Students represent multiplication of numbers up to four-digits by a one-digit number, using multiples of 10 and arrays.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Set of Place Value Cards (per group) 1 Exit Ticket (per student)

Reusable •

1 Set of base ten blocks (per group)

Consumable •

1 Resealable bag (per group)

Preparation • • • • • • • •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Station Cards and Place Value Cards on card stock. Laminate them if desired. Cut out the Station Cards and Place Value Cards. Put each set of Place Value Cards into resealable bags. Each group will need a set of base ten blocks for Part I and a set of Place Value Cards for both parts of the activity. Set up the Station Cards around the room. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS Part I 1. 2.

FACILITATION TIP Consider checking each group’s models before allowing them to move forward with the Station Cards.

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Give each group a set of base ten blocks and a set of Place Value Cards. Read the following scenario to the class: You are employees at Cra-Z-Crafts, a local craft store. You are going to help with the quarterly inventory. They need your help to figure out how many craft supplies they have in the store. We will start by finding out how much paper they have. There are 3 boxes of paper, and each box contains 123 reams of paper. Encourage students to use the base ten blocks to show how they could figure out the product of 123 and 3. Support students by asking them to think of the problem as “groups of.” a.

Students will show this in various ways such as groups and arrays.

DOK-1 What would be a good estimate of our product? Encourage students to think about their multiples of 10 and 100. 120 × 3, 100 × 3 = 300, or 12 × 3 = 36 so 120 × 3 = 360. The answer should be around 300 to 360.

Invite a student who used an array to talk through how he or she modeled the problem, or tell students that you once saw a student use an array and model it for them. Instruct students to convert their models into arrays, if they did not already do so. Make 3 equal rows of 123. Be sure to line up the ﬂats, rods, and units to make a rectangular array. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Invite a student to draw the model on the board. Explain that the hundreds (ﬂats) can be drawn as a square, tens (rods) can be drawn as a straight line, and the ones (units) can be drawn as dots to save time.

Discuss the following questions: a.

DOK-1 How many are in each row? One hundred twenty-three

DOK-1 How many rows are there? Three

DOK-1 So how many hundreds do we have in all? Explain how you know. There are three rows, and each row has 100. Three groups of 100 makes 300.

DOK-1 How could we write this as an equation to show the value of these hundreds? 100 × 3 = 300

FACILITATION TIP As students read each scenario, instruct them to ﬁrst ﬁnd the two factors needed to solve the problem.

e. DOK-1 How many groups of tens do we have now? Three groups of two tens f.

DOK-1 How could we write this as an equation to show the value of these tens? 20 × 3 = 60

DOK-1 How many ones are in each row? Three

MULTIPLICATION MODELS AND STRATEGIES

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h. DOK-1 How many rows are there? Three i. DOK-1 So how many groups of ones do we have? Three groups of three ones j. DOK-1 How could we write this as an equation to show the value of these ones? 3 × 3 = 9 k.

DOK-1 How could we ﬁnd the total product? We could add the products from the equations. We could add 300 + 60 + 9, which equals 369.

l. DOK-1 Was this around our estimation? Yes, because our product is 369, which is close to 360. 5. 6.

Read the following scenario to the class: Now, we will ﬁnd out how many pencils they have. Pencils come in boxes of 2,305, and we have 4 boxes. Allow students to try using the base ten blocks to solve. They should have a problem with this. There are not enough blocks, and it would take a very long time. Introduce the Place Value Cards, and show the students how the cards can be used to represent a number in a row without having to line up a lot of tens. When students are done building, discuss the following questions: a.

DOK-1 How many thousands are in each group? 2

DOK-1 How many groups of 2,000 do we have? 4

DOK-1 What equation could we write for 4 groups of 2,000? 4 × 2000

DOK-1 How many hundreds are in each group? 3

STEMscopes Tip Found in the Engage section, the Foundation Builder is used to ﬁll the learning gaps identiﬁed in the Accessing Prior Knowledge activities and bridge students’ learning to the current scope. These activities use manipulatives to review prerequisite student knowledge. Also included are possible student preconceptions about a topic and suggestions on how to overcome those preconceptions.

e. DOK-1 How many groups of 300 do we have? 4 f.

DOK-1 What equation could we write for 4 groups of 300? 4 × 300

DOK-1 How many tens are in each group? 0

h. DOK-1 How many ones are in each group? 5 i. DOK-1 How many groups of 5 do we have? 4 j. DOK-1 What equation could we write for 4 groups of 5? 4 × 5 k.

DOK-1 How do we ﬁnd the total amount? Add all of the products from each group.

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Multiplication Models and Strategies Explore 1 – Multiply up to Four-Digit by One-Digit Numbers – Arrays Part II 1. FACILITATION TIP

Have student partners create the array models and area models ﬁrst. Then, return and guide them in completing the Equation portion. FACILITATION TIP Model how to complete the Equation section of the Student Journal for the ﬁrst station.

Give a Student Journal to each student. Assign each group to start at a different station. Students will read their Station Cards. They will build a model of the problem and record their work on their Student Journals. They will record how many groups of each Place Value Card they have and make a corresponding equation. They will also record a solution sentence that explains what they found. a.

3. 4. 5.

Give groups about 8 minutes before either rotating Station Cards or having the students physically rotate to the next station. Students will repeat the previous steps until they have completed each station. Discuss the following questions:

STEMscopes Tip The Exit Ticket, located within each Explore, gives teachers insight into student learning. This quick formative assessment helps teachers guide their future instruction. It can also be used to reinforce the skills and concepts at any time during the scope. Exit Tickets, Answer Keys, and editable ﬁles are located on the right side of the screen in the list of print ﬁles.

Take time to ﬁnd some more relevant real-world examples of multiplication for students.

FACILITATION TIP Consider having the class review some skip counting with different numbers.

DOK-1 How many rows are you going to have in this array? Answers may vary. 4 rows

DOK-1 What do you call the rows? The rows are “groups of.”

DOK-1 How many are in each row? Answers may vary. 245

DOK-2 How did making this array help you solve the problem? Answers may vary. I could see the amount in each place value and how many groups there were. Then, I could easily multiply the amount in each place value by the number of groups.

e. DOK-2 How does multiplying each place value by the number of groups make multiplying large numbers easier? Answers may vary. When I multiply each place value, I use multiples of 10 and 100, which are easy to multiply. 6.

FACILITATION TIP

Students can use lines and label the length in order to eﬃciently draw the arrays they built.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How did what you learned in third grade prepare you to work with these larger numbers? In third grade, I learned to multiply one-digit numbers by tens. I used the same strategies to multiply one-digit numbers by hundreds and thousands. • DOK-2 How can arrays be used to multiply large numbers? We can break the larger number apart by place value to find the total number of thousands, hundreds, tens, and ones. Then, we can combine those two totals. • DOK-1 How did you find the total of all the tens? I treated it like an array to find the total number of tens and then multiplied that amount by 10. I skip counted by 10. • DOK-1 How did you find the final total? I added the total from each place value to find the final total. •

Post-Explore FACILITATION TIP

On this Exit Ticket, consider allowing students to use their preferred method to show their thinking.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Multiplication Models and Strategies Explore 2 – Multiply up to Four-Digit by One-Digit Numbers – Area Models ACTIVITY PREPARATION Students will use what they have learned about arrays to create area models to multiply numbers up to four digits by one-digit numbers.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Place Value Cards (per group, reuse from Explore 1) 1 Exit Ticket (per student)

Reusable • • • •

3 Sheet protectors (per group) 3 Sheets of plain white paper (per group) 1 Dry-erase marker (per group) 1 Eraser or tissue (per group)

Preparation • • •

• • •

Plan to have students work in groups of 2 to 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. The Place Value Cards can be printed on card stock and laminated (optional). They are the same cards used in Explore 1, so you can reuse them if they’ve already been created. Put a plain white sheet of paper inside each sheet protector so there are enough for each group to have 3. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Model several examples for the whole class and then slowly release various partners.

4. 5.

136

Give each group 3 sheet protectors with the white paper inside. They will also need a dry-erase marker, an eraser, and a set of Place Value Cards. Give each student a Student Journal. Read the following scenario to the class: Illumination Theater is an amphitheater that is used to entertain large groups. The company has several amphitheaters around the state. Each theater is used to hold concerts, plays, symphonies, etc. The theater has a certain number of rows, and each row has a certain number of seats in it. We need to figure out how many total seats there are in each theater! Tell students to build an array to model the rows and seats in each row for the first theater. The first theater has 5 rows with 628 seats in each row. They will build their models on top of the clear sheet protectors. They will then use dryerase markers to trace all the cards in their arrays. Have them draw lines between the hundreds, tens, and ones. Students can lay the blank, covered papers end to end so the arrays will fit. Tell students to remove their cards. They have now created their area models! Allow students to label the length and width of each rectangle of their area models. Explain that when using this method, we are finding the area (the space inside the rectangle) of each rectangle. Have students find the total areas of each piece of their models and record them using equations. These equations will be written inside their area models. They should circle the products. Finally, they will add the total from each piece of their models to find the final products. © Accelerate Learning Inc. - All Rights Reserved

11.

Explain

Elaborate

Evaluate

DOK-2 What did we do to the 628 in order to multiply it by 5? We split it up into hundreds, tens, and ones. We multiplied 5 by 600, then 5 by 20, and last 5 by 8.

Explain that when we do this, we are using what is called the “distributive property.” The distributive property allows us to multiply one chunk at a time, just like students did with 628 times 5. Explain that there is a special way we can record the equations to show how we multiplied the numbers. We can use parentheses to show each part of our model. On the board, write the equation that shows the distributive property for this model: (5 × 600) + (5 × 20) + (5 × 8). Discuss the following question: a.

10.

Explore

Intervention

Acceleration

Discuss the following question: a.

Engage

FACILITATION TIP Instruct students that multiplying multi-digit numbers is a process. Point out how they are decomposing the multi-digit number on top and multiplying one digit at a time, then add. Create an anchor chart to assist students.

DOK-1 How can we now ﬁnd the total? We can add the product of 5 and 600 to the product of 5 and 20 and to the product of 5 and 8 to get the ﬁnal product.

Have students continue working to model the rest of the theater seating arrangements. Students should work with their groups to record their models, equations, and ﬁnal products on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

MULTIPLICATION MODELS AND STRATEGIES

Home

Math Chat DOK-2 What is the relationship between an array and an area model? They show the same thing. Both can be used to ﬁnd the product when multiplying. They both represent equal rows. They both help us decompose a number and multiply one place value at a time. • DOK-2 What is the relationship between the equation and the area model? Each part of the equation represents a part of the area model. We write each part using parentheses and add the parts together to ﬁnd the total. • DOK-2 How do you know the product of the equation that represents the tens place? I know that 20 is made up of 2 tens. If I have 5 groups of two tens, then I know I have 10 tens. The value of 10 tens is 100. •

FACILITATION TIP Display some engaging real-world models of array and area models. For example, interlocking toy blocks, video game territories, construction, and landscaping projects.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP For this Exit Ticket, establish clear criteria for success. Consider allowing some students to use any method to show their thinking.

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Multiplication Models and Strategies Explore 3 – Multiply Two-Digit by Two-Digit Numbers – Arrays ACTIVITY PREPARATION Students use arrays to represent two-digit by two-digit multiplication.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Equation Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • • • •

1 Set of base ten blocks (per group) 1 Dry-erase marker (per group) 1 Eraser or tissue (per group) 1 Container (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print four equation cards for each group. Cut the cards apart, and laminate them so students can write on them with dry-erase markers and reuse them. Place base ten blocks in containers for each student group. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS Part I: Measurement Tools

FACILITATION TIP Discuss with the class how they will build on their skills from Explore 2 to multiply 2-digit numbers by 2-digit numbers. The process will be similar.

1. 2. 3.

FACILITATION TIP If time is limited, allow students to model with sketches rather than tracing on Step 2.

FACILITATION TIP

Remind students that the area is the length multiplied by the width.

Divide the class into groups. Distribute materials to each student group. Students should begin by tracing a flat, a rod, and a unit on their Student Journals. Read the following scenario to the class: Your scout troop has decided to have a fundraiser selling bags of mulch to the people in local neighborhoods in order to raise money for a new playground in the park! The mulch order form asks people to write down the length and width of their flower beds that need mulch. Since the bags of mulch come in sizes that cover square feet, you will model the flower beds with tools to figure out the total number of square feet of mulch needed for each flower bed. Have students label the length, width, and area of each base ten block they traced. Explain that these are the measurement tools students will use to build and measure the flower beds to see how many square feet of mulch is needed. Discuss the following questions: a.

DOK-1 What is the length, width, and area of a ﬂat? The ﬂat is one whole section that is 10 feet by 10 feet. The area is 100 square feet.

DOK-1 How many rods are in a ﬂat? 10

DOK-1 What is the length, width, and area of a rod? It is one-tenth of the ﬂat, or 10 feet by 1 foot. The area is 10 square feet.

DOK-1 How many units are in a ﬂat? 100

e. DOK-1 What is the length, width, and area of a unit? One unit is onehundredth of a ﬂat, or 1 foot by 1 foot. The area is 1 square foot. 138

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Measuring Orders 1.

Have students use the base ten blocks to build a model of each ﬂower bed. Each ﬂower bed should be a rectangle or square. a.

Once the array is built, students will use the equation cards to write the equation for each section of the array, and they will place the cards on top of the sections. a.

4. 5.

For example, on the first array, students should complete an Equation Card for the section with two flats (20 × 10 = 200), an Equation Card for the section of rods under the flats (20 × 5 = 100), an Equation Card for the section of rods beside the flats (3 × 10 = 30), and an Equation Card for the section of units (3 × 5 = 15).

Once a ﬂower bed is built, students should draw their models in the Array column and write the equations in the Expanded Notation column on their Student Journals. Students should write an equation that represents the model and record the total area on their Student Journals. Discuss the following questions: a.

DOK-2 How did you know what base ten blocks to use to make this flower bed? Answers may vary. The flower bed is 15 feet long and 23 feet wide. That means there are 15 groups, or rows, of 23. 10 groups of 23 is 230, so I knew I could make 1 row with 2 flats and 3 rods. That left 5 groups, or rows, of 23. I made 5 rows with 2 rods and 3 units in each row.

DOK-2 Why didn’t you trade 10 rods for a ﬂat or 10 units for 1 rod? Answers may vary. Arrays have to form a rectangle or a square. If I would have traded the rods for a ﬂat and the units for a rod, I couldn’t have made a rectangle or square.

If needed, encourage students to think of the length and width as so many hundreds, tens, and ones (expanded form). They should reason about the spaces they need to ﬁll with the measurement tools and use the dimensions they found in Part I to ﬁnd the right size of pieces. This helps students place the base ten blocks properly into the array.

DOK-1 How did you ﬁnd the product? Answers may vary. I added up the totals of all the pieces. 2 ﬂats is 200, 13 rods is 130, and 15 units is 15. 200 + 130 + 15 = 345.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How did you know which size piece to put in each spot? I used the dimensions we found in Part I to figure out which size piece could fit in each spot. • DOK-2 What did you notice about the arrays? Each array formed a rectangle or a square. Each array was built using the length and width as a tool. Most of the arrays had a combination of different-sized pieces. • DOK-1 How did you use your model to find the final product? We had to add up the totals of all the pieces. If we had more than 1 or 10 of one piece, we needed to regroup them. •

FACILITATION TIP

MULTIPLICATION MODELS AND STRATEGIES

Home

Have students take turns reading the Station Cards, identifying the variable, and making the array and area models. FACILITATION TIP If needed, provide students additional space to write their Expanded Notations here and on the upcoming Exit Ticket.

STEMscopes Tip Located under the Explain tab, Anchor Charts are designed to be used after teaching the Explore lessons. Creating anchor charts is a collaborative effort between teacher and students with each section illustrating the concepts covered in the individual Explores. A printable sample anchor chart is also included.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Multiplication Models and Strategies Explore 4 – Multiply Two-Digit by Two-Digit Numbers – Area Models ACTIVITY PREPARATION Students use area models to represent two-digit by two-digit multiplication.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • •

• • • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable • • • •

1 Set of base ten blocks (per group) 1 Dry-erase marker (per group) 1 Eraser or tissue (per group) 1 Container (per group)

•

Consumable • •

2 Large pieces of wax paper (per group) 1 Roll of tape (per class)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Place base ten blocks in containers for each student group. Tape two strips of wax paper together on the long edge so that they will ﬁt the base-ten models each student group is going to be building. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS Part I: Small Party Pizza 1.

2. FACILITATION TIP Have roles for each group member like drawing the model on the wax paper, building the model with the base ten blocks, and writing the equation. The roles can be rotated for each station.

FACILITATION TIP Monitor student groups and guide students by modeling the process in question. 140

3. 4.

Read the following scenario to the class: Paciano’s Pizza Parlor has found their customers prefer rectangular pizzas when they have a party. For their made-toorder rectangular pizzas, Paciano’s has to find the total area of the pizza in order to figure out the amount of sauce and toppings they will need so they can set a fair price for the pizza. Distribute the container of base ten blocks, wax paper, and a dry-erase marker and eraser to each group. Have students use the base ten blocks to build a model of each pizza on top of the wax paper. Each pizza should be a rectangle or square. Students will then use the dry-erase markers to trace around their models on the wax paper and label the dimensions. Students should remove one section from their models at a time, trace where the section was with their dry-erase markers, and write an equation that represents the blocks that were in that section. Students should continue this process until they are left with an area model of the pizza drawn on the wax paper. Students should record the area model and equations for each section on their Student Journals. Students will then find the total area and represent their model as an equation. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a.

DOK-2 How did you know what base ten blocks to use to make this pizza? Answers may vary. The pizza is 22 inches long and 16 inches wide. That means there are 22 groups of 16. I made 2 rows, each with 1 ﬂat and 6 rods, to show 20 × 16. Then, I made 2 rows, each with1 rod and 6 units, to show 2 × 16.

DOK-1 How did you make your area model? Answers may vary. I used the expanded form of the length, 20 + 2, and the expanded form of the width, 10 + 6, to make the area model. I drew around the base ten blocks in each section. My ﬁrst section was 2 ﬂats because 20 × 10 = 200. The section next to that was 12 rods because 20 × 6 = 120. The third section was 2 rods because 2 × 10 = 20, and the fourth section was 12 units because 2 × 6 = 12.

c. 7.

Engage

DOK-1 How did you find the final product? I added the products from each section together to find the total area.

After Part I, invite the class to a Math Chat to share their observations and learning.

STEMscopes Tip Located in the Elaborate section, the Math Story supports the literacy-math connection. After reading or listening to the teacher read the real-world passage, students are tasked with ﬁnding information within the story to solve math problems that focus on the new skills learned in the scope and to answer literacy-based comprehension questions.

MULTIPLICATION MODELS AND STRATEGIES

Home

Math Chat •

•

DOK-1 What did you notice about the area models? Each area model formed a rectangle or a square. Each area model was built using the length and width, just like an array. The area models had a combination of different-sized pieces. DOK-1 How did you use your model to find the final product? We added the products of each section in the area model together to find the total area.

Part II: Monster Pizza 1.

Read the following scenario to the class: Paciano’s rectangular pizzas have really caught on, and other pizza parlors are now making rectangular pizzas. Paciano’s and the other pizza parlors in the area have decided to have a friendly competition to see who can make the largest monster pizza based on the total area of the pizza. Students should look at each set of pizza dimensions and draw an area model using the wax paper and dry erase marker. Encourage students to imagine what the array would look like as they break apart the length and width into expanded form and ﬁnd the area of each section. a.

FACILITATION TIP Model for students how to break down the larger length and width with a different example on the board.

If needed, allow students to revisit the base ten blocks to build an array.

Discuss the following questions: a.

DOK-1 What did you do to make an area model? I wrote the length and width in expanded form. Then, I drew four sections.

DOK-1 How did you use the area model to find the final product? I multiplied each section to find the area of that section. Then, I added the partial products together to get the final product.

DOK-2 How is your area model like an array? They are both rectangles or squares. They have a length and a width.

DOK-3 What are the advantages of using an area model? Answers may vary. I can ﬁnd the ﬁnal product more quickly because I don’t have to count the number of pieces in each section. I can multiply larger numbers more easily than trying to make rows of blocks.

After Part II, invite the class to a Math Chat to share their observations and learning.

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Multiplication Models and Strategies Explore 4 – Multiply Two-Digit by Two-Digit Numbers – Area Models Math Chat DOK-2 How are area models similar to arrays? They are both rectangles with a length and width. • DOK-2 How are area models different from arrays? We can count the number of pieces in each section of the array, but we need to use multiplication to ﬁnd the total area of each section in the area model. • DOK-3 How is an area model helpful? You can multiply larger numbers with an area model. If you were to use large numbers with an array, you would need a lot of blocks. • FACILITATION TIP Reassure students that being ﬂuent with these physical models will support their further success in math as the scenarios and problems become more complex. Even if they don’t feel that they need the model to solve today’s work, the models provide helpful thinking tools for later school work and life skills.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

142

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MULTIPLICATION MODELS AND STRATEGIES

Home

143

MULTIPLICATION MODELS AND STRATEGIES

Multiplication Models and Strategies Explore 5 – Multiply Two-Digit by Two-Digit Numbers – Area Models and Partial Products ACTIVITY PREPARATION Students use area models to understand partial products and relate this to multiplying two two-digit numbers.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Area Model Template (per group) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

•

Reusable • • •

•

1 Sheet protector (per group) 1 Dry-erase marker (per group) 1 Eraser or tissue (per group)

•

Consumable •

1 Resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print one set of Scenario Cards on card stock (if desired) for each group, cut them out, and place each set in a resealable bag. Print an Area Model Template for each group. The Area Model Template should be placed inside a sheet protector so that students can write on it with the dry-erase marker. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1.

2. 3. FACILITATION TIP Use a basic example to demonstrate how to create the array model and transfer the information into an area model.

FACILITATION TIP Model the process for the ﬁrst example on the board. Have students participate in the process as much as possible. FACILITATION TIP Demonstrate the importance of place values when completing the partial products. 144

Read the following scenario to the class: The Sugar and Spice Candy Shop needs to rearrange their candy warehouse to make room for a new shipment of candy. You will be given the dimensions of the space needed for each type of candy, and you will need to report the area of each section to your manager. You may need to remind students that area is found by multiplying the length by the width. Give a Student Journal to each student and a set of Scenario Cards, an Area Model Template, and a dry-erase marker and eraser to each group. The Area Model Template should be in a clear sheet protector. For each scenario, students should use the area model template to multiply the numbers. Students should record their partial products for each part of their area models on their Student Journals. Model this as needed. Be sure to relate each section of the area model to the numbers they are multiplying in the problem and what partial product it produces. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you make this area model? Answers may vary. I used the expanded form of the length, 50 + 7, and the expanded form of the width, 20 + 8, to make the area model. I multiplied each length by width to get the partial products of the sections. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

DOK-1 How did you use the information in the area model to help you with the partial products? I used the equations from the area model on the partial products. Each partial product is like one section of the area model.

DOK-2 How are area models and partial products similar? Both area models and partial products decompose the numbers so they are easier to multiply.

Engage

DOK-3 What is the advantage of using partial products instead of area models? Answers may vary. You are still ﬁnding the partial products— you just don’t have to draw the area model. It is easier to add the partial products to get the ﬁnal product.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 Which place values do you use from each number to find partial products? I use them all. I multiply each place value in the first number by each place value in the second number, and then I add them all together. • DOK-2 How does the place value of the factors affect the partial product? If I am multiplying tens by tens, I know I will get hundreds because 10 groups of 10 is 100. If I am multiplying tens by ones, I know I will get tens because I am finding the total of ___ groups of 10. • DOK-2 Do you think this would work if you had more than two digits times two digits? Yes. You would just have to make sure you still multiply each place value in the first number by each place value in the second number. • DOK-3 How does an area model help you multiply big numbers? You can break down the big rectangle into smaller rectangles with numbers that are easier to multiply and then add together all the sections. •

Intervention

Acceleration

STEMscopes Tip Found in the Evaluate section in Grades 2-5, the Decide and Defend formative assessment presents a mathematical problem. Students respond with an argument and justify it by using mathematical evidence and reasoning in the form of written text, visual models, expressions, and equations.

MULTIPLICATION MODELS AND STRATEGIES

Home

Post-Explore 1. 2. 3. 4.

FACILITATION TIP For this Exit Ticket, establish clear criteria for success. Consider allowing some students to use any method to show their thinking.

145

MULTIPLICATION MODELS AND STRATEGIES

Multiplication Models and Strategies Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Multiply up to Four-Digit by One-Digit Numbers – Arrays Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Multiply up to Four-Digit by One-Digit Numbers – Area Models Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Multiply Two-Digit by Two-Digit Numbers – Arrays Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Multiply Two-Digit by Two-Digit Numbers – Area Models Independent practice assignment that gives students an opportunity to demonstrate their learning

Show What You Know, Part 5 Multiply Two-Digit by Two-Digit Numbers – Area Models and Partial Products Independent practice assignment that gives students an opportunity to demonstrate their learning

146

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

J & J Mowing Company

Chip and Joanna Gaines

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

The Survey Says . . .

Multiplication Problem Solving

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

PhET Interactive Simulation

Summer Vacation

Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

MULTIPLICATION MODELS AND STRATEGIES

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147

Students who are still acquiring the concept and need remediation

MULTIPLICATION MODELS AND STRATEGIES

Multiplication Models and Strategies

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

148

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can use what I know about place value and properties of operations to multiply a four-digit whole number by a one-digit whole number or to multiply two two-digit whole numbers.

What prompts will be used?

What does mastery look like?

MULTIPLICATION MODELS AND STRATEGIES

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I can accurately and eﬃciently make use of a variety of strategies when multiplying multi-digit whole numbers.

I can illustrate and explain my multiplication calculations using equations, rectangular arrays, and/or area models.

149

SCOPE 1

Division Models and Strategies Scope Introduction SCOPE SUMMARY Students extend their knowledge of division to include quotients with up to four-digit dividends and one-digit divisors. They are expected to ﬁnd and write remainders appropriately. A variety of strategies are explored based on place value and properties of operations. Students focus on illustrating and clearly explaining their calculations using equations and visual models. Student Expectations

4.NR.2.4 Solve authentic division problems involving up to 4-digit dividends and 1-digit divisors (including whole number quotients with remainders) using strategies based on placevalue understanding, properties of operations, and the relationships between operations.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Kindergarten and first grade form the foundation for our base-ten system, developing basic addition and subtraction concepts and skills. Second grade advances this progression, working with equal groups and five-by-five arrays. Third grade develops the relationship between multiplication and division based on place value and the properties of operations. Understanding this relationship, students can fluently multiply and divide within 100.

Fifth grade will extend division to two-digit divisors and use models to ﬂuently solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction. Students will relate a division strategy to a written method, consistently checking the reasonableness of their solutions. Sixth grade will apply and extend students’ understanding of division to perform operations with multi-digit decimal numbers by ﬂuently using models and student-selected strategies. Sixth-grade students will be asked to multiply and divide any combination of whole numbers, fractions, and mixed numbers by using studentselected strategies. Students will also interpret products and quotients of fractions and solve word problems.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

illustrate and explain wholenumber quotients using models and drawings.

•

solve a division problems using manipulatives.

•

express the answer using a pictorial model and a division sentence.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

represent the quotient of up to a four-digit whole number divided by a one-digit whole number, using arrays and equations.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 150

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Share Equally In this exploration, students will work with peers to solve a scenario about helping ensure each grade receives the same number of school supplies. In solving the scenario, students will: •

model division of larger numbers.

•

use ten base blocks.

•

complete Scenario Cards through modeling.

Explore 2

Explore 1

EXPLORE ACTIVITIES

Area Models In this exploration, students will solve various scenarios with peers using area models. In solving scenarios, students will: •

model division using area models.

•

ﬁnd solutions to a variety of scenarios.

In this exploration, students will complete a scenario where they pretend to own an event-planning company and must help ﬁgure out how to arrange chairs, determine how many tickets were sold, and how many supplies are needed for each client’s events. Through completing this exploration, students will: •

model the division of larger numbers.

•

use base ten blocks to build arrays.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 4

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Arrays

DIVISION MODELS AND STRATEGIES

Home

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Partial Quotients In the ﬁnal exploration, students complete Scenario Cards with group members by using place value disks and exploration resources. In solving the scenarios, students will: •

complete Scenario Cards.

•

use partial quotients to divide a number with up to four digits by a one-digit number.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

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Division Models and Strategies Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students illustrate and explain whole number quotients using models and drawings. This activity is intended to assess mastery of the following standard(s): 3.PAR.3.2 Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.

Materials

Preparation

Printed •

• • •

1 Slideshow (per class)

Reusable • • •

Prepare to project the Slideshow for students. Plan to have students work in pairs for this activity. Gather counters for each pair.

DIVISION MODELS AND STRATEGIES

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1 Projector or document camera (per class) 40 Counters (per pair) 1 Dry-erase marker (per pair)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5. 6.

Distribute one dry-erase marker and 40 counters to each pair of students. Project the Slideshow to the class, one slide at a time. Invite students to read together. Have pairs of students use manipulatives to model the scenario on their desks. Challenge students to create division sentences to represent their models. Facilitate a class discussion about how they modeled the division problems and what each part means. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. a. In the ﬁrst problem, we used 36 blocks to represent the P.E. students. Then, we counted out 6 and put them in a group. We kept counting out 6 for each group until there were no more blocks left. It turned out that we also had 6 groups. The 6 different groups are the teams, so there will be 6 teams, with 6 students (blocks) on each team. b. In the second problem, we used 28 blocks to represent Mrs. Ihedowa’s students. Since she wants 7 groups, we took 7 blocks and spread them out across our desks to represent the different groups. Then, we split the remaining blocks into those 7 groups. In the end, 4 blocks were in each group. That means 4 students would be in each of the 7 groups.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP After using the manipulatives, prompt students to sketch pictorial representations of their models on whiteboards or directly on the Student Handout so they can refer to and share them during the class discussion. FACILITATION TIP Record each division sentence, and discuss what each part of the equation represents. For example, in 36 ÷ 6 = 6, the divisor, 36, is the total number of students; the dividend, 6, is the number of players per team; and the quotient, 6, is the number of teams. In 28 ÷ 7 = 4, the divisor, 28, is the number of students; the dividend, 7, is the number of groups; and the quotient, 4, is the number of students in each group. Emphasize that in both cases, the divisor (the number you are dividing into) represents the total amount. The dividend (the number you are dividing by) and the quotient (the answer to the division problem) are the parts that make up the whole. They can represent either the number of groups or the amount per group, depending on the context of the situation and what the unknown value is.

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Division Models and Strategies Hook – Canned Food Drive ACTIVITY PREPARATION Students represent the quotient of up to a four-digit whole number divided by a one-digit whole number, using arrays and equations.

Materials

Preparation

Printed

Part I

•

1 Donations (per group)

•

Reusable • • •

Plan to show the Phenomena Video.

Part II

1 Phenomena Video (per class) 1 Projector (per class) 1 Resealable bag (per group)

• •

•

Plan to have students work in groups of 3 to complete this activity. Print out one Donations for each group. Cut out the boxes. If desired, laminate them for future use. Note that each box represents 50 donated items. You should have 27 boxes for each group to model the division. Place the sets of boxes in resealable bags.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore FACILITATION TIP

Activate prior knowledge about division with the Foundation Builder activity or a few simple practice division problems.

FACILITATION TIP Project this scenario and read through it together with students. Guide them to locate the key math values and phrases. Point out that some (younger) students might get confused by the words third, fourth and ﬁfth and think it was part of the math problem.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Third, fourth, and ﬁfth grade all collected the same number of cans in the school’s canned food drive. If they collected 1,350 food items altogether, how many items did each grade level collect? Discuss the following questions: a.

DOK-2 What are some ways you can solve this problem? You can make equal groups of food items until you have used 1,350 items. You can count how many items are in each group.

DOK-1 What operation do you think you would use to solve the problem? You would use division to solve the problem.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

FACILITATION TIP If space is limited, give groups small math manipulatives that can be arranged into an array rather than large boxes of donated items. 154

After students have completed all the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-2 What are some ways you can solve this problem? You can make equal groups of food items until you have used 1,350 items. You can count how many items are in each group.

DOK-1 What operation do you think you would use to solve the problem? You would use division to solve the problem.

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Each student can represent one grade level in the group (3rd, 4th, 5th). Have the students distribute their boxes among the grade-level representatives to determine how many donated items each grade level collected. Discuss the following questions: a. b.

Engage

DOK-1 What would this equation look like? The equation would look like this: 1,350 ÷ 3 = 450 items.

FACILITATION TIP

Challenge students to identify more than one way to represent this scenario. For DOK-2 How did you solve the problem? We gave one box to each grade example, they can use a multiplication sign, level, and then one more box to each grade level. We kept doing that repeated subtraction, or a fraction bar. until all the boxes were gone. Then, we counted how many boxes each grade level had. Each grade had nine boxes. Since each box had 50 items in it, we multiplied 9 × 50 or counted by 50 nine times and got 450.

Tell students to create an array with their boxes. Discuss the following questions: a.

DOK-1 How many rows of boxes do you have? There are three rows to show the three grades.

DOK-1 How many columns of boxes do you have? There are nine columns.

DOK-1 How many items are in each box? There are 50 items in each box.

DOK-1 How many items total do you have in each of the three rows? There are 450 items.

e. DOK-2 How does making an array model help you with this problem? We can organize the boxes to make sure we have equal groups. Arrays allow us to see that multiplication and division are related.

DIVISION MODELS AND STRATEGIES

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FACILITATION TIP Continue to reinforce to students that these physical models become very useful as conceptual tools later in math and in real life.

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Division Models and Strategies Explore 1 – Share Equally ACTIVITY PREPARATION Students model division of larger numbers, using base ten blocks and generic school supplies.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 2 Sets of Scenario Cards (per class) 1 Exit Ticket (per student)

•

Reusable •

• • •

10 Packages of school supplies, such as boxes of crayons, markers, pencils, etc. (per group) 8 Small paper plates (per group) 1 Set of base ten blocks (per group) 6 Containers (shoe box size, per class, optional for organizing Part II materials)

Plan to have students work in groups of 3 or 4 to complete this activity. Find 10 packages (boxes, etc.) of the same type of school supplies for each group. For example, one group could have 10 boxes of markers, while another group could have 10 boxes of pencils. Print two sets of Scenario Cards, and place one card in each container. Place a set of base ten blocks in each container, along with eight small paper plates. Use the guidelines below to make sure there are enough blocks based on the scenario. • • •

•

Scenario 1: 4 hundreds, 2 tens, 30 ones Scenario 2: 1 hundred, 16 tens, 8 ones Scenario 3: 1 thousand, 12 hundreds, 26 tens, 16 ones

For students who need more support in recalling information, please see our Base Tens, Sharing Mats, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS Part I 1. 2. FACILITATION TIP

The paper plates and manipulatives allow students to explore the division process.

FACILITATION TIP It is important for students to explain the reasoning for their strategies and how they chose to share the packages.

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Each group should get a set of 10 school supplies and three paper plates labeled “Classroom A,” “Classroom B,” and “Classroom C.” Student groups should work to share the school supplies equally between the three classrooms. Each classroom could be represented by a paper plate. Students should record what they did to share the school supplies in their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 What did you do to share the school supplies? We had 10 boxes, so we knew we could at least give three of them to each class because three groups of three is nine. Then, we had one left. We had to open it and split up the separate pieces to make it even. Note that students may still have some left over. That is okay. Encourage them to share them as equally as possible.

DOK-1 How much did each classroom get? Answers may vary depending on how many of each supply is in a package. Each classroom got three packs of markers and three extra markers. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

DOK-1 Did you have any left over (remaining)? Yes, there were a few markers we couldn’t give out because then it wouldn’t be fair.

Explain that the leftovers are called the “remainder.”

Evaluate

Intervention

Acceleration

e. DOK-2 Why did you share the packages ﬁrst instead of sharing all the individual pieces? Each package is the same, so giving one to each classroom is fair. It is faster to pass out wholes than to pass out a bunch of separate markers. f.

DOK-2 Why did you split up a package? We couldn’t give one whole leftover package to a class, since that wouldn’t be fair. That would give one class four and the other two classes three each. We split up the extra package to make it as equal as possible.

Part II 1.

2. 3. 4.

Distribute containers of base ten blocks, paper plates, and Scenario Cards to each group. Distribute them so each set will rotate between three groups of students. Students should read the scenario they received and describe it in their own words on their Student Journals. Students will then solve the problem using the base ten blocks and paper plates. Students should draw and label what they did to solve the problem in their Student Journals and then write a statement and an equation that represents their answer. When students are done with their scenario, have them place all the materials back in the container. Rotate the containers and repeat the process above until each group has solved all three scenarios. a.

7. 8.

10.

Be sure to check in frequently with the group working on Scenario 3, as it is the most challenging. If students try to split the blocks into individual groups of six, have a conversation about how splitting the total into groups of six is the same as splitting a total into six equal groups.

Allow groups of students to share how they solved each scenario. Encourage other groups to ask clarifying questions or to add to the explanation using the sentence stems and questions below. a.

I agree with ________ because ________.

Why did you ________?

What could you have done differently?

How did you know what to do ﬁrst?

Allow more than one group to share their process so students can see multiple pathways to each solution. As students describe their group’s process, model what they are saying using the virtual base ten blocks or allow students to do the demonstration as they describe their process. Have students reﬂect on the best way to divide up a large amount and record their thoughts in their Student Journals. If needed, discuss the following questions: a.

DOK-2 Would you start with the small, individual pieces or with the larger groups of items? It was easier to start by giving out the larger pieces ﬁrst. If I had an extra piece, I could split it up into smaller pieces.

DOK-3 What other math skills can help you do this? Knowing my multiplication facts helped me know how many smaller pieces I could put on each plate.

DIVISION MODELS AND STRATEGIES

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FACILITATION TIP Make sure each student in the group has a role to complete the problem. Have the students rotate roles for the next scenario.

FACILITATION TIP As you monitor each group’s strategies, be sure the students are splitting the larger pieces ﬁrst. Model how it is easier to regroup from largest to smallest units to share equally.

STEMscopes Tip The Vertical Alignment Chart can be found in the Essentials section of the Teacher Toolbox. This chart encompasses Kindergarten through Grade 5 and details the organization of the standards, the grade level focus across grade levels, and the vertical alignment of the standards by domains.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

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Division Models and Strategies Explore 1 – Share Equally Math Chat DOK-2 How did you know how many groups (paper plates) you would need for your problem? When we read the problem, we had to look for how items were being put together or grouped—for example, by teams, coaches, or ounces in one cup. • DOK-1 What process did you use to share the materials? We began sharing the greatest place value ﬁrst because if we ran out of a place value block, we could regroup it into the next smallest place value. • DOK-2 What other math skills/operations does this remind you of? This reminded me of multiplication because we have groups with an equal number in each group. •

FACILITATION TIP When you preview this Exit Ticket with students, make time to answer questions about the images and ensure that students understand the 3-D representations.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DIVISION MODELS AND STRATEGIES

Home

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DIVISION MODELS AND STRATEGIES

Division Models and Strategies Explore 2 – Arrays ACTIVITY PREPARATION Students model the division of larger numbers using base ten blocks to build arrays.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable •

• • • •

1 Set of base ten blocks (per group) •

Plan to have students work in groups of 3 or 4 to complete this activity. Place a set of base ten blocks in a container for each group so they can be distributed and collected easily. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Base Tens, Sharing Mats, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

Creating array models is a scaffold into writing equations. Array models will also help with fraction operations. STEMscopes Tip STEMcoach in Action, located under the Scopes tab, provides teachers with professional development for the STEM-centered classroom. Explore a variety of topics that are broken into 3–6 subtopics with overviews describing teacher, classroom, and student expectations; FAQs and resources; and/or video libraries.

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Read the following scenario to the class: You own an event-planning company in which you help people host concerts, weddings, conferences, and more! Part of your job is planning how many chairs you will need and how to arrange them. You also supply tickets and raﬄe tickets for fundraising events and other supplies needed by large groups and teams. The criteria for each event is listed on your Student Journal. Figure out how to arrange the chairs, how many tickets sold, or how many supplies are needed for each of your client’s events. Distribute the base ten blocks, and instruct students to use the base ten blocks to represent chairs by arranging them in arrays. If necessary, review what constitutes an array and how one is built with larger numbers. Once students build models of the seating arrangement, they should record their plans on their Student Journals. Remind students that we can break apart, or decompose, a dividend and represent it using more than one expression so it is easier to solve. Explain that each part of the decomposed divisor should be divided by the divisor; this is called the “distributive property.” We can then add the quotient from each expression together, giving us the ﬁnal quotient. See the example below for what students should be doing. Each expression in parentheses represents one section of the array.

Placeholder AW

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 When you build a rectangle with the same number of pieces in each row, what is that type of model called? It’s called an array.

DOK-2 What number sentences can we use to represent our seating arrangement? 4 rows × 21 in each row = 84 chairs; 84 chairs ÷ 4 rows of chairs = 21 in each row.

DOK-2 How were the base ten blocks helpful? They helped us see how to split up the pieces. We had 8 tens, so we knew we could make 4 groups of 2 tens and start with 20 in each row. Then, we had 4 ones, so we put 1 extra piece in each row.

DOK-1 How many tens did we use? What is the value of tens? We used 8 tens. The value of 8 tens is 80.

e. DOK-1 What expression could we use to show just how we divided up the tens? We could use 80 ÷ 4. We can use parentheses to show the expression by itself.

Intervention

DOK-1 How many ones did we use? What is the value of them? We used 4 ones. The value is just 4.

DOK-1 What expression can we use to show how we divided up the ones? We can use 4 ÷ 4.

FACILITATION TIP

DIVISION MODELS AND STRATEGIES

Home

Some students may need the array models as a visual representation of the problem, while other students may be able to solve it on their own.

Allow groups time to complete the seating arrangements for each of the clients. FACILITATION TIP For each problem, students should draw and label their models, write a statement A strategy to solve multi-digit division that explains the answer, and write two equations to represent the quotient. problems is to decompose the dividend into Encourage students to solve problems using only drawn models once they feel more than one expression. comfortable. Students can draw cubes for thousands, squares for ﬂats, lines for FACILITATION TIP rods, and dots for units. After groups have completed several a. If they need to use the blocks for support, they can. scenarios, have them share. Discuss the strategies used, address misconceptions, b. Students may need to start by drawing a model of the dividend before and model as needed. Then, release the drawing the array. Students can always try to solve the problems using groups to complete the last scenarios on drawings and check their work with the blocks. their own. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

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DIVISION MODELS AND STRATEGIES

Division Models and Strategies Explore 2 – Arrays Math Chat •

•

STEMscopes Tip Communicate Math – Making Connections is located under the Communicate Math tab of the Teacher Toolbox. Students learn mathematical concepts by linking them to their prior knowledge and experiences. Teachers can emphasize the connections from this page to help students bridge their knowledge from concept to concept. Examples of possible connection types are provided.

•

DOK-2 How did you solve the problem? Student responses will vary based on which problem is being discussed. We used the blocks to build the number and then divided it between the number of rows we needed. Sometimes we had to trade in a block for smaller pieces. DOK-2 How is this similar or different from what you did with the paper plates? It is similar because we are still splitting up a total into equal groups. It is different because the equal groups are now rows of blocks instead of being placed on paper plates. DOK-2 What is the relationship between the array and your equations? The total amount shown in the array is the first number in my equation. It is the total we are splitting up into equal groups. The second number in the equation shows how many rows we need, and the final quotient shows how many we will have in each row. DOK-2 How did you use the distributive property to help you solve the problems? I simplified the problem by splitting up the total into parts that were easy to divide into the number of groups I needed. Then, I divided each of those parts by the number of groups. When I had the quotients of each part, I added those quotients together to get the final quotient. It made dividing the problem much easier. DOK-2 How did you solve the problem using only pictures? We drew the total first, and then we crossed off the blocks as we drew our array. I counted by tens as I drew tens, and when I didn’t have enough to put one in each row, I started drawing ones.

Post-Explore FACILITATION TIP Before having students complete this Exit Ticket, establish your criteria for success. Some students may want to use a division algorithm different from the models used in this class.

1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DIVISION MODELS AND STRATEGIES

Home

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DIVISION MODELS AND STRATEGIES

Division Models and Strategies Explore 3 – Area Models ACTIVITY PREPARATION Students model division of large numbers using area models.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Area Model Cards (per group) 1 Exit Ticket (per student)

Reusable •

1 Dry-erase marker (per group)

• • •

• •

Consumable •

1 Resealable bag (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print and cut apart the Area Model Cards for each group, and place them in a resealable bag for easy distribution and collection. Test to make sure student desks can wipe clean after being written on with a dryerase marker. If not, plan to use another dry-erase surface, such as a laminated poster. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Base Tens, Sharing Mats, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS 1. FACILITATION TIP

Demonstrate several area models for students on the board. Begin with simpler problems; then, progress to a more challenging problem.

FACILITATION TIP The Area Model Cards assist students in decomposing the dividend into units of 100, 10, or 1.

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Explain to students that they are to create area models using value cards to ﬁnd solutions to a variety of scenarios. Give each group a set of Area Model Cards and a dry-erase marker. Allow students a few moments to discover the materials and discuss how these could be used to create area models. Introduce students to the Area Model Cards by showing them that the 1,000 card represents a row of 1,000, a 100 card represents a row of 100, etc. Challenge students to use the cards to model the ﬁrst problem on their Student Journals. Discuss the following questions: a.

DOK-2 How could you use the values on the cards to help build your model? I knew we could put a 10 in each row since 10 × 6 = 60; then, we only had 36 left. Since 6 × 6 = 36, we knew we could put 6 ones in each row. So 6 groups of 10 plus 6 groups of 6 = 16 groups of 6.

DOK-1 What were the dimensions of the rug? The width of the rug was 16 feet, and the length was 6 feet.

DOK-1 What was the total area of your model? The total area was 96 square feet.

Have students outline their models on their desks (or other dry-erase surface) using the dry-erase marker. Students should draw a line between the tens and the ones. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Evaluate

DOK-2 What equations could we use to represent this problem? 96 ÷ 6 = 16 or (60 ÷ 6) + (36 ÷ 6) = 16 i.

Remind students that we can break apart, or decompose, a dividend and represent it using more than one expression so it is easier to solve. Explain that each part of the decomposed divisor should be divided by the divisor; this is called the distributive property. We can then add the quotient from each expression together, giving us the ﬁnal quotient. 10 6

Elaborate

Intervention

Acceleration

Students should remove the cards and label the dimensions of their drawings and the area of each piece, as shown below. Explain that this is called an area model. The inside of the rectangle is the area or the total. The number on the left is the divisor. It shows how many rows or groups there are. The numbers across the top combine to make the quotient or how many are in each row or group. a.

Explain

FACILITATION TIP Model for students how to transfer the area models into writing an equation with decomposed numbers.

DIVISION MODELS AND STRATEGIES

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6 36

Encourage students to continue to work collaboratively on the rest of the problems on their Student Journals. For each area model they build, they should trace it on their desks with the dry-erase markers and label the dimensions and area of each piece. Students should record what their group’s drawing looks like on their Student Journals. a.

Students should always start with the largest place value and think, “How many [largest place value] can I place in each row?” Students can trade in larger place values for smaller pieces, just like they did with the base ten blocks.

Student knowledge of basic multiplication and division facts can help them when dividing each place value.

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 For problem 2, could you put a 100 in each row? Explain. No, there were only 4 hundreds and 8 rows, so we had to break up the hundreds into tens. That left us with 44 tens.

DOK-2 How is this model similar to or different from the arrays you have built before? It is similar because we are still building a rectangle. It is different because the area model just shows the total of one piece, while an array shows each piece.

DOK-2 How did you ﬁgure out how many tens went into each row? We knew putting 6 tens in each row wouldn’t work because 6 × 8 = 48. So we put 5 tens in each row and had 4 left over because 8 × 5 = 40 and 44 – 40 = 4.

DOK-1 What did you do next? We had to trade in the 4 tens for 40 ones, combine them with the 8 ones we already had, and divide those between each group. We ended up with 48 ones. This allowed us to place 6 ones in each group because 6 × 8 = 48.

STEMscopes Tip Content Support, found in the Home section of each scope, provides teachers who might need additional background knowledge with a complete explanation of student expectations, mathematical vocabulary, an explanation of the progression of the related standards learned, strategies for instruction, possible misconceptions and obstacles, and more.

e. DOK-1 How did you decompose 448? 400 + 48 f.

DOK-2 How did decomposing 448 make this problem easier to solve? Both 400 and 48 can be placed into equal groups of 8. It is easier than trying to ﬁgure out how many groups of 8 we can make from 448. It simpliﬁes the problem.

DOK-1 What property allows us to decompose a number into sections that are easier to divide? Distributive property

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Division Models and Strategies Explore 3 – Area Models i. DOK-1 What is another way we could write this equation? We could use expressions for each piece of the model. For this problem, it would be (400 ÷ 8) + (48 ÷ 8) = 56. j. DOK-2 Why not divide just one expression by 8? We decomposed 448 into 400 + 48. We need to divide 400 into 8 groups and 48 into 8 groups. It’s the same as dividing 448 into 8 groups.

STEMscopes Tip The Foundation Builder, located in the Engage section, is used to bridge students’ learning to the current concept by addressing foundational knowledge from previous grade levels. Foundation Builder activities use manipulatives to review prerequisite student knowledge. Possible student preconceptions about a topic, with suggested solutions on how to resolve the preconceptions, are also included.

Encourage students to solve problems using only drawn models once they feel comfortable. If they need to use the cards for support, they can.

Students may need to start by decomposing the dividends before drawing the area models. Students can always try to solve the problems using drawings and check their work with the Area Model Cards.

Have students work together as a group to draw area models to represent problems on their desks using the dry-erase markers. Students should follow the same process of drawing the left side of the area model and ﬁnding each piece, starting with the biggest place value. Students should record two equations for each model and a statement that explains the quotient on their Student Journals. a.

FACILITATION TIP Provide directions on the board and at the tables to guide students step by step through the process.

10.

Monitor students as they work. Allow them to use the cards for support as needed.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP Continue to reinforce to students that these physical models become very useful as conceptual tools later in math and in real life.

FACILITATION TIP When you preview this Exit Ticket with students, address the image of the road so that students don’t imagine that the curves affect the square footage.

DOK-2 Why do you think we are modeling division in this way? Division is the opposite of multiplication. You can use multiplication to find the total on the inside, using both sides. This means you can use the total and one side to divide and find the missing side. • DOK-2 Why would we start with the biggest place value first? That takes the most away from the dividend, and you can see if you need to break up a large piece into smaller pieces. • DOK-2 Does this model only work for problems that need things put into equal rows? No, each row could represent a group. You can use this model to divide any amount into equal groups. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DIVISION MODELS AND STRATEGIES

Home

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DIVISION MODELS AND STRATEGIES

Division Models and Strategies Explore 4 – Partial Quotients ACTIVITY PREPARATION Students use partial quotients to divide a number with up to four digits by a one-digit number.

Standards for Mathematical Practice • •

MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

1 Student Journal (per student) 1 Partial Quotients Work Mat (per group) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

Reusable • • • • •

• • • •

•

1 Box of colored pencils (per student) 1 Set of place value disks (per group) 1 Dry-erase marker (per group) 2 Sheet protectors (per group) 2 Resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Scenario Cards for each group. Cut them out; laminate them for durability, if desired; and place them in a resealable bag. Print one Partial Quotients Work Mat for each group. Place each page in a sheet protector, or laminate it so students can use dry-erase markers on it. Tape the 2 pages side by side, with page 1 on the left and page 2 on the right. Prepare a set of place value disks in a resealable bag for each group containing at least the following amounts: •

•

• 36 × 100s

4 × 1,000s

• 74 × 10s

• 46 × 1s

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

If needed, take time to carefully review divisor, dividend, and quotient. Post a visual guide on your word wall.

FACILITATION TIP After students have made an area model, demonstrate a step-by-step process of using the Partial Quotients Work Mat. Demonstrate the partial quotients model for division. FACILITATION TIP The Partial Quotients Work Mat is used to break each group using place value disks. Instruct students to be very neat with each place value while working the problem. The different colors will assist in this process. 168

Distribute the place value disks and Scenario Cards to each group. Give each student a Student Journal. Invite students to read scenario 1 and solve the problem using an area model. Have them use a different colored pencil for each part of the problem (dividend, divisor, and quotient). Their model should look similar to this:

7 3.

300 +

2,100

420

= 365

Guide students to work out the same problem using the place value disks and the Partial Quotients Work Mat. Page 1 of the Partial Quotients Work Mat goes on the left, and page 2 goes on the right. Use a dry-erase marker to ﬁll in the dividend for this problem. Have students build the dividend using place value disks.

Engage

Explore

Explain

Elaborate

Evaluate

On the grid on the left, students should cross out any rows (groups) with numbers greater than the divisor. a.

DOK-1 Which rows should we cross off? None. Since our divisor is 7, we will use all the rows.

DOK-1 Why do you think we are using seven rows? Each row is a group, and dividing is splitting something into equal groups.

Model for students how to write the dividend and divisor on the Partial Quotients Work Mat.

Intervention

Acceleration

STEMscopes Tip The Math Chat, embedded in each Explore lesson outline as well as in printable form, provides a forum where students collaboratively discuss their ideas and strategies and develop their number sense, mathematical vocabulary, and math thinking skills. Discussing the concepts taught helps students formulate stronger reasoning and critical thinking skills.

DIVISION MODELS AND STRATEGIES

Home

Placeholder AW

Students should then distribute the disks evenly to each of the seven groups, starting with the thousands place. a.

DOK-1 How do we distribute the 2 thousands disks? Since there are more than 2 groups, we will need to trade the 2 thousands disks for 20 hundreds disks. Now we have 25 hundreds disks in all.

DOK-1 How do we distribute the 25 hundreds disks? We should be able to distribute 3 hundreds disks to each group; then, we will have 4 left.

DOK-1 If we put 3 hundreds in each group, what is the ﬁrst part of our quotient? We know the ﬁrst part of our quotient is 300.

10.

Carefully choose the members of each group. Consider using small-group intervention with step-by-step modeling.

Refer students to their original area models, and ask the following question: a.

FACILITATION TIP

DOK-2 What is the relationship between what we did with the place value disks and your area model? The first step we did was the same first step with the area model. Using both strategies, we ended up with the first part of our quotient being 300.

Model for students how to record what they did using partial quotients. Students should write the partial quotient on the right-hand side of the Partial Quotients Work Mat (300). They should then subtract the amount that was distributed from the total. a.

DOK-2 What do we do with the rest of the hundreds disks? Since we have more than 4 groups, we will need to trade the 4 hundreds disks for 40 tens disks. Now we have 45 tens disks in all.

DOK-1 How do we distribute the 45 tens disks? We should be able to distribute 6 tens disks to each group; then, we will have 3 left.

DOK-2 What would happen if we tried to distribute 7 tens disks to each group? We wouldn’t have enough tens disks that could evenly be divided into 7 groups.

DOK-2 What would happen if we tried to distribute 5 tens disks to each group? We would have too many tens disks left. We would have enough tens disks to evenly distribute into 7 groups one more time.

Again, students should write the partial quotient on the right-hand side of the work mat (60). Students should then subtract the amount that was distributed from the total. Have students relate this step to their area models. a.

DOK-1 What do we do with the rest of the tens disks? Since we have more than 3 groups, we will need to trade the 3 tens disks for 30 ones disks. Now we have 35 ones disks in all.

DOK-1 How do we distribute the 35 ones disks? We should be able to distribute 5 ones disks to each group. We will have none left.

FACILITATION TIP Monitor groups as they work. A T-chart with multiplication facts could be used as a reference for students.

FACILITATION TIP Post a step-by-step process with an example at the tables and on the board for students to refer to.

169

DIVISION MODELS AND STRATEGIES

Division Models and Strategies Explore 4 – Partial Quotients 11.

Again, students should write the partial quotient on the right side of the Partial Quotients Work Mat (5). Students should then subtract the amount that was distributed from the total. The ﬁnal partial quotients work space should look like this:

Placeholder AW

12.

Finally, students should add up the partial quotients to get the ﬁnal quotient.

Placeholder AW FACILITATION TIP Have students multiply the quotients and dividends to check their work. Allow them to revisit any problems they answered incorrectly. If time is short, consider allowing students to skip transferring the work on to the Student Journal.

13. 14.

15.

FACILITATION TIP

Make sure students then transfer their work to their Student Journals. Students should use the same colors they used for the area models so they can see the correlation between the area model and partial quotients strategies. Encourage students to collaborate to solve the rest of the scenarios. If needed, they can create an area model ﬁrst to support their understanding of partial quotients. As students collaborate, monitor their work and use the following guiding questions to assess student understanding:

Discuss the importance of knowing multiplication facts when approaching division problems.

STEMscopes Tip The Anchor Charts element, located in the Explain section, guides teachers and students in creating a summary to showcase strategies, skills, and concepts learned during each Explore. An included printable sample anchor chart can be referenced for ideas on how to highlight key learning.

170

16.

DOK-2 How is the partial quotients strategy similar to the area models strategy? They are similar because you are dividing chunks of the total and adding up parts of the answer.

DOK-2 How do you know how many of a certain place value could go into each group? I used the math facts that I know. For example, I know that 7 × 3 is 21, which is less than 25, and 7 × 4 is 28, which is more than 25. Since I only had 25 hundreds to pass out, I knew I could pass out 3 to each group and would have some left over.

DOK-2 In both strategies, why did you decompose the total into 2,100, 420, and 35? I broke 2,555 into parts that could be easily divided into groups of 7. 2,100, 420, and 35 can all easily be divided by 7.

DOK-1 What property allows us to decompose a number into sections that are easier to divide? Distributive property

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-1 What 3 steps do you repeat at each place value when you are using the partial quotients strategy? (1) Figure out how many of each place value can go in each group to get the partial quotient. (2) Multiply the divisor by the partial quotient to ﬁnd how much of the total we passed out. (3) Subtract that amount from the dividend that’s left after the previous step. • DOK-2 Why do you subtract in the middle of a division problem? We divided up one place value at a time. Once we are able to divide part of the number, we need to subtract it from the total in order to ﬁgure out how much is left to divide into each group. •

•

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-3 If you multiply the partial quotient by the divisor and end up with a product that is greater than the dividend that is left, why can’t you subtract it from the remaining dividend? While we can add numbers in any order and get the same sum, we can’t subtract numbers in any order and get the same difference. If we multiply a partial quotient by the divisor and get a greater product than the remaining dividend, it means we should have used a smaller partial quotient. If the partial quotient is less than the dividend that’s left, we can subtract it from the remaining dividend. DOK-2 Could you use this process to divide an even bigger dividend? Yes, you could use the same process.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP

DIVISION MODELS AND STRATEGIES

Home

Before having students complete this Exit Ticket, establish your criteria for success. Some students may want to use a division algorithm different than the models used in this class.

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DIVISION MODELS AND STRATEGIES

Division Models and Strategies Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Share Equally Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Arrays Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Area Models

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Partial Quotients

Independent practice assignment that gives students an opportunity to demonstrate their learning

172

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

The Scenic Route

Marty Aronoff

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Our Night at the Museum

Division Algorithms

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

The Grand Opening

Division Problem Solving

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

PhET Interactive Simulation

Interactive Practice

Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

Asteroid Defense

DIVISION MODELS AND STRATEGIES

Home

A game to practice the skills established by the standards in the scope

173

Students who are still acquiring the concept and need remediation

DIVISION MODELS AND STRATEGIES

Division Models and Strategies

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

174

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can use my understanding of place value, properties of operations, and the relationship between multiplication and division to divide a four-digit number by a one-digit number.

What prompts will be used?

What does mastery look like?

DIVISION MODELS AND STRATEGIES

Home

I can ﬁnd quotients that result in whole numbers and remainders.

I can illustrate and explain division calculations using a variety of strategies (equations, rectangular arrays, and/or area models).

175

SCOPE 1

Generate Patterns Scope Introduction SCOPE SUMMARY

Student Expectations

4.PAR.3.1 Generate both number and shape patterns that follow a provided rule.

In fourth grade, students generate and analyze a number or shape pattern that follows a given rule. Students are also representing problems by using an input-output table and numerical equations to generate a number pattern that follows a given rule. They identify features within the resulting sequence and explain why the pattern repeats. Students reason about how patterns and rules are related: A pattern is the repeating sequence, and the rule dictates the process for how the sequence is repeated. Students make generalizations about the features and relationships between numbers or shapes of a pattern. The process of identifying and generating patterns results in being able to justify a resulting sequence by relating the pattern to its corresponding rule.

4.PAR.3.2 Use input-output rules, tables, and charts to represent and describe patterns, ﬁnd relationships, and solve problems.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Students are introduced to patterns in kindergarten, when they begin to create, extend, and describe repeating patterns with numbers, shapes, and the passing of time. Students build on that knowledge in ﬁrst grade, when they investigate, create, and make predictions about repeating patterns with up to 3 elements resulting from repeating an operation, as a series of shapes, or a number string. In second grade, students identify, describe, and create growing and shrinking patterns resulting from a repeated operation, such as addition and subtraction, up to 20. In third grade, students identify patterns involving multiplication and explain them using a hundreds chart, a multiplication chart, and properties of operations.

In ﬁfth grade, students generate two numerical patterns using two given rules, and they identify relationships between the corresponding terms. Fifth-grade students form ordered pairs of the corresponding terms and graph them on a coordinate plane. Fifth graders examine these relationships within sequences of ordered pairs graphed on a coordinate plane. The resulting graphs are analyzed to determine the relationship between the two patterns.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

understand numerical patterns.

•

identify a sequence based on a description of the pattern.

•

ﬁnd missing numbers with a sequence.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

use information provided to determine the pattern to solve a problem.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 176

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Shape Patterns In this exploration, groups of students will solve a scenario about different video games. In solving the scenario, students will: •

identify, analyze, and generate shape patterns.

•

use manipulatives to discover the rule or the pattern for each video game.

•

make predictions.

Explore 2

Explore 1

EXPLORE ACTIVITIES

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Number Patterns In this exploration, students will work in groups to solve a scenario where they are tasked with determining the total cost of various party supplies needed. Through solving the scenario, students will: •

explore patterns using manipulatives to generate numerical expressions.

•

use pattern blocks or color tiles to help determine amounts.

•

write expressions.

GENERATE PATTERNS

Home

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Input-Output Tables In this exploration, students will represent problems using input-output tables and numerical equations to generate number patterns. Students will: •

determine the rule by developing an equation using letters to stand for the variables.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

177

GENERATE PATTERNS

Generate Patterns Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

178

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students identify arithmetic patterns and make observations about those patterns. This activity is intended to assess mastery of the following standard(s):

GENERATE PATTERNS

Home

3.PAR.3.1 Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.

Materials

Preparation

Printed • •

•

1 Slideshow (per class) 1 Set of AB Answer Cards (per class or per student)

•

Reusable •

Prepare to project the Slideshow, or print a Slideshow for each group. Print one A card and one B card to hang on opposite sides of the classroom, or print one set of AB Answer Cards double-sided per student

1 Projector or document camera (per class)

PROCEDURE AND FACILITATION POINTS 1. 2.

4. 5.

Project the Slideshow to the class, and allow students time to read the ﬁrst question and think about their answers. Instruct students to go to the side of the classroom and stand near the answer they agree with. This can also be done from their seats by asking students to hold up either the A side or the B side of their cards. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Repeat steps 2–4 for questions 2–6. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Students may need clariﬁcation about what the term sequence means. Explain that a sequence, just like a series of counting numbers, does not end but that we can write or examine part of a sequence to investigate numerical patterns. FACILITATION TIP Challenge students to observe patterns within each sequence. For example, ask, “Are the numbers within the sequence all even or all odd, or do they alternate between even and odd? Do the numbers increase or decrease within the sequence?”

179

GENERATE PATTERNS

Generate Patterns Hook – Grow the Gold ACTIVITY PREPARATION Students generate a number pattern that follows a given rule and identify the features of a pattern that were not explicit in the rule itself.

Materials

Preparation

Printed

Part I

•

1 Student Handout (per group)

•

Reusable • • •

Plan to show the Phenomena Video.

Part II

1 Phenomena Video (per class) 1 Projector (per class) 45 Counters (per group, optional)

• • •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Handout for each group. Give each group at least 45 counters. This is optional; groups can use the counters as gold to help them see the pattern.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP Project the Student Handout on the board. Guide students to identify the patterns.

STEMscopes Tip Spiraled Review, located in the Elaborate section, provides students with a contextual scenario used to solve four different problems. This activity helps students maintain essential knowledge, see how mathematical skills connect from one topic to the next, and experience real-world applications of previously learned skills.

DOK-1 What do we need to ﬁnd out? We need to ﬁnd out what pattern is making the gold grow and by how much each day.

DOK-2 How do you think we could ﬁnd the pattern? I think we should look at how the stacks of coins are growing each day and remember that we started with 3 coins.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

180

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You want to make your gold grow by using a pattern to make it grow in value daily. The ﬁrst stack has 3 coins in it. Each of the stacks shows what the total stack would look like after each day. You will need to identify the pattern that is helping your gold grow and by how much it is growing each day. Discuss the following questions:

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do we need to ﬁnd out? We need to ﬁnd out what pattern is making the gold grow and by how much each day.

DOK-2 How do you think we could ﬁnd the pattern? I think we should look at how the stacks of coins are growing each day and remember that we started with 3 coins. © Accelerate Learning Inc. - All Rights Reserved

4. 5.

Explore

Explain

Elaborate

Evaluate

Give each group a Student Handout. Instruct students to look at the table to see whether they can identify the pattern. You can also choose to give each group 45 counters to show the total gold after each day. Review the problem, and then allow students to solve it. Have each group ﬁll in the blanks on the table after they have identiﬁed the pattern. Gather students in a whole group, and discuss the following questions: a.

DOK-2 What did you notice when you looked at the table? I noticed that the operation in the middle was multiplying the day by 4 and then adding 3. I knew that we started with 3 gold coins on day 0, so, I determined that is why there is a +3. Then, we realized that there must be 4 coins added each day, and that is where the ×4 came from in the pattern.

DOK-2 If you used the counters to help you solve, how did you use them? We ﬁrst put 3 counters in a stack to represent the 3 coins we began with. We could see in day 2 there were 11 coins in total. We subtracted 11 minus 3 and got 8. Then, we thought 4 coins were being added each day since 8 ÷ 2 = 4.

Engage

Intervention

Acceleration

FACILITATION TIP Provide highlighters of various colors. Have students highlight the 4 with one color, the multiplication symbol with another color, and the plus sign with a third color.

GENERATE PATTERNS

Home

FACILITATION TIP You may need to guide students with the ﬁrst few pattern sequences until they can take over the process.

DOK-3 What are some features of the pattern that you notice that don’t have to do with the rule or operation? I noticed that the total number of coins was always an odd number. I think that is because we started with 3 coins, which is an odd number. Since we were adding 4 coins each day, which is an even number, then the total would always be odd.

Review the table, and have students discuss the reasonableness of each answer. Notes

181

GENERATE PATTERNS

Generate Patterns Explore 1 – Shape Patterns ACTIVITY PREPARATION Students identify, analyze, and generate shape patterns.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• • • • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Exit ticket (per student)

Reusable •

6 Sets of colored tiles (per class)

•

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Station Cards. (Optionally, print on colored card stock.) Place Station Cards around the room gallery-walk style to create each station. Place a set of colored tiles at each station. For students who need more support in recalling information, please see our Number Charts and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Color Tiles)

PROCEDURE AND FACILITATION POINTS Part I: Playing the Games FACILITATION TIP

A pattern also generates or grows from one stage to the next. 2.

FACILITATION TIP Before switching stations, make sure the students return the tiles to their main pile or bag so that the next group can go through the process of modeling the pattern with the tiles. FACILITATION TIP Ask students to observe whether the number of items increases or decreases between stages. Patterns that increase involve addition or multiplication, and patterns that decrease involve subtraction or division. 182

4. 5.

DOK-2 Begin by asking students to turn and talk to discuss what a pattern is and where we see patterns. Invite a student to share their answer. A pattern is something that repeats over and over. It can be with numbers, shapes, colors, etc. Read the following scenario to the class: Gerard is off to the Pattern Arcade to play some games. In order to win each game, Gerard will have to figure out the pattern and what will happen in the next stage. Will you help Gerard find the patterns and help him win the games? Give a Student Journal to each student, and explain that the Station Cards will give them the information they need to complete each task. They will write the number in each stage in the table provided on their Student Journals and then answer the questions. Show students the manipulatives at each station to help discover the rule for that game. Assign each group to a station. Have the groups rotate through each station. Give them a sufficient amount of time at each Station Card. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How can you use the manipulatives to ﬁnd the rule and discover the pattern? I can use the tiles to visually lay out each stage. I can ﬁnd the rule by looking to see how to get to the next stage using each operation to solve.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

After Part I, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

• •

DOK-2 What can you say about the pattern in each game going from stage to stage? The pattern reflects the rule and the starting number. For example, if the rule is × 3, each stage will be a multiple of 3. If the rule is adding 2, each stage will be counting by 2s. DOK-2 What strategy did you use to determine the pattern and rule at each game? I used the manipulatives to show each stage. I found ways to get from the first stage to the second and then determined if that same way applied to get to the third stage. If it did, this became the rule. DOK-1 Did each game use the same operation for the rule? Explain. No, each game had a different operation. DOK-2 What strategy did you use to find another rule for Cloudy with a Chance of WINNING!? Since each stage increased the previous stage by 3 and I knew that I would need two operations, I decided to add 6 and then subtract 3 so the rule would still increase by 3.

Part II: New Game 1. 2.

FACILITATION TIP Take some time to gather some additional real-world examples of uses of repeating addition and subtraction patterns. Some students might connect with a visual representation of the times tables, while others might enjoy being read a favorite picture book story that includes a growing or shrinking number pattern.

GENERATE PATTERNS

Home

FACILITATION TIP Encourage students to start with just looking to see if the pattern ﬁrst goes up/grows or goes down/shrinks. Many students can get overwhelmed by examining the whole pattern.

Divide the class back into the same groups. Students will work with their groups to create their own arcade game using one set of the square tiles. They will need to choose a name and a rule, create each stage, and then answer the questions about their new game in their Student Journals.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

183

GENERATE PATTERNS

Generate Patterns Explore 2 – Number Patterns ACTIVITY PREPARATION Students explore patterns using manipulatives to generate numerical expressions.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

Reusable •

7 Sets of pattern block or colored tiles (per class)

Preparation • • • • • •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Station Cards (use card stock and laminate them for durability, if desired), and cut them apart. Place the cards at different locations around the room. Place a set of pattern blocks or colored tiles at each station. For students who need more support in recalling information, please see our Number Charts and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Pattern Blocks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP You can post different types of patterns on the board to provide context for the questions.

3. FACILITATION TIP For each Station Card, have students take turns reading the card to the group. The other group members should listen and follow directions. The group members should work together to write the expression to ﬁnd the pattern.

DOK-1 What is a pattern? A pattern is something that repeats over and over.

DOK-2 Where do you see patterns? Answers will vary. I see patterns in colors, shapes, objects, numbers, etc.

Read the following scenario to the class: Your cousins, Amari and Fynn, share the same birthday. Your family would like to throw a celebration extravaganza for both of them! You need to help your family plan the party! Give a Student Journal to each student, and show students the chosen manipulatives. Explain that they will use manipulatives to model the relationships described at each station. Then, they will use their models to identify the rule and continue the pattern. Discuss the following questions: a.

5. 184

Discuss what students already know about patterns:

DOK-2 How do you think you can ﬁnd out what is happening with the numbers in the right column? We can use manipulatives to model each situation. Then, we can look at the manipulatives and see the relationship between the numbers. We can see if the numbers are multiples of each other, or we can see if there is the same amount between numbers. We can see if that same relationship happens with the other number pairs, too. If it does, then we can ﬁgure out the number pattern and write an expression.

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you know what information to put in the columns? We looked at the column headings to make sure we were putting the numbers in the correct columns. We couldn’t write the expression until we could see the relationship between the numbers.

DOK-1 What did you notice about the number pattern in this scenario? We noticed the numbers in the right column were multiples of the numbers in the left column; we noticed the numbers in the right column were always a little more than the numbers in the left column.

DOK-1 How were you able to ﬁgure out the situations that weren’t on the table? Since we knew the pattern and were given one number, we could use the expression to ﬁnd out the other number.

After students ﬁnish all the stations, have them complete the reﬂection questions on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-3 What strategies did you use to figure out the patterns in these scenarios? I acted out the problem. I looked at the relationship between the numbers to see the pattern. DOK-3 When might finding a number pattern be useful? Number patterns are useful if we know how much a few of something is and we are trying to find out a bigger amount of the same thing. If we know the number pattern, we can predict how much something will be. DOK-2 What could you do if you were given the number in the right column and needed to find out the number in the left column? We could do the opposite operation. If there was a multiplication relationship, we could divide. If there was an addition relationship, we could subtract.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Intervention

Acceleration

STEMscopes Tip Supplemental Aids, located in the Intervention section, provide materials that will meet the needs of diverse learners. These materials include graphic organizers, handouts, and manipulatives that can further support students.

GENERATE PATTERNS

Home

FACILITATION TIP In the Math Chat, have students look at the Student Journal to compare the different patterns.

FACILITATION TIP These exercises and discussions about patterns are an important conceptual basis for graphing linear equations. Encourage students by reassuring them that their older siblings are also doing patterns when they do their algebra homework.

185

GENERATE PATTERNS

Generate Patterns Explore 3 – Input-Output Tables ACTIVITY PREPARATION Students represent problems using input-output tables and numerical equations to generate number patterns that follow a given rule representing the relationship of the values in the resulting sequence and their position in the sequence.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Circuit Cards (per class) 1 Set of Toy Strips (per class) 1 Exit Ticket (per student)

Consumable •

1 Piece of chart paper (per class)

Preparation Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Circuit Cards, and hang them in various locations around the room. Print the Toy Strips, and cut them apart. Make sure you have a Toy Strip for each group. Draw an input-output table on the chart paper. For students who need more support in recalling information, please see our Number Charts and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Color Tiles and Pattern Blocks)

• • • • • •

•

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

2. 3.

Take time to complete the ﬁrst Circuit Card together as a class. Using letters as variables and creating a rule may be new for many students. Provide structured instruction before they collaborate at the stations.

FACILITATION TIP To simplify station rotation, consider having students rotate in an established pattern rather than using the riddles and toys. 186

Read the following scenario to the class: Uncle Santiago needs your help! He loves to make toys to give to children. While there is a relationship between the number of toys or materials and the amount or type of materials he needs to build the toys, he isn’t always sure what that relationship is. Give each student a Student Journal. Read the introduction on the Student Journal. Show students where the Circuit Cards are located. Give one Toy Strip to each group. Have each group start at a different Circuit Card. Students should ﬁnd the table that represents the toy they are working with and determine the rule by developing an equation using letters to stand for the variables. Students will then use the rule (equation) to ﬁnd the missing information on the table. Once the information is complete, students will read the riddle at the bottom of the Circuit Card, solve the riddle, and move to that toy’s Circuit Card. a.

Have students cross out the toy they got on the Toy Strips after completing the information for each Circuit Card. They will have crossed out all the toys once they have completed the information at all the circuits. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

DOK-2 Do you see a pattern? Where? Answers may vary. Yes, there is a relationship between the number of planes and the number of wings. Each plane has two wings. That means the number of wings is always double the number of planes.

DOK-1 What is the rule? Answers may vary. Multiply the number of planes by two.

DOK-2 How are number patterns between the car and the dog different? There are always three people in each car. That means there is one group of three people for each car. As the number of cars increases, the number of people groups increases, so I multiply the number of cars by three. For the dog, the number of body parts always increases by two round wood scraps, not two groups of round wood scraps. So I add two round wood scraps to each dog.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

• •

Intervention

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

Engage

DOK-2 How did you figure out the type or amount of materials Uncle Santiago needs based on the number of toys he makes or the materials he has? I looked for the relationship between the two numbers. Then, I looked to see if that relationship was always the same with all the sets of numbers. If it was, I knew the pattern. Once I saw the pattern, I could figure out the rule that I needed to use to make that pattern. If I knew the rule, I could always figure out the correct relationship between the number of toys or materials and the amount or type of materials he needed. DOK-3 How are input-output tables useful? They can help you see the relationships between numbers more easily. DOK-3 When would knowing the rule that shows the relationship between numbers be helpful? If there is a problem that follows a pattern, I can figure out the solution by using the rule. DOK-2 What operation do you use if you know the input but don’t know the output? I use whatever number operation the rule says. DOK-2 What operation do you use if you know the output but don’t know the input? I use the opposite operation that is the inverse of the rule. If the rule says to multiply, I divide. If the rule says to add, I subtract.

FACILITATION TIP Post these guiding questions as students collaborate. Encourage students to focus their conversations around these questions to be prepared for the Math Chat.

GENERATE PATTERNS

Home

STEMscopes Tip The Kindergarten through Grade 5 Vertical Alignment Chart is located in the Essentials section of the Teacher Toolbox. This printable document explains how standards are organized, provides a table identifying the K–5 grade level focus, and displays vertical alignments of each of the six domains.

FACILITATION TIP Help students see the real-world connections for these input-output tables and rules. Reassure students that they are the foundation of computer game design, algebraic equations, and programming jobs.

Post-Explore 1. 2. 3. 4.

187

GENERATE PATTERNS

Generate Patterns Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Shape Patterns Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Number Patterns Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Input-Output Tables Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

188

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Good Times at the End of the School Year

Alan Turing

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Coming Up: Arbor Day!

Problem Solving with Patterns

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

GENERATE PATTERNS

Home

Problem-Based Task The Board Game Challenge Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

PhET Interactive Simulation Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

189

GENERATE PATTERNS

Generate Patterns Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

190

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

What prompts will be used?

GENERATE PATTERNS

Home

What does mastery look like?

I can connect each term in a growing or shrinking number pattern with its term number.

I can explore and extend growing patterns using shapes.

I can explore and extend number patterns using a given rule.

I can justify the progression of a pattern using the pattern rule.

I can represent a number pattern in an input-output table to ﬁnd relationships and solve problems.

191

SCOPE 1

Problem Solve Using the Four Operations Scope Introduction SCOPE SUMMARY Students use various strategies to estimate and solve multistep problems using the four operations. They determine which operations are needed in solving a problem and represent the problem by using drawings or diagrams or by writing equations. A letter is used within an equation to represent an unknown quantity. Students interpret remainders within a given context when solving problems. They use mental computation and estimation strategies to determine the reasonableness of an answer. Student Expectations

4.NR.2.5 Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Kindergarten students develop a conceptual foundation of addition and subtraction as a means of joining and separating numbers. In ﬁrst grade, students use objects, drawings, and equations to represent problems involving addition and subtraction of whole numbers within 20. In second grade, students use addition and subtraction within 100 to solve one- and two-step word problems. Third-grade students represent two-step problems involving all four operations by writing equations with a letter standing for the unknown quantity. They assess the reasonableness of answers by using mental computation and estimation strategies, and they use properties of operations to identify and explain arithmetic patterns.

In ﬁfth grade, students use parentheses, brackets, or braces to write and evaluate multistep numerical expressions. Fifth-grade students generate two numerical patterns using two given rules, graph the pairs of corresponding terms on a coordinate plane, and identify relationships between them.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

solve one- and two-step real-world problems involving any of four operations with whole numbers.

•

analyze multiple-choice questions.

•

explain which answer is correct.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope. If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK.

192

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

represent and solve a multistep problem involving one or more of the four operations with whole numbers and equations, with a letter standing for the unknown quantity.

•

assess the reasonableness of the answer using mental strategies.

•

determine various ways to solve the problem.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Interpret Remainders In this exploration, students will learn how to solve division problems and interpret the meaning of remainders. With participation in this exploration, students will: •

solve division problems.

•

interpret the meaning of remainders.

•

solve Problem Cards and scenarios about remainders.

Explore 2

Explore 1

EXPLORE ACTIVITIES

Problem Solve Using the Four Operations (Level 2) In this exploration, students will solve a real-world problem about the amount of dough, glaze and sprinkles for their own doughnut shop. In solving scenarios, students will:

In this exploration, groups of students will help plan for a concert by solving the scenario cards about seating, concessions, and ticket sales. Through completing this exploration, students will: •

represent multistep problems involving the four operations with whole numbers..

•

use strip diagrams.

•

write equations with a letter standing for the unknown quantity.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 4

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Problem Solve Using the Four Operations (Level 1)

Problem Solve Using the Four Operations (Level 3) In the ﬁnal exploration, students will complete Scenario Cards with group members by using place value disks and exploration resources. In solving the scenarios, students will:

•

represent multistep problems involving the four operations with whole numbers.

•

represent multistep problems involving the four operations with whole numbers.

•

use strip diagrams.

•

use and draw strip diagrams.

•

write equations with a letter standing for the unknown quantity.

•

build and write equations with a letter standing for the unknown quantity.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

PROBLEM SOLVE USING THE FOUR OPERATIONS

Home

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

193

PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

194

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students solve a series of two-step problems and choose the correct answers. This activity is intended to assess mastery of the following standard(s): 3.PAR.2.2 Apply part-whole strategies, properties of operations and place value understanding, to solve problems involving addition and subtraction within 10,000. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions. 3.PAR.3.6 Solve practical, relevant problems involving multiplication and division within 100 using part-whole strategies, visual representations, and/or concrete models.

Materials

Preparation

Printed • •

•

1 Slideshow (per class or per group) 1 Set of ABCD Answer Cards (per class)

•

Prepare to project the Slideshow one slide at a time for students, or print a Slideshow for each group. Print a set of ABCD Answer Cards to hang on different walls around the classroom.

Reusable •

PROBLEM SOLVE USING THE FOUR OPERATIONS

Home

1 Projector or document camera (per class)

Consumable •

1 Sheet of scratch paper (per student)

PROCEDURE AND FACILITATION POINTS 1. 2. 3.

4. 5.

Project the ﬁrst problem onto the screen for the class to read, or distribute the Slideshow to each group. Allow students time to read the problem and try to work it out on scratch paper. Instruct students to stand near the answer card with which they agree. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Students can volunteer to show how they solved the problem and discuss the different ways to solve. Repeat steps 2–4 with the second problem. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Alternatively, provide each group with a set of Answer Cards, and have them hold up the card that shows their answer choice. FACILITATION TIP Keep an ongoing list of division strategies students use (such as forming equal groups, using related multiplication facts, or writing an equation). Post this list for students to refer to and add to throughout this scope.

195

PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Hook – Star Good Behavior ACTIVITY PREPARATION Students represent and solve a multistep problem involving one or more of the four operations with whole numbers and equations, with a letter standing for the unknown quantity. Students assess the reasonableness of the answer using mental strategies by determining various ways to solve the problem.

Materials

Preparation

Printed

Part I

•

1 Student Handout (per group)

•

Reusable • • • •

Plan to show the Phenomena Video.

Part II

1 Phenomena Video (per class) 1 Projector (per class) 1 Marker (per group) 1 String (per group)

• •

Plan to have students work in groups to complete this activity. Use a permanent marker to label 3 of the craft sticks. Each group should have sticks labeled as follows:

Consumable •

•

6 Craft sticks (3 labeled “PE Teacher,” “Art Teacher,” and “Music Teacher;” and 3 blank per group) 1 Sticky note (per group)

• • •

•

PE teacher

•

Art teacher

•

Music teacher

Cut the string as long as 3 craft sticks laid end to end. Fold the sticky note around the string to stick to itself. The students will use their markers to label the total amount (90) here. Print a Student Handout for each group.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP

Write down on chart paper students’ ideas about how to solve the problem. Revisit the chart paper after the Explore activities.

FACILITATION TIP Project the scenario and read it along with students. Guide them to read through it more than once and note the necessary math values and phrases.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: The art, music, and PE teachers gave out 90 good behavior stickers last week. The PE teacher gave out 40. The art and music teachers each gave out an equal number. How many good behavior stickers did each of the teachers give out? Discuss the following questions: a. DOK-1 What information do we know? There were 90 good behavior stickers given out. The PE teacher gave out 40 of them. The art and music teachers each gave out the same number of the remaining stickers.

DOK-2 What operations could be used to solve this problem? Addition, subtraction, multiplication, and division could be used. It depends on how you want to solve it

DOK-2 Could there be more than one way to solve this problem? Yes, I think there could be lots of ways to solve it.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 196

3. 4. 5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a.

DOK-1 What information do we know? There were 90 good behavior stickers given out. The PE teacher gave out 40 of them. The art and music teachers gave out the same number of the remaining stickers.

DOK-2 What operations could be used to solve this problem? Addition, subtraction, multiplication, and division could be used. It depends on how you want to solve it.

DOK-2 So, could there be more than one way to solve this problem? Yes, I think there could be lots of ways to solve it.

Give each group a Student Handout, one string with a sticky note on it, a marker, 3 labeled craft sticks, and 3 blank craft sticks. Have the students use the craft sticks, string, sticky note, and marker to make a model to represent the problem. Have students write the quantities (including a letter representation of the unknown) on the blank craft sticks. Have students write the total on the sticky note on the string and stretch the string across the top of the craft sticks. Each model should look something like the image below when students are done. Students may use any letter for the variable. Adjust the amount of prompting you give to groups as needed to get the model made.

FACILITATION TIP Groups are creating strip diagrams similar to the Explore activities.

PROBLEM SOLVE USING THE FOUR OPERATIONS

Home

Placeholder AW

Instruct students to ﬁll out the Student Handout together in their groups. a.

Have students draw the model they made at the top of the page.

Instruct students to write down as many equations as they can think of to represent this problem. Suggest that their groups come up with at least three different equations with the variable present in each.Have each student choose one of the equations that their group came up with to solve the problem.

c. 8. 9.

Have students ﬁll in the blanks at the bottom once all students have solved the problem and agree on the answer.

When the groups are done, let each group in turn write one equation on the board. Cycle through all the groups to ﬁnd as many equations as possible. Gather students in a whole group, and discuss the following questions: a.

DOK-2 How many good behavior stickers did each teacher give out? We knew the PE teacher gave out 40. So that meant there were 50 left and they were equally shared between the art and music teachers. I divided 50 by 2, so I knew that each teacher gave out 25 stickers.

DOK-2 Can someone tell us another way to solve the problem? I thought about what number would be added to 40 to give me 90. I knew that it had to be 50. Then, I thought about what two numbers could be added together and were the same to give me 50. I thought of money and knew two quarters make 50 cents. So it had to be 25 stickers each.

DOK-3 Why do different equations work to get the same answers? Sometimes problems have more than one step. There are times when you can do one step ﬁrst before doing the other step. Sometimes equations are showing the same steps, just in a different way.

DOK-3 Why did you choose the equation you used to solve? It made the most sense to me and seemed the most reasonable. I knew the steps to take to solve it the way I chose.

FACILITATION TIP Have groups share with another group their 3 equations and discuss how they developed the different equations.

FACILITATION TIP Provide base ten blocks for students to work with to solve the problem.

197

PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Explore 1 – Interpret Remainders ACTIVITY PREPARATION Students solve division problems and interpret the meaning of remainders.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics.

Materials

Preparation

Printed • • • •

1 Student Journal (per student) 1 Set of Problem Cards (per pair) 1 Set of Ignore It or Round It? Cards (per pair) 1 Exit Ticket (per student)

• • •

•

Reusable •

2 Resealable bags (per pair)

•

Consumable •

100 Pieces of candy (per class)

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of the Problem Cards for Part I and the Ignore It or Round It? Cards for Part II for each pair of students, and cut the cards apart. Place each set in a small resealable bag. For students who need more support in recalling information, please see our Base Tens, Sharing Mats, and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS Part I 1. 2.

Give a Student Journal to each student. Ask students to read the example problem and solve as much of it as they can. Discuss the following questions:

FACILITATION TIP

DOK-1 What operation did you use for this problem? I used division.

In the Student Journal, have students circle the numbers and the question in the problem. Then, ask, “What operation is needed to solve the problem?”

DOK-1 How many trains will be on each shelf? He will be able to ﬁt 23 on each shelf.

DOK-1 Did all trains ﬁt on the shelf equally? No.

DOK-1 How many trains will not ﬁt on the shelves? There were two left over that did not ﬁt.

FACILITATION TIP Some students may need manipulatives to draw an array model.

3. 4. 5.

FACILITATION TIP Explain that whether to “Ignore It!” or “Round It!” depends on each situation. For example, in the Hook activity, all students need to have a seat at a lunch table, so we would need to round the remainder. 198

Explain to students that when you have leftovers after a division problem, those are called “remainders.” On the whiteboard, model for students how to write a quotient with a remainder (23 R2). Have them record this solution on their Student Journals. Have the student pairs work through the rest of the Problem Cards and answer the questions on their Student Journals.

Part II 1. 2.

Write “Ignore It!” and “Round It!” on the board. Explain to students that they will be voting on what to do with the remainders of a few problems. The categories will be “Ignore It!” and “Round It!” Explain what both of these mean by having students act out two different scenarios. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Take the 100 pieces of candy, and pass them out to the class, dividing them so each student has the same amount of candy (there should be some left over that cannot be passed out fairly). Remind students not to eat the candy we are using to solve the math problem. Discuss the following questions: i. DOK-1 What equation could I use to represent what we just did? You could use 100 pieces of candy divided by 22 students: 100 ÷ 22 = _____. ii. DOK-1 How many pieces of candy did everyone get? Everyone got four pieces. iii. DOK-1 I have 12 pieces of candy left. Would it be fair to pass out these pieces of candy? No, because then some students would have more than others. It wouldn’t be equal. iv

DOK-2 What should we do with the remainder? Can we round the number in each group up to ﬁve and say we all got 5 pieces of candy, or should we ignore the remainder? Ignore it!

Tell students the class is going on a field trip! Each car can take five students. Have students divide themselves into groups of five. (A different group size can be used, if needed. Make sure the total number of students is not a multiple of the number you choose.) Have students look around the room and figure out how many cars they need.

FACILITATION TIP Explain that each group can decide whether to “Ignore It!” or “Round It!” for each situation. This is an opportunity to discuss the importance of being fair and sharing equally.

PROBLEM SOLVE USING THE FOUR OPERATIONS

Home

i. DOK-1 What equation could we use to represent what we just did? There are 22 students divided by 5 in each car: 22 ÷ 5 = _____. ii. DOK-1 How many groups of five could we make with our class? We can make four groups of five. iii. DOK-1 Will four cars work? No! There would be two students left behind! iv. DOK-2 What do we need to do about the remainder? How many cars do we really need? We need to round up our answer to include the remainder! We need five cars to make sure everyone can go! 3. 4.

5. 6.

As a class, read the first problem together. Have students work with their partners to solve the problem and interpret the remainder. Once everybody is done, have students vote on what they think should be done with the remainder of the first problem, ignore it or round it. Confirm the solution, and discuss why the remainder should be rounded or ignored. Students should repeat the process for the remaining problems with their partners. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Students can use different strategies to help them solve the problem. Have visuals and manipulatives for students to use.

Math Chat FACILITATION TIP DOK-2 How do you know when to round the answer up? We should round up if the remainder is important to the problem and when there cannot be any leftovers. Take time to explain some real-world • DOK-2 How do you know when to ignore the remainder? We can ignore the stories or examples that include rounding remainder when the remainder cannot be equally divided and is not needed to up or ignoring remainders. answer the problem. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Before students complete this Exit Ticket, establish how you want them to show their thinking and methods for solving. 199

PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Explore 2 – Problem Solve Using the Four Operations – Level 1 ACTIVITY PREPARATION Students represent multistep problems involving the four operations with whole numbers, using diagrams and equations with a letter standing for the unknown quantity.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Concert Scenario Cards (per group) 1 Exit Ticket (per student)

•

Reusable • • •

•

1 Large resealable bag (per group) 1 Whiteboard (per student) 1 Dry-erase marker (per student)

•

Consumable •

20 Strips of white paper (per group)

Plan to have students work in groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Concert Scenario Cards on card stock for each group. Cut them apart, and laminate them for future use, if desired. Place them in a resealable bag. Cut sheets of white paper into fourths lengthwise so each group has 20 strips of white paper. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

You can list the steps to complete on the board as a checklist for students.

a. DOK-1 What parts are needed to build an equation? An equal sign, symbols (operations), and numbers

FACILITATION TIP Write and label the parts of an equation on the word wall where students can refer to it any time. Take time to differentiate between an equation and an expression. FACILITATION TIP You can model the ﬁrst scenario card as an example with students providing the instructions to the teacher. Address misconceptions while modeling.

Read the following scenario to the class: Some friends are headed to a concert to see their favorite band! Many details go into planning a large event such as a concert. Solve the Concert Scenario Cards to help sort out all of the details! Explain to students that this Explore activity is going to take everything they’ve been learning and put it all together. Each scenario will require them to build an equation. Discuss the following questions:

b. DOK-1 What do you use if there is a part of an equation that is unknown? A question mark or letter 4. 5.

Explain that they will use letters to represent an unknown quantity. Write a few equations on the whiteboard. Do a few quick examples as a class. Tell students they will be writing equations using letters on their dry-erase boards as practice. Students should write each equation on their boards and then share and discuss with their groups. (Remind them that they don’t need to solve the equations right now. Just build them.) a. DOK-1 The number 247 minus 43 equals some number. 247 – 43 = x b. DOK-1 The number 34 times some number equals 612. 34 × m = 612 c. DOK-1 Some number divided by 28 equals 4. y ÷ 28 = 4 d. DOK-1 The number 1,200 plus some number equals 1,399. 1,200 + n = 1,399

200

6. 7. 8.

9. 10. 11. 12.

13. 14.

Engage

Explore

Explain

Elaborate

Evaluate

Give a set of 20 strips of white paper and a set of Concert Scenario Cards to each group. Give a Student Journal to each student. Tell students they will need to represent every problem with a diagram, build an equation, estimate the solution, and then solve. Tell students they can use the paper strips to create diagrams with their groups. Ask students if they need a refresher on any of those tasks. Tell them all the work should be done collaboratively in groups and discussed before anything is recorded on individual Student Journals. Let students work in groups to solve the problems on each Concert Scenario Card. They can do the problems in any order. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

What is the question asking you for?

What information does the problem give you?

What information is missing?

How could you model what is happening in the problem?

Have students complete the reﬂection questions at the end of their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-2 What are the different ways you represented the problem? We created diagrams, and we built equations. • DOK-2 How does estimating your solution help you check your work? When I estimate, I can see if my estimated answer is close to my actual answer. If it is, I know my answer is reasonable and probably correct. If my estimated answer is not close to my actual answer, I know I need to check my work again to see if I might have made a mistake. • DOK-1 What does a letter represent in an equation? Letters in equations represent unknown quantities. •

Post-Explore

2. 3.

Acceleration

FACILITATION TIP Encourage students to use estimation before finding an exact solution. Some students are very hesitant to find inexact or rounded answers; they may find the exact answer first and THEN do the estimating. FACILITATION TIP These tape diagrams are helpful physical and conceptual models that students can use later with percents and fractions.

STEMscopes Tip

Math Chat

Intervention

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

The Planner is located along the menu bar. It provides a calendar planning tool for teachers that can be visible to students if desired. Monthly, weekly, or lists of plans can be downloaded, printed, saved, or shared. Access grade-level scopes and virtual-learning options with embedded links to scope elements from the Elements tab. Drag and drop elements into the calendar and add personal planning notes.

PROBLEM SOLVE USING THE FOUR OPERATIONS

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FACILITATION TIP Use speciﬁc math language when discussing variables. Students may have heard of variables and constants in different (science) contexts.

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PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Explore 3 – Problem Solve Using the Four Operations – Level 2 ACTIVITY PREPARATION Students represent multistep problems involving the four operations with whole numbers, using diagrams and equations with a letter standing for the unknown quantity.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Donut Scenario Cards (per teacher) 1 Exit Ticket (per student)

Reusable •

1 Pair of scissors (per group)

Consumable •

Preparation Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Donut Scenario Cards on card stock, and tape them on walls in different locations in the room. For larger classes, consider printing two sets of cards so there are not too many students at each one. Cut sheets of white paper into fourths lengthwise so each group has 20 strips of white paper. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

• • •

20 Strips of white paper (per group)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP If time and space are limited, consider providing a template of 20 (strip/tape) diagrams and allow students to draw the models rather than using loose papers. FACILITATION TIP

1. 2. 3.

Model for students how to make the tape/ strip diagram and solve for a problem with a different example of making doughnuts. 5. FACILITATION TIP Allow time for other groups to attempt to solve another group’s made-up problem. 202

Give a set of 20 strips of white paper to each group. Give a Student Journal to each student. Read the following scenario to the class: Congratulations! You are now the proud owner of a donut shop called the Dapper Donut. Before you can oﬃcially open, you will need to learn some of the basics of the business. Read each problem together with your group, and then solve. When you are done, you will attempt to learn more about the business by creating and solving your own word problem. Tell students that each of the Donut Scenario Cards will designate a station. Tell them they will need to represent every problem with a diagram, build an equation using a letter for an unknown quantity (maybe even two letters for two unknown quantities!), estimate the solution, and then solve. Tell students to use the paper strips to create a diagram and complete the steps listed above as a group before recording their work on their Student Journals. When each group is done with the problem they are working on, have them rotate to the next problem. When a group is done with all three problems, have them sit with their group to create their own multistep problem involving their donut shop. Tell them they will need to write out the problem as well as model it using diagrams and equations, estimate the solution, and then solve it. If time permits, allow each group to share their problem with the class. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

What is the question asking you for?

What information does the problem give you?

What information is missing?

How could you model what is happening in the problem?

FACILITATION TIP

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Check to see if the (strip/tape) diagrams are made correctly with each scenario card before groups proceed to answer the questions.

Math Chat DOK-2 What was challenging about this set of problems? Sometimes we had to solve for part of the problem before we could solve the whole problem. There were several steps. • DOK-1 How many diagrams did you have to draw for each problem? We had to draw two. • DOK-2 Why did you have to draw more than one diagram for each problem? We had to draw more than one because they were multistep problems. • DOK-2 How did you check your work for reasonableness? I used estimation and rounding to see if my actual answer was close to my estimated answer. If it was, then my actual answer was reasonable. •

Post-Explore 1. 2. 3.

FACILITATION TIP Reassure students that these tape/ strip diagrams are helpful physical and conceptual models that students can use later with percents and fractions. Taking time to become ﬂuent with them now will help them be more successful later in math and real life.

PROBLEM SOLVE USING THE FOUR OPERATIONS

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Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Explore 4 – Problem Solve Using the Four Operations – Level 3 ACTIVITY PREPARATION Students represent multistep problems involving the four operations with whole numbers, using diagrams and equations with a letter standing for the unknown quantity.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Scenario Cards (per pair) 1 Exit Ticket (per student)

Reusable • • •

1 Resealable bag (per pair) 1 Whiteboard (per student) 1 Dry-erase marker (per student)

Preparation • • • • • •

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Scenario Cards on card stock for each pair. Place each set of Scenario Cards in a resealable bag. Gather whiteboards and dry-erase markers for each student. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP

1. 2. 3.

Have group members take turns completing each part of the scenarios. While reading the Scenario Cards, have students circle the variables.

4. 5.

Give a resealable bag of Scenario Cards to each pair. Give a Student Journal, a whiteboard, and a dry-erase marker to each student. Tell students that for every problem, they will need to draw a diagram on their whiteboards, build an equation using a letter for an unknown quantity (maybe even two letters for two unknown quantities!), estimate the solution, and then solve. Remind students to take their time and do one step at a time. Let students work in pairs on the four problems. Instruct students to do the work on their dry-erase boards ﬁrst so they can share their ideas and discuss with their partners. Once both partners agree and understand each other’s solution, they should record their work on their Student Journals. a.

FACILITATION TIP

Provide manipulatives like the virtual models, base ten blocks, or manipulatives as a visual aid to solve each problem.

204

Note that students working together do not have to record the same diagram, equation, or process, but they do need to take the time to understand the similarities and differences between their process and their partners’.

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

What is the question asking you for?

What information does the problem give you?

FACILITATION TIP

What information is missing?

Post the questions on the board to guide students in addressing the problem.

How could you model what is happening in the problem?

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat DOK-2 Which problem was the hardest, and why? Answers may vary. DOK-2 What helped you develop an equation to solve? The diagram helped me see what I needed to do to the numbers to ﬁnd the value I was looking for. • DOK-2 Explain your estimation strategy for solving. Answers will vary, but students should explain how they rounded each number and whether it was a reasonable answer compared to their actual answer. • •

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Before having students complete this Exit Ticket, determine your requirements regarding their models and strategies shown.

Notes __________________________________________________________________________________________________________________________________________________

PROBLEM SOLVE USING THE FOUR OPERATIONS

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205

PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Interpret Remainders Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Problem Solve Using the Four Operations – Level I Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Problem Solve Using the Four Operations – Level 2

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Problem Solve Using the Four Operations – Level 3

Independent practice assignment that gives students an opportunity to demonstrate their learning

206

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

The Fishing Trip

Reporter

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Dragon’s Tongues and Mermaid’s Purses

Problem Solving with the Four Operations

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

PROBLEM SOLVE USING THE FOUR OPERATIONS

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Problem-Based Task Party Time! Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

PhET Interactive Simulation Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

207

Students who are still acquiring the concept and need remediation

PROBLEM SOLVE USING THE FOUR OPERATIONS

Problem Solve Using the Four Operations

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

208

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can use various strategies to solve multistep problems using the four operations.

I can determine which operations are needed in solving a problem.

What prompts will be used?

What does mastery look like?

PROBLEM SOLVE USING THE FOUR OPERATIONS

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I can interpret remainders when solving problems.

I can represent a problem using an equation with a letter that stands for the unknown quantity.

I can use mental computation and estimation strategies to determine the reasonableness of an answer.

I can determine when the use of estimation is appropriate.

209

SCOPE 1

Compare Fractions Scope Introduction SCOPE SUMMARY Students start by reasoning about the size of a whole and realizing that the size of the whole is important. They then compare two fractions with either the same numerator or the same denominator by drawing models and writing a comparison statement, and then they reason about their answer. Students extend this knowledge to comparing fractions with different numerators and denominators, using benchmark fractions, number lines, concrete models, and common numerators or denominators to determine comparisons. Student Expectations

4.NR.4.2 Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole. 4.NR.4.3 Compare two fractions with different numerators and/or different denominators by ﬂexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students partition circles and rectangles into two and four parts of equal size, and they name the parts of the whole by using the terms halves or fourths. In second grade, students explore fractions by using circular or rectangular area models partitioned into two, three, or four parts of equal size. Students describe the parts by using the words halves, thirds, and fourths. They recognize that a whole is composed of two-halves, threethirds, or four-fourths, and they recognize that equal-size parts of identical wholes may not have the same shape. In third grade, students build on their knowledge of fractions to represent fractions with denominators of 2, 3, 4, 6, and 8, including fractions greater than one, using strategies such as diagrams and number lines. Students extend this knowledge to comparing two unit fractions by ﬂexibly using a variety of tools and strategies.

Fifth-grade students plot, order, and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators. Instruction includes using an appropriately scaled number line and reasoning about relative sizes of fractions. Students reason about distances of each fraction from benchmark fractions. Comparisons will be made by using the symbols >, <, or =, accompanied with a justiﬁcation of the comparison.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

accurately plot, order, and compare fractional numbers with the same numerator or denominator.

•

analyze and explain true or false statements that involve the comparison of two fractions with the same numerator or denominator.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

compare fractions with the same numerator and different denominators using fraction models.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 210

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

In this exploration, students will compare fractions by reasoning about the size of the whole while comparing taco ingredients. Students will: •

construct a model for different fraction comparisons.

•

explain how to determine the larger fraction of two fractions.

Explore 2

Compare Fraction Wholes

In this exploration, students will work collaboratively to determine the amount of ingredients for different recipes. Students will: compare the size of two fractions with like denominators or numerators using words, symbols, objects, and pictorial models to justify.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Comparing Fractions with Models

Comparing Fractions with Number Lines

In this exploration, groups of students will play a game to compare fractions with different numerators and denominators. In playing the game, students will: •

use fraction tiles and circles as models to create fractions.

•

choose tiles or circles for same-size whole models.

•

use equivalent fractions to make comparisons of fractions with different denominators.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 5

Compare Fractions with the Same Numerator or Denominator

•

Explore 4

Explore 3

Explore 1

EXPLORE ACTIVITIES

COMPARE FRACTIONS

Home

In this exploration, groups of students will solve a scenario where they are asked to compare the distance of different restaurants from road signs. Through solving the scenario, students will: •

compare fractions and mixed numbers by using number lines and fraction tiles.

•

build a model of each distance on the road sign using fraction tiles.

•

write two comparison statements to justify answers.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Comparing Fractions Using Benchmarks In the last exploration, students will use benchmark fractions to compare fractions with different numerators and denominators. In completing the last exploration of the scope, students will: •

use benchmarks of 0, one-fourth, one-half, three-fourths, and 1 to compare the distance walked over a 10-day period.

•

discover that using benchmark fractions makes comparing fractions easy and why.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

211

COMPARE FRACTIONS

Compare Fractions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

212

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students compare two unit fractions and decide whether the justiﬁcation of the conclusion using symbols, words, and pictorial models is true or false. This activity is intended to assess mastery of the following standard(s): 3.NR.4.2 Compare two unit fractions by ﬂexibly using a variety of tools and strategies.

Materials

Preparation

Printed •

• • •

1 Student Handout (per group)

Reusable •

COMPARE FRACTIONS

Home

Prepare to project the Student Handout for students. Print one Student Handout for each group. Plan to have students work in groups for this activity.

1 Projector or document camera (per class)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5.

Distribute a Student Handout to each group. Project the Student Handout for the class, and read the first problem to the class. Show students the first set of fractions and the justification. Students who agree with the conclusion should give a thumbs-up; students who disagree with the conclusion should give a thumbs-down. Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. 1

Repeat the process for the second set of fractions. 1

a. The statement that _4_ is greater than _5_ is true. When there are more pieces in the whole or set, the pieces get smaller. Lisa has eaten more of the candy bar than Allison. 7.

Before students participate in the discussion that follows, challenge them to adjust the false statement to make it true.

a. The statement _6_ < _8_ is false. The number of pieces in the whole is not the same, so the fewer pieces they are, the larger the pieces. Six is less than eight, so the symbol should be the greater than symbol. Tim has completed more of the math assignment than John. 6.

FACILITATION TIP

FACILITATION TIP If students struggle to understand the comparison, refer to fraction tiles, fraction circles, or fraction towers to model the fractional sizes. If needed, use the Foundation Builder for further support with this type of investigation.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

213

COMPARE FRACTIONS

Compare Fractions Hook – It’s a Piece of Cake ACTIVITY PREPARATION Students compare fractions with the same numerator and different denominators using fraction models.

Materials

Preparation

Printed

Part I

•

1 7-Inch Cake Circle (per student)

• •

Reusable • • • •

Plan to show the Phenomena Video. Print and cut 1 7-Inch Cake Circle for each student.

Part II

1 Phenomena Video (per class) 1 Projector (per class) 2 Different-colored crayons (per pair) 1 Straight edge (per pair)

•

Plan to have students work in pairs to complete the activity.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP Print and project this scenario for students to read. Have students think silently for one minute, then pair up to discuss, and ﬁnally share with the whole class. FACILITATION TIP

In addition to the 7-inch Cake Circle, model using a rectangular cake pan. Fluency with a rectangular model will help students as they proceed through more complex concepts and operations with fractions.

FACILITATION TIP Review numerator and denominator and check for understanding before proceeding to the Explore activities. Sometimes, students need help remembering denominator can be “d for down below.”

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You and your best friend baked two identical chocolate cakes. You divide your cake into four equal pieces, and your friend divides her cake into three equal pieces. You and your friend each eat two pieces of your own cake. Your friend says she ate more cake than you did, but you say that you both ate two pieces so you ate the same amount. Who is correct? Show students the 7-Inch Cake Circle that will be used to make the models of the cakes. Discuss the following questions:

DOK-2 How will making a model of the cakes help us ﬁnd who ate more 2 cake? Making fraction models can help us determine whether _4_ is 2 greater than, less than, or equal to _3_.

DOK-2 What does the number of pieces the cake was cut into represent? The number of pieces the cake was cut into represents the denominator of the fraction. DOK-2 What does the number of pieces of cake eaten represent? The number of pieces of cake eaten represents the numerator of the fraction.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

214

DOK-2 How will making a model of the cakes help us ﬁnd out who ate 2 more cake? Making fraction models can help us determine whether _4_ is 2 greater than, less than, or equal to _3_ © Accelerate Learning Inc. - All Rights Reserved

3. 4.

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What does the number of pieces the cake was cut into represent? The number of pieces the cake was cut into represents the denominator of the fraction.

DOK-2 What does the number of pieces of cake eaten represent? The number of pieces of cake eaten represents the numerator of the fraction.

Give each pair of students two cake circles, a straight edge, and two colors of crayons. Instruct students that they need to make models of the two cakes. a.

Your cake was divided into four equal pieces (fourths).

Your friend’s cake was divided into three equal pieces (thirds).

Intervention

Acceleration

COMPARE FRACTIONS

Home

FACILITATION TIP In addition or alternatively, have students use a rectangular model. For some students, dividing a rectangle into equal parts is much simpler than a circle.

Give students about 10 minutes to create the two cakes by using pencils and rulers to indicate how many equal-sized pieces each cake was divided into. a.

Have students use the crayons to show how many pieces of cake were eaten.

Have students use different colors to represent the two different cakes.

Have students then cut out the portion of each cake that was eaten to compare the fractions.

Instruct each pair to tell the class who ate more cake. Who ate more cake—you or your friend? Did everyone in the class agree? Gather students in a whole group, and discuss the following questions: a.

DOK-2 How did you compare the fractions in your models? Answers will vary. We compared them side by side. We put one on top of the other.

DOK-3 What did you learn about the size of the denominator? The larger the denominator is, the smaller the pieces of cake are.

DOK-3 What did you learn about the size of the numerator? The larger the numerator is, the more pieces of cake there were that got eaten.

DOK-3 Which mattered more for ﬁguring out who ate more cake? The denominator and the numerator were both important for solving the problem. The denominator determined the size of the pieces, and the numerator determined how many of the pieces were to be counted. The size and number of pieces were equally important.

FACILITATION TIP Encourage students to use these two vocabulary terms aloud in their answers. Provide sentence stems like, “The denominator is_______”; and “A larger denominator means__________”; and “The numerator represents ________”.

e. DOK-1 What fraction of the cake did you eat? I ate _4_ of the cake (which is one-half of the cake). 2

DOK-1 What fraction of the cake did your friend eat? She ate _3_ of the cake (which is more than half of the cake).

DOK-1 Who ate the larger amount of cake? My friend ate the larger amount of cake.

h. DOK-1 Compare the fractions using the terms greater than, less than, or 2 2 equal to. _4_ < _3_. Two-fourths is less than two-thirds.

FACILITATION TIP Review these symbols consistently and have students use the phrases in between two values frequently. Saying aloud, 2 2 “ _4_ is less than _3_” is much clearer than just saying “less than” as students would often like to do.

215

COMPARE FRACTIONS

Compare Fractions Explore 1 – Compare Fraction Wholes ACTIVITY PREPARATION Students compare fractions by reasoning about the size of the wholes while comparing taco ingredients.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments, and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • • •

1 Student Journal (per student) 1 Compare Task Card (per class) 1 Set of Taco Task Cards (per class) 1 Set of Station Cutouts (per class) 1 Exit Ticket (per student)

Reusable •

1 Projector or document camera (per class, optional)

• • • • •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Plan to project the Compare Task Card for the class or print one copy for each group to view. Print a set of Taco Task Cards, cut them out, and place them around the room, creating six stations. Print a set of the Station Cutouts on card stock. Optionally, Station Cutouts can be laminated for durability. •

•

Cut out each ingredient as accurately as possible for accurate measuring, and place each ingredient at its appropriate station.

For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP

1. 2.

Bring in some different sized taco shells, jalapenos, or tomatoes to engage students and create a real-world connection. FACILITATION TIP Call on different students to share their partner’s thoughts for each question. This encourages students to actively listen.

216

3. 4.

Display the Compare Task Card for the class. Read the following scenario to the class: The new restaurant Taco Hacienda is bringing you in to show you how they make their tacos. They have received complaints from their customers and have asked you to help them ﬁgure out why. Customers are complaining that their serving sizes are not fair. Why do you think customers are complaining? Invite students to discuss the tacos with their shoulder partners. Encourage students to share their discussions with the class. a.

DOK-2 What did you notice about the tacos? The tacos looked the same, but they were not the same size.

DOK-2 What might be the reason for the customers’ complaints? The tacos are not the same size. Some people are getting bigger tacos than others.

DOK-2 You plan to share a taco equally with your friend and you are really hungry. Which taco would you rather have half of? Explain. I would rather have half of the bigger taco. Half of a bigger taco will be a bigger half than a half from the smaller taco. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Explore

Explain

Elaborate

Evaluate

Give a Student Journal to each student. Divide the class into 6 groups, and assign each group to a station. Explain that each station has one taco ingredient that needs to be evaluated. It is the students’ job to determine if the ingredients are being fairly distributed to each customer’s taco. Students will need to draw the portions and explain their reasoning for whether the portions are fair or not on their Student Journals. Actively monitor each station while listening to discussions for misconceptions. a.

Engage

Intervention

Acceleration

FACILITATION TIP At each station, have students circle the fraction on each Taco Task Card then compare the Station Cut-Outs.

COMPARE FRACTIONS

Home

For students struggling to discover whether or not the wholes are the same size, encourage them to physically compare the ingredients at each station by placing one on top of the other.

Have the groups rotate after giving them an appropriate amount of time at each station. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How did you determine if each taco got the same amount of ingredients? I compared the size of the whole ingredients to see if they were the same. • DOK-3 Why does the size of the whole ingredient matter when comparing fractional parts? If the two wholes are not the same, then the fractional parts will not be the same, even if the fraction is the same. I may take half of two blocks of cheese, but those halves will not be the same size if the two blocks are different sizes. • DOK-3 What would you report to the restaurant owners about why their customers are complaining? I would tell them that they need to be careful about the size of their whole ingredients. Giving people a fractional part of an ingredient is only fair if the whole ingredients are the same size.

FACILITATION TIP As you monitor students, check for misconceptions in comparing the size of the fractions and creating the fractions to match the fraction.

•

2. 3.

Take time to ﬁnd and share some real-world images or examples about how the size of the whole matters when comparing fractions.

FACILITATION TIP

Post-Explore 1.

FACILITATION TIP

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

When you preview this Exit Ticket with students, consider creating some constraints on the pizza drawings. For example can students draw any shape? (circles, squares, or rectangles?)

217

COMPARE FRACTIONS

Compare Fractions Explore 2 – Compare Fractions with the Same Numerator or Denominator ACTIVITY PREPARATION Students compare the sizes of two fractions with like denominators or like numerators using words, symbols, objects, and pictorial models to justify their comparisons.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments, and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Recipe Riddles Cards (Per group) 1 Exit Ticket (per student)

• • • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Recipe Riddles Cards on card stock, cut them apart, and laminate them for future use if desired. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP To engage students in this Explore activity, encourage them to bring in their favorite recipes from home. FACILITATION TIP Each group member can take turns reading the Recipe Riddle Cards, identifying the two ingredients that are being compared, and creating a model. 218

2. 3.

Read the following scenario to the class: As the local cooking experts, you are the ones your friends and family come to for help! Your loved ones are looking over different recipes and have some questions. They have shared their recipe riddles with you to help them answer their questions. Can you help? Give a set of Recipe Riddles Cards to each group and a Student Journal to each student. Students should read recipe riddle 1 together as a group. Students will then record the fractions they are comparing, draw a model, write a comparison statement, and record their reasoning on their Student Journals. Students will complete the same steps for each Recipe Riddle Card and answer the reﬂection questions. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

If students are struggling to reason about the size or number of fractional parts, allow them to create a concrete model of the fractions using manipulatives. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-2 What strategy did you use when the fractions had the same numerator? When the numerators are the same, look at the denominators to compare the size of the pieces. A smaller denominator means there are fewer pieces. Fewer pieces means each piece is bigger. DOK-2 What strategy did you use when the fractions had the same denominator? When the denominators are the same, you can compare only the number of pieces (or numerators) because the pieces are the same size. DOK-2 If you made the denominator a larger number, what would happen to the size of the parts? Explain. The parts would be smaller because you are breaking the whole into more pieces. DOK-2 If you made the denominator a smaller number, what would happen to the size of the parts? The parts would be larger because you are breaking the whole into fewer pieces.

Intervention

Acceleration

FACILITATION TIP In the Intervention section, the Fraction Strips could be used to support students. Additionally, providing standardized number lines or rectangular templates would help clarify concrete models.

COMPARE FRACTIONS

Home

FACILITATION TIP Post these Math Chat Questions from the Print Files. Encourage students to use the math vocabulary terms when they respond. Provide sentence frames or starters as support. For example, students should say, “When fractions have the same denominator...,” or “A larger denominator means...”

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP This Exit Ticket could be used as a preassessment for some students who may beneﬁt from the Acceleration activities.

219

COMPARE FRACTIONS

Compare Fractions Explore 3 – Compare Fractions with Models ACTIVITY PREPARATION Students use the <, >, and = symbols to compare fractions. They justify their reasoning by using concrete manipulatives and visual models.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Would You Rather Cards (per group) 1 Exit Ticket (per student)

Reusable • •

1 Set of fraction tiles (per group) 1 Set of fraction circles (per group)

• • • • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Would You Rather Cards for each group. Prepare a set of fraction circles and fraction tiles for each group. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Engage students by practicing with a few questions. Consider ﬁnding a video with age appropriate “Would you rather?” questions.

FACILITATION TIP A follow-up question might be about younger students and why they often get “tricked” by fractions. Ask, “Why would a younger sibling think that one-ninth would be bigger than one-third?”

FACILITATION TIP

Depending on your students, consider using only fraction circles or fraction tiles to start. If you can, provide one complete set per student. 220

Ask students if they have ever played the “Would You Rather?” game. Allow 1 or 2 minutes of sharing time. Explain to students that they are going to use math tools to help them play the “Would You Rather?” game. DOK-1 Ask them what they know so far about comparing fractions. If the denominators are the same, then look at the numerator. The bigger the numerator, the bigger the fraction. If the numerators are the same, then look at the denominators. The smaller the denominator, the bigger the fraction. Write what they remember on the board so they can refer to it throughout the activity. Ask students what they would do if the numerators and denominators were both different. Allow students to share ideas. Students will likely say they could build a model of each and see which one is larger or smaller. Some students may say they could create equivalent fractions so that they do have the same numerator or denominator. Explain that students should read each card and build a model of the fractions given using the fraction circles and fraction tiles.

7. 8.

9. 10.

Engage

Explore

Explain

Elaborate

Evaluate

Distribute sets of fraction circles and fraction tiles to each group. Once the model is built, students should explore ways to create equivalent fractions so the fractions they are comparing have the same numerator or the same denominator. Students will then use the models to decide which option they would prefer. Each decision should be recorded and explained in their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

When drawing their fraction models, be sure each drawing of one whole are the same size on their Student Journals.

DOK-2 Can you build one option with the tiles and the other option with the circles? Explain. No, because those are different-sized wholes. To compare fractions, you have to compare the same-sized whole.

DOK-2 How can you ﬁnd equivalent fractions for the ones you are comparing? We can trade out the pieces for smaller pieces and ﬁnd a fraction that is the same size. We are breaking up each unit fraction into smaller pieces.

DOK-1 How do you know which fraction is greater or less? If one model is larger than the other, then that fraction is greater.

Intervention

Acceleration

FACILITATION TIP Provide templates for students to trace if needed. Fraction strips are provided in the Intervention section. FACILITATION TIP Be prepared to provide some time for students to explore and organize the manipulatives. Their time may depend on the size of the sets, their completeness, and the colors.

COMPARE FRACTIONS

Home

FACILITATION TIP Provide templates for students to trace if needed. Fraction strips are provided in the Intervention section.

e. DOK-1 How could you represent your choice using symbols? I could use symbols like >, <, and = to show which fraction is greater or less. 11. 12.

When students are ﬁnished, discuss the activity as a class. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-3 What connections did you make while you were working on this Explore activity? I noticed that each model is composed of unit fractions. I noticed how a smaller denominator means the whole is only broken into a few pieces, so the pieces are larger! I noticed we could make equivalent fractions by breaking each piece into equal pieces. DOK-3 Describe the process you used to make your decision on each card. I looked at the two fractions and built a model of each. I then created an equivalent fraction so the fractions I was comparing either had the same denominator or the same numerator. If I wanted more of something, I chose the greater fraction. If I wanted less of something, I chose the lesser fraction. DOK-3 How did you decide which math tools to use? It didn’t really matter whether we used tiles or circles as long as we built both options with the samesized whole. DOK-2 What would happen if the whole wasn’t the same size? We wouldn’t be able to tell which one was actually larger or smaller. The models wouldn’t be helpful. DOK-2 If you didn’t have the math tools in front of you, what could you do? We could draw fraction circles or fraction tiles. As long as we have the same size of whole on both models and partition it evenly, we can use our drawings to compare the fractions. I could also use the drawn model to create equivalent fractions so that they have the same numerator or denominator. That would help me compare them without having the math tools.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

STEMscopes Tip “I can...” statements that describe what students will know and be able to do when they have mastered the standard(s) of the scope are found in the Key Concepts element of the Home tab. Posting these statements at the beginning and end of the Explore activities for students to reference will help them see their progress in achieving the goals of the scope.

FACILITATION TIP Before having students complete this Exit Ticket, determine your criteria for success on student-drawn models. The Exit Ticket answer key shows equivalent fractions with different denominators. 221

COMPARE FRACTIONS

Compare Fractions Explore 4 – Compare Fractions with Number Lines ACTIVITY PREPARATION Students compare two fractions by using number lines and ﬁnding common denominators.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • • • •

•

1 Student Journal (per student) 1 Teacher Road Sign (per class) 1 Set of Number Lines (per group) 1 Set of Student Road Signs (per class) 1 Exit Ticket (per student)

• • • • •

Reusable • • • • •

1 Projector or document camera (per teacher, optional) 1 Dry-erase marker (per group) 1 Set of fraction tiles (per group) 1 Sheet protector (per group) 1 Dry-erase eraser (per group)

Consumable •

•

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Prepare a set of fraction tiles for each group. Print a set of Number Lines for each group. Put them in a clear sheet protector. Plan to project Teacher Road Sign, if desired. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

1 Sheet of chart paper (per teacher, optional)

PROCEDURE AND FACILITATION POINTS Part I

FACILITATION TIP Have students use the fraction tiles to create a model for each distance. Then, students can transfer the distances to the number lines on their Student Journals. FACILITATION TIP Challenge students to change the fractions greater than a whole into mixed fractions. 222

Distribute fraction tiles and sets of Number Lines. Give each group a dry-erase marker and eraser.

DOK-1 Show the Teacher Road Sign on the board. Ask students to turn and talk with the partner next to them about what the sign says and where they might have seen a similar sign. Listen to discussions to ensure students are naming 1 fractions correctly, such as, “The fraction _4_ should be said as ‘one-fourth,’ not ‘one dash four’ or ‘one over four.’” Explain to students that, many times, highway signs will show the distance from one point to another point. This would mean that the distance from where the sign is to the place listed on the sign is how far apart they are. Discuss the following question:

DOK-1 When we look at this sign, what information is it telling us? 1 4 Math Road is _4_ of a mile away, Science Avenue is _8_ of a mile away, and 9 Reading Court is ___ of a mile away. 12 © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

Tell students to build a model of each fraction on the road sign using their fraction tiles. On the Number Lines, they will work together in groups to create a number line for each fraction as well. If needed, students can use the fraction tiles to help them build a number line. Students should align one edge of their fraction tiles to easily see a comparison of the fractions. Discuss the following questions: a.

DOK-2 Are all of these fractions equivalent? How do you know? No, they are not because when I line up my fraction tiles, they are not the same amount. When I look at the location of the three points on my number lines, they are not all the same distance from zero.

DOK-1 What do you notice about the numerators in these fractions? They are different.

DOK-1 What do you notice about the denominators in these fractions? They are different.

DOK-2 How can we compare these fractions? We could look at our tiles to see which fraction is larger or smaller. We could look at the number line to see which fraction is closer to one.

Intervention

Acceleration

FACILITATION TIP Be sure students are using the correct fraction tiles for each scenario. Direct their attention to the denominator both in the scenario and on the fraction tiles.

COMPARE FRACTIONS

Home

e. DOK-1 Which street is the farthest away? How do you know? Reading 9 Court is the farthest. If I look at my fraction tiles, ___ is greater than the 12 9 ___ other fractions. My point for 12 is closest to 1 on the number line. f.

DOK-1 Which street is closest? How do you know? Math Road is closest. 1 If I look at my fraction tiles, _4_ is the smallest amount. If I look at my 1 number line, my point at _4_ is closer to 0 than the other fractions are.

DOK-2 Look at _8_ using your fraction tiles and on your number line. What 1 can you determine about this amount? It is equal to _2_; 4 out of 8 pieces is half. My point on my number line is right in the middle between 0 and 1.

h. DOK-1 What fraction is _8_ equal to? The fraction _2_ is equal to _8_.

i. DOK-2 What if you didn’t have a model to build the fractions? What could you do? We could draw a number line to compare them. We could create common denominators or common numerators to compare the fractions.

7. 8.

Brieﬂy review how to ﬁnd equivalent fractions. Create the tables below on the board. 1 1

STEMscopes Tip Located under the Explore tab, the Virtual Manipulatives offer classrooms an alternative to concrete manipulatives. They require no setup and can be accessed from any digital device. Students can interact with a variety of virtual manipulatives to explore mathematical concepts. These manipulatives help teachers enhance equity and empower learning outside the classroom.

4 4 8 9 12 9.

Invite students to create equivalent fraction tables on their desks with dry-erase markers.

223

COMPARE FRACTIONS

Compare Fractions Explore 4 – Compare Fractions with Number Lines 10.

11.

Challenge them to generate equivalent fractions and ﬁnd a common numerator or denominator. Students will collaborate to complete each table until they ﬁnd an equal numerator or denominator for all three fractions. Call on volunteers to come up to the board and complete the tables until an equal denominator is reached. Students may quickly see that multiplying the numerator and denominator in a fraction by 2, then 3, then 4 results in skip counting by each. This strategy can be used to quickly generate equivalent fractions. 1

STEMscopes Tip

Within the Explain section, Interactive Notebook activities are designed to engage students by organizing information in a way that they ﬁnd understandable. Students use cut-andglue activities to display their learning from the Explore activities and can add the activities to a notebook to use for reference whenever needed.

12.

Students will circle their three fractions with equal numerators or equal 6 ___ 18 12 denominators. They should circle ___ , , and ___ . Ask them what the numerators 24 24 24 for these fractions are. Students should see that the numerators are different. Discuss the following question: a.

13.

DOK-1 How can we compare these fractions now that we have equal denominators? We can look at the numerators and compare the fractions based on those. Since the denominators are the same, we know we are comparing same-sized pieces, so looking at the numerator can let us know how many of those pieces we have for each fraction.

Emphasize the usefulness of having a common numerator or denominator when comparing fractions.

Part II 1. 2. 3.

FACILITATION TIP

Consider using one of the other manipulatives at a time with students. 5. 6. 7.

224

Give a Student Journal to each student. Each group will need one Student Road Sign, a set of fraction tiles, and a set of Number Lines. Read the following scenario to the class: Your family is taking a long road trip. As you drive, you see various road signs showing restaurants nearby. The signs show you how far away each restaurant is from where you are on the highway. Look at each Road Sign, and compare each restaurant’s distance. Students will work cooperatively to compare the distances of the restaurants on their road signs. They will use fraction tiles and number lines to compare the two fractions. In addition, they will ﬁnd equivalent fractions with equal denominators using an equivalent fraction table to compare the fractions. All of these strategies will help determine which restaurant is closer or farther and lead students to write two comparison statements to justify their answers. Give students about 8 minutes to complete their Student Journals for each road sign before rotating signs among the groups. Come back together as a whole group to discuss the models that were created and the comparison of each set of fractions. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Engage

Explore

Explain

Elaborate

Evaluate

•

DOK-2 What is the relationship between the fraction tiles and the number line? They both show the same fractions, just two different ways. The fraction that was greater when I built it with the tiles is the same fraction that is closer to 1 on the number line. Each tile is like a section of the number line. DOK-2 Why is it helpful to ﬁnd a common numerator or a common denominator? If I have a common denominator, I could look at the numerators and determine which was smaller or larger since the equal denominators tells me the size of the pieces will be the same for both fractions. If I have common numerators, I can judge which pieces are larger or smaller based on the denominator because I know I have the same number of pieces.

Post-Explore 1. 2. 3.

Acceleration

FACILITATION TIP

Math Chat •

Intervention

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Print the Math Chat questions from the Print Files and record a few student responses. A follow up would be to share some real-world examples of comparing fractions.

COMPARE FRACTIONS

Home

FACILITATION TIP For this Exit Ticket, struggling students may need rectangles, number line, and common denominator chart templates provided on the assessment. Challenge other students to ﬁnd additional common denominators and create more equivalent fractions.

225

COMPARE FRACTIONS

Compare Fractions Explore 5 – Compare Fractions Using Benchmarks ACTIVITY PREPARATION Students compare fractions with different numerators and denominators using benchmark fractions.

Standards for Mathematical Practice • • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials Printed • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable •

Preparation • • • •

1 Set of fraction circles (per group) •

Plan to have students work in groups of 3 or 4 to complete this activity Print a Student Journal and an Exit Ticket for each student. Prepare a set of fraction circles for each group. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS Part I FACILITATION TIP

Distribute Student Journals to students.

Read the following scenario to the class: For the next 10 days, Cecia will _1_ -mile walking challenge. Her goal is to walk __ _1_ a mile or participate in the 10-day, __ 2 2 more each day for 10 days. Use fraction circles to determine whether or not she met her goal. Allow students to use fraction circles to decide whether Cecia met her goal each day. As students are working, discuss the following questions:

Demonstrate the fraction benchmarks using the Supplemental Aids: Fraction Strips in the Intervention section. 3.

FACILITATION TIP The fraction tiles and students’ fraction models are scaffolds to help students determine the trail marker. 226

DOK-1 How do you know whether or not she met her goal? If the fraction is equal to or more than one-half, she met her goal. If the fraction is less than one-half, she did not meet her goal.

DOK-2 If she met her goal on one day but did not meet her goal on another day, which fraction would be bigger? The fraction for when she met her goal would be bigger because it would be equal to or more than one-half, while the other fraction would be less than one-half.

DOK-2 Could I use one-half as a benchmark to compare other fractions? Yes. If you know that one fraction is more than one-half and one fraction is less than one-half, you can tell which one is bigger.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

e. DOK-2 What are some examples of this? Three-thirds is greater than one-half. I know this because three-thirds is a whole, and one-half is less than a whole. One-fifth is greater than one-tenth. I know this because when you separate something into five pieces and separate something equal into ten pieces, the one separated into five pieces will have larger pieces. Part II 1.

Read the following scenario to the class: Now that Cecia is through her ﬁrst 5 days, she’s looking for more of a challenge. She decided to compare her walk days to her friend Jill’s. Use what you know about comparing benchmark fractions to help Cecia see if she walked farther than Jill on a given day. Allow students to complete Part II in their Student Journals. As you observe students’ work, be sure to encourage explanation by comparing the sizes with benchmark fractions. Prompt students to explain their reasoning with you. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How does knowing whether a fraction is greater or less than a half help you compare fractions? When comparing fractions, if you know that one fraction is larger than one-half and another fraction is smaller than one-half, you can immediately tell which fraction is larger without doing any other work. • DOK-2 For the day 10 comparison, how does knowing your unit fractions help you decide who walked farther that day? If I know the sizes of unit fractions, I can tell which of the fractions is missing a larger piece. Whichever one is missing a larger piece is the smaller amount. • DOK-3 Are benchmark fractions similar to another math concept used before? How? They are similar to rounding and estimating. Because you don’t need an exact answer.

COMPARE FRACTIONS

Home

FACILITATION TIP Provide sentence stems on the board to assist students in writing their comparisons.

•

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Record student responses to this question about benchmarks and post some visual examples. Make the connection to their future; they will be using benchmark decimals and percents in later math standards and in real life. FACILITATION TIP

On this Exit Ticket, consider allowing students to examine just the chart before reading the sentence frames. Project the Days of the Week and Fractions for students to make observations before the assessment. Encourage students to make notes or write equivalent fractions next to the Fraction of Order of the Fries on their tickets.

227

COMPARE FRACTIONS

Compare Fractions Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Compare Fraction Wholes Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Compare Fractions with the Same Numerator or Denominator Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Compare Fractions with Models

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Compare Fractions with Number Lines

Independent practice assignment that gives students an opportunity to demonstrate their learning

Show What You Know, Part 5 Compare Fractions Using Benchmarks Independent practice assignment that gives students an opportunity to demonstrate their learning

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Engage

Explore

Explain

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Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

The Pie-Eating Contest

Joe Torre

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Valentine’s Day Report

Compare Fractions – Unlike Numerators and Denominators

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

COMPARE FRACTIONS

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Problem-Based Task A Sweet Tooth Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

PhET Interactive Simulation Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

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Compare Fractions Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

What prompts will be used?

COMPARE FRACTIONS

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What does mastery look like?

I can use fraction models, common denominators, or common numerators to compare fractions.

I can recognize that comparisons are valid only if both fractions refer to the same whole.

I can record comparisons using the symbols >, =, or <.

I can justify comparisons using a fraction model.

I can use benchmark fractions to compare fractions.

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SCOPE 1

Equivalent Fractions Scope Introduction SCOPE SUMMARY Students use visual models, such as area models and number lines, as they generate and explain equivalent fractions. Fractions include denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and explore adding these equivalent fractions together. This is used in a problem-solving context. Student Expectations

4.NR.4.1 Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fractions, including fractions greater than one, and explain the identity property of multiplication as it relates to equivalent fractions. Generate equivalent fractions using these relationships. 4.NR.5.1 Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students build on their knowledge of fractions to represent fractions with denominators of 2, 3, 4, 6, and 8, including fractions greater than one, using strategies such as diagrams and number lines. Students extend this knowledge to comparing two unit fractions by ﬂexibly using a variety of tools and strategies. They understand two fractions as equivalent if they are the same size or the same point on a number line. Fourth grade develops fraction equivalence so that students can explain why two fractions are equivalent by using visual models.

There is a direct link between student proﬁciency with fractions and rational numbers. Students in ﬁfth grade extend the development of fractions and decimals learned in fourth grade to solve problems with fractions and decimals. Fifth grade uses equivalent fractions to add, subtract, multiply, and divide fractions.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

recognize and generate simple equivalent fractions.

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

use visual fraction models to recognize and generate equivalent fractions.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

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Explain

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Intervention

Acceleration

Model Equivalence with Area Models In this exploration, students will collaborate and discuss with their groups to solve scenarios that involve building and modeling ways to serve pie. In solving the scenario, students will: •

use objects and area models to generate equivalent fractions.

•

participate in collaborations with peers.

•

use fraction manipulatives for building and modeling.

Explore 2

Explore 1

EXPLORE ACTIVITIES

•

recognize when two fractions are equivalent.

•

recognize when two fractions are equivalent.

•

use fraction circles.

Explore 4

Explore 3

In this exploration, students will be introduced to a real-world scenario involving a pet shop where they are tasked with helping ensure each animal is not overfed or underfed. In solving the scenario, students will:

In this exploration, students will begin exploring angles by analyzing and classifying angles for a real-world scenario involving a quilt design. Through solving the scenario, students will: •

analyze and classify angles.

•

draw an angle, classify it, and explain the reasoning for each classiﬁcation.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment. Recognize and Generate Equivalent Fractions

Model Equivalence on a Number Line

EQUIVALENT FRACTIONS

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Equivalent Fractions with Denominators of 10 and 100 In the ﬁnal exploration, students will help solve a scenario involving mail packages and cost of postage for each package. In solving the scenario, students will: •

modify fractions with denominators of 10 into equivalent fractions with a denominator of 100.

•

add totals to ﬁnd cost.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

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Equivalent Fractions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students use visual fraction models to identify equivalent fractions. This activity is intended to assess mastery of the following standard(s): 3.NR.4.4 Recognize and generate simple equivalent fractions.

Materials

Preparation

Printed •

EQUIVALENT FRACTIONS

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1 Student Handout (per student)

• •

Prepare to project the Student Handout for students. Print a Student Handout for each student.

Reusable • • •

1 Projector or document camera (per class) 1 Pair of scissors (per student) 1 Quart-size resealable bag or envelope (per student)

PROCEDURE AND FACILITATION POINTS 1. 2. 3.

Project the Student Handout to the class, and distribute a Student Handout to each student. Give students time to cut out the fraction pieces and identify equivalent fractions. Facilitate a class discussion where students explain how they know the two fractions they have chosen are equivalent. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Invite students to explain their reasoning using the model projected on the board. 2 1 1 a. _4_ = _2_ because 2 of the _4_ pieces lined up side by side takes up the same 1 amount of space as 1 of the _2_ pieces when that same 1 whole is

divided into only 2 pieces. That means if Elise has 4 friends, she has invited 2 of them.

3 1 1 b. _6_ = _2_ because 3 of the _6_ pieces lined up side by side takes up the same 1 amount of space as 1 of the _2_ pieces when 1 whole is divided into 6

equal pieces. That means if Elise has 6 friends, she has invited 3 of them.

4 1 1 c. _8_ = _2_ because 4 of the _8_ pieces lined up side by side takes up the 1 same amount of space as 1 of the _2_ pieces when 1 whole is divided

into 8 equal pieces. That means if Elise has 8 friends, she has invited 4 of them.

4 2 1 d. _6_ = _3_ because 4 of the _6_ pieces lined up side by side takes up the same 1 1 amount of space as 2 of the _3_ pieces. It takes 4 of the _6_ pieces because

when 1 whole is divided into 6 equal pieces, the pieces are smaller than

when the same 1 whole is divided into only 3 pieces. That means if there are 6 kids in Mike’s class, he ran faster than 4 of them. 4.

FACILITATION TIP Cutting out the fraction pieces may be time consuming, and if students don’t make accurate cuts, the pieces will not work effectively for comparison work. If fraction bars or other fraction models are available, consider using those instead. Alternatively, opt to cut out the fractional pieces ahead of time and store them in a resealable bag. FACILITATION TIP Challenge early ﬁnishers to ﬁnd other pairs of equivalent fractions and to share them during the discussion that follows.

STEMscopes Tip Located in the Elaborate section, the Problem-Based Task is designed to have students work together to solve an open-ended, real-world math challenge. Students apply the knowledge and skills they learned in the scope to solve the problem. They will recognize that solutions to the problem can be approached in multiple ways and with multiple responses.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

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Equivalent Fractions Hook – Pizza Pizza! ACTIVITY PREPARATION Students use visual fraction models to recognize and generate equivalent fractions.

Materials

Preparation

Printed •

•

1 Pizza Pizza! (per pair)

Part II

Reusable • • • • •

Plan to show the Phenomena Video.

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Pair of scissors (per pair) 1 Box of crayons or colored pencils (per pair) 1 Ruler (per pair)

• •

Plan to have students work in pairs to complete this activity. Print a Pizza Pizza! for each pair of students. Gather supplies for each pair of students, including crayons or colored pencils, scissors, and rulers.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP

Project the text of this scenario and read it along with students. Guide students to ﬁnd the math phrases and values. FACILITATION TIP To create engagement with this scenario, project numerous images of pizzas of different shapes that are cut differently. Have students discuss the images in their discussion about Bobby.

5. 236

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Bobby’s mom threw Bobby a birthday party. She served pizza. When she called to order the pizzas, Bobby heard his mom request to have the pizzas cut into smaller slices. Bobby’s mom told him that she could order fewer pizzas and save money because people would eat the same number of slices but it would be less pizza. When Bobby saw the large pizzas, he noticed that they were cut into 12 pieces instead of the usual 8 pieces. Bobby ate 6 slices of pizza that night when he usually only ate 4 slices of pizza. When he told his mom how much pizza he had eaten, she laughed and said her plan did not work. What did she mean? Did Bobby eat more, less, or the same amount of pizza as he usually did? Show students Pizza Pizza! Then, discuss the following questions: a.

DOK-1 Are the pizzas the same size? Yes, the whole pizzas on all 3 pages are the same size.

DOK-2 Why is having the size of the pizzas equivalent important when ﬁnding the solution? Fractions can only be compared when there are same-sized wholes.

DOK-1 Are the pizza slices the same size? No, the regular pizza has bigger slices than the party pizza. The last pizza has no slices at all; it is just a whole pizza.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4. 5.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Show students a copy of Pizza Pizza! Then, discuss the following questions: a.

DOK-1 Are the pizzas the same size? Yes, the whole pizzas on all 3 pages are the same size.

DOK-2 Why is having the size of the pizzas equivalent important when ﬁnding the solution? Fractions can only be compared when there are same-sized wholes.

DOK-1 Are the pizza slices the same size? No, the regular pizza has bigger slices than the party pizza. The last pizza has no slices at all; it is just a whole pizza.

Give each pair of students a box of crayons or colored pencils, a ruler, a pair of scissors, and Pizza Pizza! Tell students they can quickly color each of the three pizzas a different color. Have students cut out the number of slices of pizza Bobby usually eats from a regular pizza and the number of slices Bobby ate from the party pizza. Tell students they may want to cut out the slices as a block because they are easier to manipulate that way. a.

DOK-2 Have students compare the amounts of pizza/numbers of slices Bobby ate from the two differently prepared pizzas by putting them side by side or on top of one another. The comparison should be done in fraction form.

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FACILITATION TIP After students color each pizza, ask, “Which pizza did Bobby eat the most?” This is an opportunity to informally assess students before completing the activity. STEMscopes Tip The Skills Quiz is housed in the Evaluate section. This assessment includes multiple question types and is designed to formatively evaluate students’ computational knowledge. Aligned to the scope’s standards, the assessments can also be used as a review of the concepts learned throughout the scope.

Discuss the following questions: a.

DOK-1 Did Bobby eat more than, less than, or the same amount as

6 4 are usual? Bobby ate the same amount as usual. The fractions _8_ and ___ 12

equivalent.

DOK-2 Have students look at the third pizza with no slices indicated on it and decide how they could generate a fraction that is equivalent to both 48 and 612 . Instruct them to use their ruler and crayons or colored pencils to generate an equivalent fraction by creating a visual fraction model. A sample student answer is shown.

FACILITATION TIP Having students compare the pizza models creates an opportunity for students to discover equivalent fractions.

Placeholder AW

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Equivalent Fractions Hook – Pizza Pizza! 7.

8. 9.

Give students about 10 minutes to color the three pizzas, cut out the fractions, compare them, recognize and generate a third equivalent fraction on the whole pizza, and create a visual fraction model of it. Instruct each pair to tell the class whether the fractions were equivalent or not. Then, have each pair share their third equivalent fraction. Gather students in a whole group, and discuss the following questions:

FACILITATION TIP

While monitoring groups, ask students, “How many slices are in each pizza? What is the denominator?” This scaffolded question strategy will help students make the connection between the two.

DOK-2 What did the denominator in each fraction represent? The denominator represented the number of slices the pizza was divided into.

DOK-2 What did the numerator in each fraction represent? The numerator represented the number of slices that Bobby ate.

DOK-2 Which was more important in determining whether the fractions were equivalent? Both are equally important. Equivalent fractions cannot be determined without knowing both numerators and denominators.

DOK-2 How does a visual fraction model assist in determining whether fractions are equivalent? Visual fraction models show an image, which often makes it easy to see whether fractions are equivalent. Cutting out and matching up fractions makes it more accurate as long as the wholes are the same size.

FACILITATION TIP Write or have students write all the equivalent fractions on the board with the term equivalent fractions.

e. DOK-1 What were some of the equivalent fractions students generated? 1 2 3 5

Answers will vary. _2_, _4_, _6_, ___ , etc. (Any fraction that is equivalent to _2_ is 10

correct.)

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Explain

Elaborate

Evaluate

Intervention

Acceleration

EQUIVALENT FRACTIONS

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Equivalent Fractions Explore 1 – Model Equivalence with Area Models ACTIVITY PREPARATION Students use objects and area models to generate equivalent fractions.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of Task Cards (per group) 1 Exit Ticket (per student)

• • • •

Reusable • • • •

1 Set of fraction circles (per group) 1 Set of fraction tiles (per group) 1 Set of markers (per group) 1 Pair of scissors (per teacher)

•

Consumable •

1 Sheet of 12″ by 18″ construction paper (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Gather materials in order to distribute them to each group. Print and cut out a set of Task Cards for each group. Cut the construction paper into four strips so that each student has one strip measuring 3″ × 18″. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles and Fraction Tiles)

PROCEDURE AND FACILITATION POINTS Part I 1.

FACILITATION TIP Students can trace the fraction circles to make each fraction. Have them work in pairs to describe the similarities and the differences.

2. 3.

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Read the following scenario to the class: You are planning all of the different ways your new bakery can serve their pie. Build each fraction of a pie to model one way the pie could be served. Give each group a set of fraction circles and fraction tiles. Students should build the fractions shown on their Student Journals using the fraction circles and fraction tiles. Students should choose one type of model to draw on their Student Journals. Students should analyze the fractions they built and record any similarities or differences they notice between their models. Discuss the following questions: a.

DOK-1 What is the same about the fractions you modeled? They all equal one whole pie. They all have the same digit as the numerator and denominator.

DOK-1 What is different about the fractions you modeled? They each have different-sized pieces. They each have a different number of total pieces in the pie.

Read the following scenario to the class: At your bakery, you have received a few orders for cookie cake slices! Each of your cookie cakes are the same size, and customers can order by the slice. Sometimes, your customers order slice sizes you don’t have. You will need to ﬁgure out how much cookie cake to send them so they get the amount they ordered. © Accelerate Learning Inc. - All Rights Reserved

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Pass out a set of Task Cards to each group. Students should read each Task Card and use the fraction circles or fraction tiles to generate equivalent fractions. Students should start by building a model of the customer’s order. They will then overlay the size of pieces the Task Card says the cake is cut into on top of that model to generate an equivalent fraction. Students should draw both the model of the cookie cake slice the customer ordered and the model of the cookie cake pieces they are using to fulﬁll the customer’s order. Instruct groups to look at the ﬁrst Task Card. Discuss the following questions: a.

DOK-1 How much cookie cake did the customer want? The customer wanted two-thirds.

DOK-1 What size pieces did you have? We had sixths.

DOK-1 How many sixths did it take to make the same size as a third? It took two of them.

DOK-1 Each third is a group of how many sixths? Each third is a group of two-sixths.

e. DOK-1 The customer wanted two-thirds, so how many pieces should the whole have been split into? It should have been split into three pieces. f.

DOK-2 What expression can we use to show how many pieces are in the whole cookie cake we needed to use? We have three groups of twosixths. i. Have students record this in the equation section of their Student Journals for the denominator.

DOK-2 The customer asked for two of those thirds. What expression can we use to show how many pieces of the cookie cake we needed to ﬁll the order? We needed to use two groups of two-sixths.

Intervention

Acceleration

FACILITATION TIP Group members may take turns reading the Task Card, identifying the information from each Task Card, and creating the fraction model. FACILITATION TIP Project fractions and their written forms on the board for students to reference.

EQUIVALENT FRACTIONS

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FACILITATION TIP The challenge for students is to create an equivalent model for each order. Model as needed for students.

STEMscopes Tip Available in Grades 3–5, Create Your Own is found in the Acceleration section. Designed to ignite students’ creativity, this open-ended task requires students to brainstorm, plan, and create a new product based on the skills and concepts they learned in the scope. A rubric to assess students’ creative process is also included.

i. Have students record this in the equation section for their numerator. h. DOK-1 What new fraction were you able to build when you multiplied the numerator and denominator of two-thirds by 2? We were able to build four-sixths. 10. 11.

As students are working in their groups, discuss the mathematical relationship with each group. After Part I, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

FACILITATION TIP Students will write the equivalent fractions from their models. Demonstrate how to complete the equation portion using the fractions from the two models.

DOK-1 What did you notice about the models you drew for each order? The pieces were different-sized, but the shaded parts were the same amount of the whole. DOK-1 What operation do we use when we are generating an equivalent fraction? Why? We use multiplication because we have to multiply the numerator and denominator by the same digit in order to break up each original piece into the same number of pieces.

Part II 1.

Read the following scenario to the class: Today is your birthday! Family and friends have gathered together to celebrate your special day. Your friends at the bakery have created a large sheet cake to share with you and your guests. You want to serve half the cake and save the other half for later. Use the strip of construction paper to represent your cake. Follow the directions on your Student Journal to ﬁgure out what portion of the whole cake each slice is, depending on how you cut it. Give each student a large strip of construction paper and a set of markers. Students should continue to work in their groups.

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EQUIVALENT FRACTIONS

Equivalent Fractions Explore 1 – Model Equivalence with Area Models 3.

STEMscopes Tip

Access the Interventions section from the Teacher Toolbox. Here, teachers will ﬁnd intervention strategies for students who need support with communication, physical, cognitive, social and emotional, and adaptive development. The strategies are broken down by roadblock behaviors and detail how to assist students to help them overcome those roadblocks.

5. 6.

Students should follow the directions in their Student Journals to fold their “cake” in half multiple times. The ﬁrst time they fold it, they will shade in one-half with their pencil. Each subsequent time they fold it, they should draw a dark line with the marker on the creases left from the fold and record what fraction of the whole cake the shaded part represents in the table. Students should draw their model and write an equation that represents how the model has changed on their Student Journals. Once students have recorded all the values in the table, have them look for patterns in the table. After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What did you notice about your cake each time you made a cut? The pieces got smaller, and we ended up with more pieces. The shaded amount stayed the same, and the size of the whole cake stayed the same. Each time we made a cut, it divided each piece into two equal pieces. • DOK-2 What is similar about each equation you used to represent the change in the model? Explain. We always multiplied the numerator and denominator by the same number because we split each piece of the original model into equal groups. • DOK-3 How can you make an equivalent fraction? We can multiply the numerator and denominator by the same digit. •

Post-Explore FACILITATION TIP

This Exit Ticket (or a very similar one) could be used as a pre-assessment tool as well as an Exit Ticket after the Explore activity.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Explain

Elaborate

Evaluate

Intervention

Acceleration

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Equivalent Fractions Explore 2 – Model Equivalence on a Number Line ACTIVITY PREPARATION Students generate and model equivalent fractions on number lines.

Standards for Mathematical Practice • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Number Line Work Mat (per pair) 1 Set of Number Line Spacers (per pair) 1 Exit Ticket (per student)

•

Reusable • • • • • •

•

1 Pair of scissors (per pair) 1 Resealable bag (per pair) 1 Sheet protector (per pair) 1 Dry-erase marker (per pair) 1 Set of colored pencils (per pair) 1 Eraser or tissue (per pair)

•

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Number Line Work Mat, and place it in a sheet protector for each pair of students. Print and cut out a set of Number Line Spacers for each pair. Students could cut them out on their own, if desired. Place Number Line Spacers in a resealable bag. For students who need more support in recalling information, please see our Assorted Number Lines and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

To help students recall prior knowledge, have the class use images or manipulatives to make a few equivalent fractions. FACILITATION TIP Demonstrate writing the equation. Write a rule on the board about how to create an equivalent fraction using a common multiple. FACILITATION TIP This Student Journal is 3 pages. Consider using one of the pages to demonstrate or model for the students. Copying one paper front to back will simplify the activity. 244

3. 4.

Read the following scenario to the class: You are in charge of planning a color run! The color run is a two-mile fun race where people enjoy colorful bubbles, powdered paint, music, snacks, and more. It takes a lot of different people to make a color run happen, and you are the one who needs to organize all the volunteers and vendors. You want to make sure everyone is in the right place, so you must be ready to communicate everyone’s location in a variety of ways. DOK-1 Ask students what they have already learned about equivalent fractions. I have learned that you can make an equivalent fraction by breaking up each piece of the whole into smaller, equal pieces. The new fraction is equivalent to the original fraction. I learned that you can multiply the numerator and denominator by the same number to create an equivalent fraction. Distribute a Number Line Work Mat, dry-erase marker and eraser, colored pencils, and a set of Number Line Spacers to each pair of students. Start with the first detail of the race listed on the Student Journal. Students will use the spacers to partition their number lines appropriately and locate the point described on the number line. Challenge students to find all of the different ways they can describe that exact location. They should record their findings and sketch their number line models on their Student Journals. Students can use different colored pencils to show the different ways they partitioned their number lines. Challenge students to record an equation that proves the fractions they found are equivalent to the original. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Students should repeat the same process for each detail and answer the reﬂection questions at the end. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How could you find an equivalent fraction to represent this location? I could partition the number line in different ways and find one way that lines up with the current spot. I could partition each section of the number line into equal pieces and find the equivalent fraction.

DOK-1 How do you know if two fractions are equivalent on a number line? They have to be in the exact same spot. If they’re not, then they’re different values and are not equal.

Support students in the way they think about the Salty Snacks area.

Intervention

Acceleration

FACILITATION TIP Monitor groups and guide students to the understanding that in this case, division should be used instead of multiplication to ﬁnd equivalent fractions.

EQUIVALENT FRACTIONS

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Use guiding questions to help students see that they can combine equal groups of pieces to ﬁnd an equivalent fraction as well. Students 4

should see how division can be used to show how a fraction like ___ is 12 9.

1 2 equivalent to _3_, _6_, etc.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What connections did you make between this activity and what you’ve done before? Here, we were partitioning a number line in different ways. Before, we were partitioning objects and pieces of paper in different ways. Both times, we were finding equivalent fractions. • DOK-1 Look at the spacers. What do you notice about the fractional parts? As the denominator gets larger, the pieces get smaller, and there are more of them! • DOK-1 How could you find an equivalent fraction using a number line? We could partition the number line in different ways. We could make each section of the number line a group of 2, 3, or 4 sections and then find the new equivalent fraction. • DOK-2 Why can you multiply the numerator and denominator by the same number to create an equivalent fraction? When you multiply, you are combining equal groups. When you multiply the numerator and denominator by the same number, you are showing that each fractional part you had is now a “group of” a certain number of pieces. The fraction’s amount doesn’t change, but the size and number of pieces do. •

STEMscopes Tip On the Lesson Planning Resources page, found in the Essentials section in the Teacher Toolbox, is the Depth of Knowledge (DoK) Levels document. This printable resource assists teachers with choosing which elements to use based on their DoK levels. Teachers can differentiate by using the DoK levels to match elements with student needs.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP When you preview this Exit Ticket, take time to answer questions. Some students may interpret the directions to mean that they must list all possible fractions equivalent 8

to _6_ . Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Equivalent Fractions Explore 3 – Recognize and Generate Equivalent Fractions ACTIVITY PREPARATION Students recognize when two fractions are equivalent and generate three equivalent fractions using models and equations.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Matching Cards (per group) 1 Exit Ticket (per student)

•

Reusable •

1 Set of fraction circles, fraction tiles, or fraction towers (per group, if needed)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Matching Cards for each group. Matching Cards can be printed on card stock and laminated for durability, if desired. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, Assorted Number Lines, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

2. FACILITATION TIP

Students can use various strategies to match the cards.

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FACILITATION TIP

Some students will need to create fraction models ﬁrst. Other students might be able to match the equivalent fractions on their own.

FACILITATION TIP

Consider writing a rule on the board about multiplying and dividing fractions with the same number. Include several examples.

Read the following scenario to the class: You work at a pet store, Paulita’s Pet Shop. You have been given the very important task of feeding the animals, and you’re so excited to have this responsibility! You feed the animals their food the first night, and all goes well. The second night, you realize the scoops you used are dirty, and you need to use the other sets of scoops for tonight. The scoops are equivalent to the original scoops, but you have to match them to make sure each animal doesn’t get overfed or underfed. Give a Student Journal to each student and a set of Matching Cards to each group. Instruct the students that they will be matching animals’ scoops by finding the cards for equivalent scoops in fraction form. They will need to prove that their matches are equal by providing an equation and a visual model in whatever form they choose. They will be working with their groups to make three matches. Allow students to use fraction manipulatives to help them build equivalent fractions, if needed. The goal is for students to identify and generate equivalent fractions without the use of physical manipulatives. If needed, remind students that they are multiplying or dividing the numerator and the denominator by the same number to make the equivalent fraction. Allow students to work at their own pace to complete the matches and their Student Journals. If students finish early, challenge them to create additional equivalent fractions for each match. After the Explore, invite the class to a Math Chat to share their observations and learning. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat •

•

• •

•

DOK-1 If we only multiply the numerator or only multiply the denominator, are we creating equivalent fractions? No. You have to multiply both the numerator and denominator to ﬁnd equivalent fractions because each piece is being decomposed into more pieces. DOK-2 Do equivalent fractions have the same value? Why or why not? Yes, they are equal and have the same value even though they look different. The size of the parts may be different, but it is still the same portion of the whole as before. DOK-3 What are some situations where we might encounter equivalent fractions? Cooking, measuring, etc. DOK-3 Share one equivalent fraction match and how you came up with it. Accept all answers that showed they multiplied or divided the numerator and the denominator by the same number. Accept all pictures that demonstrated that they knew how to generate an equivalent fraction. Example: We multiplied the numerator and denominator by 4. DOK-3 What do all of these answers have in common? We all either multiplied or divided the numerator and denominator by the same number to ﬁnd an equivalent fraction.

FACILITATION TIP Take extra time to emphasize the importance of multiplying both the numerator and the denominator by the same number. A common error for students is to only multiply the numerator. Provide extra skill practice using individual whiteboards whenever time allows.

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FACILITATION TIP Take time to gather some additional relevant real-world applications of equivalent fractions to support this Math Chat. Consider looking for some in students’ social studies and science texts.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Equivalent Fractions Explore 4 – Equivalent Fractions with Denominators of 10 and 100 ACTIVITY PREPARATION Students change fractions with denominators of 10 into equivalent fractions with a denominator of 100 for items in a package. Students will then add the total to see how many stamps they will need to send each package.

Standards for Mathematical Practice • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Package Cards (per group) 1 Exit Ticket (per student)

Reusable •

•

4 Envelopes or resealable bags (per group) •

Plan to have students work in groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Package Cards for each group. Cut apart and place each set into its own resealable bag or envelope. Each group will have four of these—one for each package. For students who need more support in recalling information, please see our Base Tens and Base Ten Grid Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS STEMscopes Tip The Planner, accessed along the menu bar, provides a calendar planning tool for teachers. Download, print, save, or share your plans. Use the Elements tab on the left to access grade-level scopes and virtual-learning options with embedded links to all scope elements. Drag the elements you want to implement into the calendar, and click on each element to enter element details and personal planning notes.

2. 3.

FACILITATION TIP As groups read the Package Cards, have them circle the denominators. Then, have students sort the cards by the different denominators before creating equivalent fractions.

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Read the following scenario to the class: A local Boy Scout troop needs your help sorting some mail to determine how much postage will cost for shipments. They have been busy putting together care packages for the less-fortunate citizens in our city. Now they need to know how much postage they will use so they can gather the money to pay for the packages to be sent out. The price of postage depends on how much each package weighs. Give a Student Journal to each student and one set of Package Cards to each group. Tell students that in each package, there are different items weighing different amounts. Their goal is to ﬁnd the total weight of the package and determine the cost of the postage. DOK-1 Have students begin with the ﬁrst package. They should lay out the items and share what they notice about the weights. All denominators are either 10 or 100. a.

DOK-2 How can you combine fractional parts that are not the same? We can create an equivalent fraction so they have the same denominator. That would mean they are the same-size fractional pieces and we can combine them.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 How can you create equivalent fractions so your denominators are all the same? I take the fractions that have 10 as a denominator and multiply the numerator and denominator by 10. That allows us to have all the fractional parts in hundredths so we can add them together.

DOK-1 If you have more than 100 hundredths, what do you need to do? We need to create a mixed number. A hundred hundredths is equal to one whole.

DOK-2 What would happen to the expression ____ after you regrouped? 100

172

We would take 100 of those hundredths and make 1 whole. Then, we 72

left over. The new fraction would be 1____ . would have ____ 100 100

Ensure students are filling in their Student Journals as they work. They must convert all values to hundredths and add the fractions for a total weight. Once they find the total weight, they will have to figure out how much postage would be necessary for each package. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 Why do the values need to have the same denominator before you can combine them? Hundredths and tenths are different-sized pieces. To add them, you need to have all pieces the same size. • DOK-3 Is it necessary to multiply both the numerator and denominator by the same number? Why or why not? Yes, you have to multiply the numerator and denominator by the same number. If not, you won’t have the same value, and it will not be an equivalent fraction. • DOK-2 How did you ﬁnd the total amount of weight? Did you add both the numerator and denominator? No. We only added the numerators. The denominator just tells you the size of the pieces, so we don’t add the denominators. The numerators tell you how many you have, so we added the numerators. •

Post-Explore 1. 2. 3. 4.

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

Intervention

FACILITATION TIP As students practice this multistep process, have them show the step of multiplying by an equivalent of 1. For example,

10 30 10 20 3 ___ 2 ___ ___ • = ____ and ___ • = ____. 10 10 100 10 10 100

EQUIVALENT FRACTIONS

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FACILITATION TIP If necessary, demonstrate how to use 10 rods to create 100 units. Ask students, “How can we create an equivalent fraction with 10 and 100 as the denominators?” FACILITATION TIP Some students may need support with ﬁnding fraction values in between when calculating the postage costs. For example, 76 Package #2 is 1____ which is in between 100 51 1____ and 2. 100

FACILITATION TIP

Guide students with questions such as the following: What is the rule about creating equivalent fractions? Now that we have equivalent fractions, what process can we use to ﬁnd the total postage? FACILITATION TIP Take extra time to emphasize the importance of multiplying both the numerator and the denominator by the same value. A common error for students is to only multiply the numerator. Provide extra skill practice using individual whiteboards whenever time allows.

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Equivalent Fractions Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Model Equivalence with Area Models Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Model Equivalence on a Number Line Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Recognize and Generate Equivalent Fractions

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Equivalent Fractions with Denominators of 10 and 100

Independent practice assignment that gives students an opportunity to demonstrate their learning

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Going Green

Antoni Gaudi

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further.

Math Story

Fluency Builder

Felicity and the Family Bakery

Add Equivalent Fractions – Denominators of 10 and 100

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

S’more Sharing

Equivalent Fraction Models – Denominators 2, 3, 4, 6, 8, 10, 12, 100

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

EQUIVALENT FRACTIONS

Home

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

PhET Interactive Simulation Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

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Equivalent Fractions Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

What prompts will be used?

EQUIVALENT FRACTIONS

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What does mastery look like?

I can use concrete materials, drawings, and number lines to demonstrate and explain the relationship between equivalent fractions.

I can explain the identity property of multiplication as it relates to equivalent fractions.

I can recognize and generate equivalent fractions based on the principle that the numbers and sizes of the parts may differ even though the fractions themselves are the same size.

I can use concrete materials and fraction models to demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100.

I can use concrete materials and fraction models to add two fractions with denominators of 10 and 100.

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SCOPE 1

Compose and Decompose Fractions and Mixed Numbers Scope Introduction SCOPE SUMMARY Students decompose a fraction into a sum of fractions with the same denominator using concrete and pictorial models, recording the results with symbolic representations. Visual models, such as fraction strips, squares, circles, or number lines, are used to justify the decompositions.

Student Expectations

4.NR.4.4 Represent whole numbers and fractions as the sum of unit fractions. 4.NR.4.5 Represent a fraction as a sum of fractions with the same denominator in more than one way, recording with an equation.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students partition circles and rectangles into two and four equal shares. Second grade continues partitioning, adding thirds. Students recognize that equal shares of identical wholes need not have the same shape. Third grade develops an understanding of fractions as numbers, with a focus on unit fractions. Students represent fractions on a number line and explain equivalence of fractions. This scope will extend students’ understanding of fractions by decomposing a fraction into a sum of fractions with the same denominator.

Students in fourth grade will add and subtract mixed numbers with like denominators. Fifthgrade students will model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators. Students will extend their previous understanding of multiplication and division to multiply and divide fractions. They in sixth grade will ﬂuently add and subtract any combination of fractions to solve problems. Students will also build upon ﬁfth-grade knowledge to multiply and divide any combination of whole numbers, fractions, and mixed numbers using student-selected strategies.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to:

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to:

•

represent unit fractions.

•

interpret unit fractions.

•

label fractional parts based on their distance from zero to a numberline point.

decompose portions into a unit fraction using an equation.

•

use a pizza model to decompose the whole into parts.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 254

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Compose and Decompose Unit Fractions In this exploration, groups of students will determine the number of pie slices handed out at different stations at a bakery’s grand opening. In solving the scenario, students will: •

use manipulatives to draw a model.

•

write an equation to determine the total number of pie slices given away.

•

compose and decompose unit fractions.

Explore 2

Explore 1

EXPLORE ACTIVITIES

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Compose and Decompose Fractions in Multiple Ways In this exploration, groups of students will be presented with a scenario involving cake through which they are tasked with decomposing a fraction in more than one way into a sum of fractions with the same denominator. Through completing the assigned tasks, students will: •

determine how a whole cake is divided equally into various parts.

•

write the fraction and the improper fraction for each slice of cake.

•

ﬁnd different possible combinations of cake slices handed out.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

Notes __________________________________________________________________________________________________________________________________________________

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

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COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

Compose and Decompose Fractions and Mixed Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students label fractional parts based on how far they are from zero to a point on a number line and justify the numerator and denominator using the visual model to explain. This activity is intended to assess mastery of the following standard(s): 3.NR.4.3 Represent fractions, including fractions greater than one, in multiple ways.

Materials

Preparation

Printed •

• • •

1 Student Handout (per group)

Reusable •

Prepare to project the Student Handout for students. Plan to have students work in groups for this activity. Print a Student Handout for each group.

1 Projector or document camera (per class)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4.

Project the Student Handout to the class. Give a Student Handout to each group. Instruct them to work individually and to label each of the points on the number lines. Invite students to explain how they decided on each denominator to their groups. Facilitate a class discussion about how students labeled the points on the number lines. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. a. In the ﬁrst model, the denominator is 4 because one whole (from 0 to 1 on the number line) is divided into 4 equal parts. b. In the second model, the denominator is 8 because one whole (from 0 to 1 on the number line) is divided into 8 equal parts. c. In the ﬁrst model, the numerator is 1 because where Leah will stop is past one of the three equal spaces between 0 and 1. d. In the second model, the numerator is 7 because the dot is past seven of the eight equal spaces between 0 and 1.

Invite students to share their answers on a document camera by explaining their thinking in relation to the number lines. FACILITATION TIP Ask students whether they can observe the relationship between the number of increments and the denominator signifying the fractional parts: the number of increments is always one less than the denominator.

Challenge students to name and explain other fractions that they see on the number lines. As students start naming other fractional parts represented on the number line, they are starting to decompose the whole number 1. When a student 2 answers _4_ for the ﬁrst model, ask the following question: a.

FACILITATION TIP

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

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How many more fourths do we need to get to 1 whole? _4_ more

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope. Notes

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COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

Compose and Decompose Fractions and Mixed Numbers Hook – Pizza Sharing ACTIVITY PREPARATION Students decompose fractions with the same denominator in more than one way, using equations to demonstrate understanding. Students will then check their equations using a pizza as a model.

Materials

Preparation

Printed •

•

1 Large Pizza (per small group)

Part I

Reusable • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Pair of scissors (per group)

Print 1 Large Pizza to show to the class.

Part II • • •

Consumable •

Plan to show the Phenomena Video.

1 Piece of printer paper (per small group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print 1 Large Pizza for each group. Gather enough pairs of scissors and sheets of printer paper for each group to have one of each.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP

Project this scenario and read it along with students. Guide students to read it more than once, helping them locate the math phrases and the important values. STEMscopes Tip The Communicate Math – Questioning page, found under the Communicate Math tab of the Teacher Toolbox, includes questioning strategies teachers can use to help challenge and stimulate students’ ability to clarify and extend their mathematical thinking. Examples of possible questioning types are provided.

5. 258

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Sam, Jackson, and Ethan pooled their money and ordered one large pizza to share. The large pizza came with 8 pieces, _1_ of the pizza. The boys ate the whole pizza. Sam had the so each piece made up __ 8 _1_ of the pizza. Jackson ate more than Sam, and smallest appetite and ate only __ 8 Ethan ate the most of the three boys. Using fractions, what are the ways the pizza could have been divided up? How can each boy’s portion be written in an equation that uses unit fractions? Show students the Large Pizza, and discuss the following questions: a.

DOK-2 How does using a model (from Large Pizza) help us solve the problem? The visual fraction model helps us understand the ways the pizza can be divided up. It also helps because the model works as a manipulative to help compose and decompose fractions in a concrete manner.

DOK-1 What is a unit fraction? A unit fraction is a fraction in which the numerator is 1.

DOK-2 When adding unit fractions with the same denominator, what happens to the numerators and denominators? The numerator becomes the sum of the numerators added and the denominator stays the same.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Show students the Large Pizza, and discuss the following questions: a.

3. 4.

DOK-1 What is a unit fraction? A unit fraction is a fraction in which the numerator is 1.

DOK-2 When adding unit fractions with the same denominator, what happens to the numerators and denominators? The numerator becomes the sum of the numerators added and the denominator stays the same.

Give each group the Large Pizza, a pair of scissors, and a piece of blank printer paper. Tell students they should use the information they have and their knowledge of fractions (especially unit fractions) to decompose the pizza into three fractions that represent the amount of pizza that each boy ate. They should accomplish this by cutting their copy of Large Pizza into eighths and using the manipulative unit fractions. Students should then solve for multiple solutions. Every time students find a solution that works with the parameters of the problem, have them write down the fractions that the boys ate. Then, students should decompose each boy’s portion into unit fractions using an equation. Give students about 5–10 minutes to work with their groups and the visual fraction pizza models and find multiple solutions, decomposing the whole pizza 8 as the fraction _8_ and then further decomposing each boy’s portion into fractions and finally into unit fractions and recording a variety of solutions. Note: There are two different solutions. Have a couple of groups present their solutions to the class, showing their equations and checking it with the pizza model to show how the whole pizza decomposes to create each boy’s share (fraction) of the pizza. Then, groups should further decompose each boy’s share by showing how many pieces of 1 pizza (_8_ of the pizza) each boy’s portion is. Discuss the following questions: a.

DOK-3 What were the ways you decomposed the whole pizza, 8 represented by the fraction __ , since it is divided into 8 equal pieces and 8 the boys ate the whole pizza? 8 4 3 1 i. _8_ = _8_ (Ethan) + _8_ (Jackson) + _8_ (Sam) 4 3 1 2 2 2 1 1 1 1 1 1 Ethan = _8_ = _8_ + _8_ = _8_ + _8_ = _8_ + _8_ + _8_ = _8_ + _8_ + _8_ + _8_ 3

Jackson = _8_ = _8_ + _8_ = _8_ + _8_ + _8_

FACILITATION TIP Consider having students count the number of slices in the pizza. Then, write an equation on the board that adds each piece of pizza using fractions. Have students identify the numerator and denominator as a review. FACILITATION TIP Guide students with questions such as “What is the fraction for 2 pieces of pizza? 4 pieces of pizza? 7 pieces of pizza?” Students can write their responses on dry-erase boards.

FACILITATION TIP Have students identify the information they know from the scenario. Students may use poster or butcher paper to explore the possible solutions.

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

Home

FACILITATION TIP Monitor groups as they are working. Guide the students with questions if they are struggling with the possible solutions.

STEMscopes Tip Use the Content Unwrapped element in the Home section to see the instructional expectations clariﬁed. Here you will see what students should be doing, what students should know, and implications for instruction. Included in this element is a complete vertical alignment related to this topic that shows how student expectations span across applicable grade levels.

Sam = _8_

8 5 2 1 ii. _8_ = _8_ (Ethan) + _8_ (Jackson) + _8_ (Sam) 5 4 1 3 2 3 1 1 2 2 1 2 1 1 1 Ethan = _8_ = _8_ + _8_ = _8_ + _8_ = _8_ + _8_ + _8_ = _8_ + _8_ + _8_ = _8_ + _8_ + _8_ + _8_ 1

= _8_ + _8_ + _8_ + _8_ + _8_ 2

Jackson = _8_ = _8_ + _8_ 1

Sam = _8_

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Compose and Decompose Fractions and Mixed Numbers Hook – Pizza Sharing 8

DOK-1 What operation did you use to show _8_ decomposed? Addition

DOK-2 How did you use the pizza model to check your solutions? We added all of the boys’ portions together to make sure the total added up 8 to 8 pieces or _8_, which is one whole pizza, what the boys ate altogether. We easily did this by combining the model pieces to see if the total made a whole pizza.

DOK-3 Why do all the smaller fractions have the same denominator of 8? They are all referring to the same whole pizza, which had 8 slices.

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

Compose and Decompose Fractions and Mixed Numbers Explore 1 – Compose and Decompose Unit Fractions ACTIVITY PREPARATION Students compose and decompose fractions using unit fractions.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments, and critique the reasoning of others. MP.4 Model with mathematics.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Pie Pieces (per class) 1 Exit Ticket (per student)

Preparation • • • •

Reusable • •

Plan to divide the class into 4 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart the Pie Pieces. Put one type of pie in each of the resealable bags. There will be four serving stations around the room, with a different type of pie at each station: • • • •

4 Resealable bags (per class) 4 Sets of fraction circles (per class) • •

Serving Station 1: Cherry Pie Serving Station 2: Pumpkin Pie Serving Station 3: Apple Pie Serving Station 4: Chocolate Pie

For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Print out the steps with visuals and place them at each station. Model the steps to follow for students.

2. 3. 4.

Read the following scenario to the class: Ann’s Bakery Shop is having a grand opening! They have baked several different pies and are handing out free samples at various serving stations. At each station, you will see how many slices of each type of pie was handed out at the grand opening. You will use this information to see how much pie was given out. Assign each group tol start at a different serving station. Give students about 10 minutes at each station before rotating. When students begin, they will complete the following steps at each station: a.

Read how many slices of pie were handed out at that station, and pull that many slices of pie out of the bag.

Determine how many slices make up a whole pie of that ﬂavor in order to determine the denominator for the fractional part of each piece.

Write an equation to show the sum of the fractional parts of each piece that was handed out.

Assemble the pie pieces into as many whole pies as possible. Draw a model of the slices on the Student Journal.

e. Write a mixed number representing how many slices of that ﬂavor were handed out. 262

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 How many pieces are in one whole _____ pie? Answers will vary.

DOK-1 What is the fractional part of one slice of _____ pie? Answers will vary.

DOK-1 How many slices of _____ pie were handed out? Answers will vary.

DOK-1 How could we ﬁnd the fractional part of the number of slices of _____ pie that were handed out? We could add the fractional parts for each slice handed out to ﬁnd the sum represented as a fraction.

DOK-1 How many whole pies can you make with the number of slices of _____ pie that were handed out? Answers will vary.

DOK-1 How much of the next pie do we have? Answers will vary. Students should ﬁnd the fractional amount of the pieces left over after assembling whole pies. (Model for students how this can be recorded as a mixed number.)

After completing each station, students will complete the reﬂection questions on the last page of their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

•

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions:

e. DOK-1 What do you notice about the fractional sum? The numerator is larger than the denominator, except the cherry pie. (Explain that this is called an “improper fraction.”)

Intervention

DOK-1 What part of a fraction tells you how many pieces make up one whole? The denominator does. DOK-2 How can we turn the starting information into a fraction? The number of slices in one pie is the denominator. The number of slices that were handed out is the numerator. DOK-2 What can you determine from a fraction that has a numerator greater than its denominator? When the numerator is larger than the denominator, we know that the fraction is greater than one whole. We can look at the denominator to see how many pieces will make up the whole. The numerator will help us determine how many wholes we can make based on the number of pieces there are. DOK-1 How did you add the fractions in your equations? We left the denominator the same, because the number of pieces in the whole pie did not change (the size of the slice did not change). We added all the numerators, which represented how many slices were handed out. DOK-2 How can you develop a mixed number from an improper fraction with no model? You can look at the denominator to see how many pieces one whole is broken into. Each group of that number is one whole. The leftover pieces form a fraction.

FACILITATION TIP Reveal the terms to students by using Picture Vocabulary slides and discussing their experiences as they explore the concept. FACILITATION TIP On the board, write an example of a fraction, an improper fraction, and a mixed number fraction. Have students write each term on a sticky note and then place each sticky note with the correct example.

FACILITATION TIP

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

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Using the Print Files, project these Math Chat questions and record some student responses as you guide the discussion.

STEMscopes Tip Transition students into the current concept by meeting them at their level with the Hook activity, found in the Engage section. These real-world scenario-based activities frame the overall learning throughout the scope and serve as both an introduction and concluding aspect of each concept. The Hook fosters personal growth.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Consider using part or all of this Exit Ticket as a pre-assessment for this Explore activity.

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Compose and Decompose Fractions and Mixed Numbers Explore 2 – Compose and Decompose Fractions in Multiple Ways ACTIVITY PREPARATION Students decompose a fraction in more than one way into a sum of fractions with the same denominator.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments, and critique the reasoning of others. MP.4 Model with mathematics.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Cake Cutouts (per group) 1 Exit Ticket (per student)

Consumable •

Preparation • • • • •

2 Resealable bags (per group) • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Cake Cutouts for each group of students. Cut apart all of the cookie cakes, cutting them into individual slices, and put the pieces into resealable bags. Label them “Bag 1.” Cut apart all of the mini-cheesecakes, cutting them into individual slices, and put the pieces into separate bags. Label these “Bag 2.” Give each group a bag 1 and a bag 2. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Allow students time to assemble the cakes on their own. Then, ask, “How many slices are in each cake?” Explain that the number of slices is the fraction. FACILITATION TIP Have students physically count two examples of different combinations of slices of cake before releasing them to complete the activity. 264

Read the following scenario to the class: Ann’s Bakery prepared several types of cakes to hand out at their grand opening event. Each bag contains pictures of the types of cakes that were served. There were several cookie cakes and minicheesecakes for guests to sample. For each bag, you will open it, assemble the cakes, and use the pictures to answer the questions on your Student Journal. Students will work cooperatively to assemble the cakes in bag 1. After assembling the cakes in bag 1, they will complete the following steps: a.

Determine how many slices each cake is divided into and draw them on their Student Journals.

Write the fraction for one slice of cookie cake.

Write the improper fraction for the 17 slices of cake that were handed out.

Find two possible combinations of slices that were handed out and write an equation that represents these possible combinations.

Engage

Explore

Explain

Elaborate

Evaluate

Determine how many slices each cheesecake is divided into and draw them on their Student Journals.

Write the fraction for one slice of cheesecake.

Develop two possible combinations of flavors if there are three slices of cheesecake and at least two flavors that were passed out. Write an equation to represent the combinations and label the fractions by flavor.

Develop two possible combinations of flavors if there are ten slices of cheesecake and every flavor had at least one slice passed out. Write an equation to represent the combinations and label the fractions by flavor.

FACILITATION TIP Depending on your students’ prior knowledge, consider using a rectangular model in addition or alternatively.

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How do you know what fraction each cookie or cheesecake slice represents? How many pieces is always the denominator.

DOK-1 Do you have the same combination as everyone in your group? No. Is that ok? Yes, as long as we have the same total.

DOK-1 What does the phrase at least mean? It has to have that amount or it could have more, not less.

DOK-1 Are these the only combinations? No

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-1 How can we decompose an improper fraction? We can separate it into smaller fractions with like denominators. • DOK-2 What did the fractions in your equations have in common? Explain why. They all had the same denominators. Each fraction represented one equal part of the same whole. • DOK-2 Compare your combinations for the possible 17 slices that were handed out at the bakery from bag 1. How do your combinations compare to another group’s combinations? Answers will vary, but students should see that there are many ways to reach the sum 17. The denominators in all the equations will be 8, but there are many combinations for numerators because you could have combined different amounts of different ﬂavors. • DOK-2 Does this lesson have to be about circle-shaped cakes or pies? Explain. No, as long as the slices are all the same size •

Post-Explore

2. 3. 4.

Acceleration

Students will work cooperatively to assemble the cakes in bag 2. After assembling the cakes in bag 2, they will complete the following steps:

Math Chat

Intervention

FACILITATION TIP Have students write the total number of slices in each cake and label it as a denominator. STEMscopes Tip The Exit Ticket is used as a quick formative assessment to determine whether students mastered the skills presented in the Explore or whether additional instruction is needed. It can also be used to reinforce the skills and concepts presented. Exit Tickets and Answer Keys are found in the print ﬁles on the right of the screen and can be downloaded and modiﬁed as needed.

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FACILITATION TIP Consider asking an open-ended question about fraction models. “What other shapes or models could be used to help us solve this cake problem?” FACILITATION TIP Before this Exit Ticket, determine what models (circles, rectangles, number lines, or other) students should use to show their understanding about mixed numbers.

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Compose and Decompose Fractions and Mixed Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Compose and Decompose Unit Fractions Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Compose and Decompose Fractions in Multiple Ways Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

No Bones about It

Tom Monaghan

A quick story to engage student interest along with four problems covering previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further.

Math Story

Fluency Builder

Going on a Hike

Match Improper Fractions to Mixed Numbers

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Interactive Practice

Wild Expansion

Farm Fields

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

A game to practice the skills established by the standards in the scope

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

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PhET Interactive Simulation Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

267

Students who are still acquiring the concept and need remediation

Resources

Students who have mastered the concept and need extension 268

Students

Notes

 Fluency Builder  Small-Group Intervention

 Career Connections

Students who are approaching mastery and need review

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

Compose and Decompose Fractions and Mixed Numbers

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can represent whole numbers and fractions as the sums of unit fractions.

I can decompose a fraction into a sum of fractions with the same denominator in more than one way.

What prompts will be used?

What does mastery look like?

COMPOSE AND DECOMPOSE FRACTIONS AND MIXED NUMBERS

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I can write an equation to represent each composition and decomposition.

I can use a fraction model to justify how to compose and decompose a fraction.

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SCOPE 1

Add and Subtract Fractions and Mixed Numbers Scope Introduction SCOPE SUMMARY

Student Expectations

4.NR.4.6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Students add and subtract fractions and mixed numbers by joining and separating parts of the same whole. They apply these operations to solve real-world problems. Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100. Students may find that in certain scenarios, they need to regroup a mixed number by converting a whole number into an equivalent fraction with the same denominator as the fraction before so they can find the difference. Not only do students find solutions to problems with addition and subtraction of fractions (including fractions greater than one and mixed numbers) with like denominators, they also employ the use of a variety of models and concrete objects, including pattern blocks, diagrams, fraction circles, and fraction tiles. Visual fraction models and equations are used to represent real-world problems as they work to find solutions.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students measure with rulers marked with halves and fourths of an inch. Third grade also develops an understanding of fractions as numbers, including fractions greater than one, being composed of unit fractions. They begin to use fractions to solve problems involving equivalence and comparisons, understanding that the size of a fractional part is relative to the size of the whole. In fourth grade, prior to this standard, students learn that they can compose or decompose whole numbers and fractions as a sum of unit fractions or a sum of fractions with the same denominator in more than one way. Students can then take this representation and write an equation.

In ﬁfth grade, students add and subtract fractions and mixed numbers with unlike denominators, interpret multiplication as scaling, and divide unit fractions by whole numbers and whole numbers by unit fractions.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

read, write, and represent fractions.

•

solve a scenario.

•

represent answers in various ways.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

add and subtract fractions

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 270

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Join and Separate Parts of a Whole In this exploration, students will work with groups to solve scenarios involving following recipes for snow cones, calculating the total amount of syrup each recipe, and determining how much is left over. In solving the scenario, students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

add and subtract fractions.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Add Fractions and Mixed Numbers with Like Denominators In this exploration, students will be presented with a real-world scenario where they are tasked with ﬁguring out how many miles runners have completed and how many laps or miles the runners have completed. Through solving the scenario, students will: •

add fractions and mixed numbers with like denominators.

•

use models and equivalent fractions.

Subtract Fractions and Mixed Numbers with Like Denominators In this exploration, students will be introduced to a realworld scenario involving students ﬁguring out how many essentials are left after a rock climbing adventure and how much farther the climbers must go to get to the bottom of a mountain. In solving the scenario, students will: •

subtract fractions and mixed numbers with like denominators.

•

use a variety of strategies.

Explore 4

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment. Solve Addition and Subtraction Fraction Problems In the ﬁnal exploration, students solve a variety of realworld problems to apply their skills learned within this scope. In solving the scenarios, students will: •

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

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add and subtract fractions and mixed numbers.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

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Add and Subtract Fractions and Mixed Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students read a scenario and represent the answer in various ways. This activity is intended to assess mastery of the following standard(s): 3.NR.4.1 Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. Use parts of a whole, parts of a set, points on a number line, distances on a number line and area models.

Materials

Preparation

Printed • •

1 Scenario Card (per class) 1 Set of Answer Choices (per class)

Reusable • • •

• • •

Prepare to project the Scenario Card for students. Print one set of Answer Choices for the class. Post one answer choice in each corner of the classroom. Plan to have students work in pairs to complete this activity.

1 Projector or document camera (per class) 1 Dry-erase board (per pair of students) 1 Dry-erase marker (per pair of students)

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

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PROCEDURE AND FACILITATION POINTS 1. 2. 3.

Distribute one dry-erase board and one dry-erase marker to each pair of students. Project the Scenario Card to the class, and give time for pairs of students to discuss and draw a model that represents the solution. Invite students to stand up and compare their answers to the answer choices around the room. Encourage students to determine if they agree or disagree with the answer choices and to make changes if needed. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of students’ prior knowledge and misconceptions about decomposing fractions and representing fractions on a number line and as an area model. a. Answer choice A is correct because Steve will need 6 pieces for himself and 5 friends. Since there are 6 people, each will get 1 of the 6 pieces. b. Answer choice B is correct because Steve will cut the brownies into 6 1 equal pieces. Each piece will be _6_ of the pan. c. Answer choice C is correct because Steve will cut the pan of brownies into 6 equal pieces. The number line from 0 to 1 represents the whole pan of brownies. The 6 equal pieces of the pan of brownies are 1 represented by the 6 equal parts on the number line. The dot on _6_ shows the 1 piece that each person will receive. d. Answer choice D is correct because the rectangle is divided into 6 equal 1 pieces with equal areas, so the area of each piece is _6_ of the area of the shape.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Provide students with access to linking cubes and visual fraction models. If students are relying on concrete representations, they may beneﬁt from participation in the Foundation Builder. FACILITATION TIP Record a list of the ways in which a fractional answer can be expressed (by using word form, fraction notation, a number line, or a fraction model or by describing a part of the whole, etc.) STEMscopes Tip In My Math Thoughts, a journaling activity located in the Explain section, students practice their writing skills through a collection of journal prompts. These prompts are designed to allow students to explain their mathematical thoughts, attitudes, and mindsets in relation to concepts, problem solving, and realworld application of the standard(s) addressed.

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Add and Subtract Fractions and Mixed Numbers Hook – Add and Subtract Fractions, Baby! ACTIVITY PREPARATION Students add and subtract fractions with equal denominators using objects, pictorial models, and equations.

Materials

Preparation

Printed

Part I

•

1 Student Handout (per student)

• •

Reusable • • • • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Set of 10 pieces of yellow yarn, each 12 inches in length (per pair of students) 1 Rubber band to hold yarn together (per pair) 1 Dark yellow colored pencil (per student)

Plan to show the Phenomena Video. Print the Student Handout for each student.

Part II • •

•

Plan to have students work in pairs to complete this activity. Prepare the bundles of yarn. Cut all pieces of yarn into 12-inch strands. Count out 10 strands of yarn for each pair of students. Bundle each set of 10 strands of yarn with a rubber band. Gather supplies for each pair of students: bundles of yarn and yellow colored pencils.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore FACILITATION TIP

The Foundation Builder activity can be used to practice converting mixed numbers into improper fractions. Improper fractions are needed to add and subtract fractions.

3. STEMscopes Tip Math Story, found in the Elaborate section, supports students’ literacy and addresses the math concept(s) in each scope. The teacher or students read a real-world passage, and students practice ﬁnding the information they need to solve relevant math problems. Also included are reading comprehension questions designed to strengthen students’ reading skills.

4. 5.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Your mom has to do some work on her computer and wants you and your friend to feed your baby brother Phil some spaghetti for lunch. She says if Phil eats all of his spaghetti, you can put him down for a nap and hang out with your friend. Your friend starts feeding Phil and gets 3 4 him to eat ___ of the spaghetti. You take a turn and get Phil to eat another ___ of the 10 10 spaghetti. What fraction of spaghetti is left for you to feed Phil before you can put him down for a nap? Show students the Student Handout. Discuss the following concepts and questions: a.

Show the class one set of the yarn pieces. Tell them this yarn represents all the spaghetti their mom wants them to feed their baby brother, Phil.

DOK-1 Have one student come up and count how many pieces of yarn there are. There are 10 pieces of string.

DOK-1 Ask the class, “How much of the spaghetti does each strand 1 represent?” Each strand represents ___ of the spaghetti. 10

DOK-1 Have a different student come up and show the amount your 4 friend fed Phil (___ ). The student should pull out four strands. 10

e. DOK-1 Have another student come up and show the amount you fed Phil 3 (___ ). The student should pull out three strands. 10 274

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What operations will I need to perform in what order to solve the problem? I can solve the problem in more than one way. I think the easiest way is to add the two fractions together and then subtract the total from the whole. DOK-1 In order to add or subtract fractions, what must occur with the denominators? The denominators must be the same.

h. DOK-2 How can models, both concrete and pictorial, help solve the problem? A concrete model can help us to visualize what is happening. Drawing a pictorial model can help reinforce what we have learned by helping us to both visualize it and understand it as we construct it. i. DOK-2 What is the next step after using models? The next step is writing an equation or equations to demonstrate an understanding of how to add and subtract fractions. 6.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions and questions: a.

Show the class one set of the yarn. Tell them this yarn represents all the spaghetti their mom wants them to feed their baby brother, Phil.

DOK-1 Have one student come up and count how many pieces of yarn there are. There are 10 pieces of yarn.

DOK-1 How much of the spaghetti does each strand of yarn represent? 1 Each strand represents ___ of the spaghetti. 10

DOK-1 Have a different student come up and show the amount your 4 friend fed Phil (___ )).. The student should pull out four strings. 10

e. DOK-1 Have another student come up and show the amount you fed Phil 3 (___ ). The student should pull out three strings. 10 f.

DOK-1 In order to add or subtract fractions, what must occur with the denominators? The denominators must be the same.

Intervention

Acceleration

FACILITATION TIP Refresh students’ understanding that to add and subtract fractions, the denominator must be the same. FACILITATION TIP Student experience with adding and subtracting fractions using common denominators may be limited. Take time to quickly check if students can successfully add fractions with like denominators and then unlike denominators. Use individual whiteboards. FACILITATION TIP Use the model to demonstrate that only the numerator is being added and subtracted. FACILITATION TIP Project the scenario so that students can read it along with you.

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STEMscopes Tip The Standards-Based Assessment is found within the Evaluate section for Grades 2–5. Students demonstrate mastery of the concepts covered in the scope using multiple-choice and gridded response questions aligned to the scope standard(s). This assessment can be assigned and scored digitally, printed, or edited to meet students’ individual needs.

Give each student the Student Handout and a yellow colored pencil. Give each pair of students a bundle of yellow yarn. Tell students they should act out the scenario using the yarn as a model for the spaghetti. After students have acted out the scenario with the yarn, have them use the yellow colored pencil to draw out the scenario on the top half of the Student Handout. Then, have students write the two equations necessary to solve the problem. (Most students will choose to use one addition equation and one subtraction equation, but some will use two addition or two subtraction equations.)

FACILITATION TIP Use the model to demonstrate that only the numerator is being added and subtracted. FACILITATION TIP If time is limited, have one or two students demonstrate the scenario using the yarn and the document camera.

FACILITATION TIP Students can use different strategies to solve the problem. Listen to students’ discussions, and address misconceptions. 275

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Add and Subtract Fractions and Mixed Numbers Hook – Add and Subtract Fractions, Baby! 8. 9. 10. 11. STEMscopes Tip Create Your Own, located in the Grades 3–5 Acceleration section, is an openended activity where students use the skills and concepts learned in the scope to create a new product. Create Your Own comes with a handout that takes students through the creative process and a rubric that assesses students’ plans and products.

Finally, have students solve the equations and answer what fraction of spaghetti is left to feed Phil before putting him down for a nap. Give students about 10 minutes to use the concrete model, draw the pictorial model, and write and solve the equations to ﬁnd the solution. Then, have each pair of students share their pictorial models and pictures with another pair of students and compare their solutions. Gather students in a whole group, and discuss the following questions: a.

DOK-2 What operation did you use to ﬁnd the amount of spaghetti your 3 4 7 friend and you fed Phil? We used addition. ___ + ___ = ___. (Note: some 10 10 10 students may do two steps of subtraction, and their ﬁrst step would 10 ___ 6 4 be ___ − = ___.) 10 10 10

DOK-2 What operation did you use to ﬁnd the amount you still needed to feed Phil before you could put him down for a nap? We used 10 ___ 3 7 subtraction. ___ – = ___. (Note: some students might also use addition 10 10 10 10 7 by starting at ___ and counting up to ___ . Some other students might 10 10 have used subtraction for both steps, and their second step would 6 3 3 be ___ – ___ = ___.) 10 10 10

DOK-2 What do you notice about the fractions that we added and/or subtracted? In this problem, the denominator stayed the same and the numerators changed. Or, we are adding and subtracting equal parts of 10, or tenths.

DOK-3 Are there different ways to solve this problem? Yes, most people added and then subtracted. Some people added for both steps. Other people subtracted for both steps. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Add and Subtract Fractions and Mixed Numbers Explore 1 – Join and Separate Parts of a Whole ACTIVITY PREPARATION Students explore addition and subtraction of fractions while following snow cone syrup recipes.

Standards for Mathematical Practice • • •

MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Recipe Cards (per group) 1 Exit Ticket (per student)

• • •

• • • •

Reusable • • •

1 Set of pattern blocks (per group) 1 Resealable bag (per group, optional) 1 Set of colored pencils (per student)

Plan to divide students into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student and a set of Recipe Cards for each group. You can divide the pattern blocks into bags by shape if you do not have enough for a full set for each group. Each group will need the following blocks:

• •

1 hexagon pattern block 4 trapezoid pattern blocks 5 rhombus pattern blocks (the wider ones, not the skinny ones) 6 triangle pattern blocks

For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions by using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Pattern Blocks)

PROCEDURE AND FACILITATION POINTS Part I: Mixing Syrup FACILITATION TIP

1. 2.

Have students use the trapezoid blocks and triangle blocks in different combinations to make a hexagon.

FACILITATION TIP Discuss real-world scenarios, such as how someone may adjust a recipe for more or fewer people.

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Give a set of pattern blocks to each group. Allow students a few minutes to explore the pattern blocks. Encourage students to look for relationships between the sizes of the blocks. Discuss the following questions: a.

DOK-1 What do you notice about the hexagon block? It is the biggest block. I can use the other blocks to build the hexagon.

DOK-1 What do you notice about the trapezoid block? It is half of the hexagon because it takes two of the trapezoids to make the hexagon. (Continue discussing each pattern block and what fractional part it is of the hexagon.)

DOK-1 Which block would you consider to be one whole? The hexagon would be one whole.

Read the following scenario to the class: You are working at Juicy-O Snow Cones! Your job is to mix the different ingredients to create the unique syrup ﬂavors the company offers. The company has the recipes for all the syrup ﬂavors written on recipe cards. You will need to follow the recipe and calculate the total amount of syrup each recipe will produce. © Accelerate Learning Inc. - All Rights Reserved

6. 7. 8.

Explore

Explain

Elaborate

Evaluate

• • •

Students then use the pattern blocks to model each recipe. Students should think about which size of block could represent each fractional part and make sure they use enough of those pieces to represent the ingredients listed on the cards. Students then draw their models in their Student Journals. Students should draw the shapes of the pieces inside the hexagon provided. Students should use their colored pencils to color the pieces on their Student Journals according to the ﬂavor color key on the recipe card document. Students then write an equation that shows the addition of all the recipe ingredients in order to ﬁnd the total amount of syrup. If the total amount of ingredients is greater than one, they need to write the answer as both an improper fraction and a mixed number. After Part I, invite the class to a Math Chat to share their observations and learning.

DOK-1 Look at your model for the Not Birthday Cake ﬂavor. How many thirds do 5 you have in your model? We have ﬁve-thirds (or _3_). DOK-2 Can you show the total in a different way with the fewest number of pattern blocks? We can show it with one whole hexagon and two rhombuses. 2 DOK-2 How does this look as a mixed number? It is 1_3_ 5 DOK-2 So what does this mean about the improper fraction _3_ and the mixed 2 __ number 1 3 ? They are equal.

Part II: Syrup Inventory 1. 2. 3.

4. 5.

Acceleration

DOK-2 Which block could we use to represent a whole cup? We could use the hexagon.

Math Chat •

Intervention

Have students look at the Recipe Cards. Students should notice that each part of the recipes is a fraction of a cup. a.

Engage

Read the following scenario to the class: You have a report due to your boss (teacher). I want to know how much of each syrup is left at the end of the day. Students may continue to work in small groups, or they may complete Part II individually. Students may use the pattern blocks to help them determine how much is left. They do not have to draw their models, but they can use their models to help ﬁnd how much of each syrup is left. Instruct students to write a number sentence for each type of syrup on their Student Journals. After Part II, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP If time and supplies are limited, consider allowing some students to just use letters rather than colors on their Student Journals. Students can build the shapes and draw them, but won’t need colored pencils that match the key. FACILITATION TIP Monitor groups as the students write the equations to ensure that they are converting the improper fraction to a mixed number. The pictorial models will assist students in the conversion.

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

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FACILITATION TIP Take time to show several more improper and mixed numbers that are equal. STEMscopes Tip Blackline Masters, located in the Essentials section of the Teacher Toolbox, provide teachers with frequently needed instructional print materials. There are a wide variety of printables, including an analog clock, coordinate plane, fraction strips, hundreds charts, assorted number lines, sharing mats, and ten frames.

Math Chat • •

DOK-1 What operation did you use to ﬁnd how much syrup is left? Subtraction DOK-2 What part of the model represents the difference? How many pattern blocks are left after you take away what was sold

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP When you preview this Exit Ticket with students, consider how students can show their thinking on the rectangular model. Have them use the letters of the days of the week rather than colors if needed.

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Add and Subtract Fractions and Mixed Numbers Explore 2 – Add Fractions and Mixed Numbers with Like Denominators ACTIVITY PREPARATION Students are able to solve word problems that involve the addition of fractions and mixed numbers with like denominators by using models and equivalent fractions.

Standards for Mathematical Practice • • •

MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Racing Scenario Cards (per class) 1 Set of Training Cards (per group) 1 Exit Ticket (per student)

Reusable Part I • • •

6 Sets of fraction tiles (per class) 6 Sets of fraction circles (per class) 1 Paper clip (per group)

Part II • •

6 Sets of fraction circles (per class) 6 Clear resealable bags (per class)

Preparation • •

Plan to divide the class into 4 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student.

Part I • • •

For each group of students, print a set of Training Cards. The Training Cards can be printed on card stock and laminated for durability, if desired. Cut the Training Cards apart, and paper clip them for each group. Each group gets three sets of either fraction circles or fraction tiles. Make sure they don’t have a mixture of fraction manipulatives within a group.

Part II • • • •

Print one set of the Racing Scenario Cards for the class. Optionally, the Racing Scenario Cards can be printed on card stock and laminated for durability. Cut each card apart, and place them around the room at stations. Label each resealable bag with one of the following words: “Thirds,” “Fourths,” “Fifths,” “Sixths,” “Eighths,” or “Tenths.” Gather the six sets of fraction circles, and separate each size into resealable bags. • • • • • •

• • •

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Scenario 1: the thirds from each fraction circle set Scenario 2: the fourths from each fraction circle set Scenario 3: the ﬁfths from each fraction circle set Scenario 4: the sixths from each fraction circle set Scenario 5: the eighths from each fraction circle set Scenario 6: the tenths from each fraction circle set

Place each ﬁlled bag at the correct Racing Scenario Card. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions by using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles and Fraction Tiles)

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS Part I 1.

2. 3. 4. 5. 6. 7.

Read the following scenario to the class: Some fellow runners are training to run races. Each day, they run a different amount, depending on their training schedule. It is our job to ﬁgure out how many miles each runner has completed for their training. Provide each student with a Student Journal. Give a set of Training Cards and three sets of fraction circles or three sets of fraction tiles to each group. Have students look at the Megan training card. Read the scenario together. Instruct students to work together with their groups and use their fraction circles or tiles to solve the scenario. Monitor groups as they solve, and note the different strategies they may use in order to join their mixed numbers. Once students are done, ask a few groups to share the strategy they used to solve. Groups may even demonstrate their strategy to the class by using their circles or tiles. a.

Some groups may have changed both amounts into improper fractions and added, while others may have added the wholes and then the fractional parts.

After Part I, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Using the Training Cards, students should discuss the information needed and a strategy to solve the problem.

FACILITATION TIP

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Consider allowing students some extra time to practice presenting before they share with the class.

Math Chat • • •

•

• •

9. 10. 11. 12.

DOK-1 What operation are we using in order to ﬁnd our total miles? We are using addition. DOK-1 What happens when we add our two mixed numbers? We get two wholes 4 and four-fourths (_4_). DOK-2 Can you show the total in a different way with the fewest number of pattern blocks by using regrouping? Yes, I can regroup my four fourths into a whole, and now I will have three wholes. DOK-2 Is there another way I could add my numbers without using mixed numbers? Yes, I could decompose my mixed numbers into fractional parts and get six fourths for both. DOK-1 What happens when I add my improper fractions? I have twelve-fourths, which is equivalent to three wholes. DOK-2 Why do both strategies still get us the same answer? Answers may vary. Both answers still get us the same answer because we are still working with the same amounts. They are just being represented differently based on how they were decomposed and joined together.

STEMscopes Tip Access the Assessment Builder under Assessments on the menu bar to build and save customizable assessments that can be accessed and edited at any time. Search the English and Spanish assessment item banks by standard or lesson, key words, grade level, topic, and question type. Once the assessment is built, choose to administer it in print and/or digital form.

After groups have shared their strategies and you’ve completed the Math Chat, students then record their work on their Student Journals. Next, read the Calvin scenario with the class, and encourage the groups to work together to solve it. Allow students to discuss the strategies they used to ﬁnd the total distance Calvin ran. Have the students record the model, addition sentence, and solution statement that they used to solve for Calvin on their Student Journals.

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Add and Subtract Fractions and Mixed Numbers Explore 2 – Add Fractions and Mixed Numbers with Like Denominators Part II 1.

FACILITATION TIP Write the different strategies from Part I on the board for student reference. FACILITATION TIP

4. 5.

As students read the Racing Scenario Cards, have them identify the laps. Have students discuss whether the denominators are all the same for each scenario.

Read the following scenario to the class: There are different kinds of racing competitions all over the world and in our communities. In these different races, there are different amounts of laps or miles the competitors complete. It is your job to help these competitors ﬁgure out how many laps or miles they completed. Explain that students are now to use the knowledge they gained from Part I to help them complete the stations in Part II. Encourage students to work together in using the fraction circles or tiles at each station to help them solve. Remind students that they can use any of the strategies they explored in Part I. Students record their work for each station on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP Manipulating the fraction tiles for regrouping is a scaffold for students to regroup later without the fraction tiles or model.

DOK-2 How can we represent the distances given in the scenario? Answers may vary. The whole number tells me how many wholes to create, and the fraction tells me how many fractional parts I need. If I decide to make improper fractions, I use the denominator to make sure that, when I decompose the wholes, I have the correct number of pieces. I create my model by using the numerator from my fraction and placing that many fraction tiles as my fractional parts.

DOK-2 How do we represent the joining of the distances completed? Answers may vary. I can use my fraction tiles to make a model of each mixed number or fraction, and then I add those together and regroup, if necessary. I can add by using improper fractions or keep the mixed numbers and regroup as needed when adding the fractional parts.

DOK-2 How can we use the model to help us solve the scenario? Answers may vary. My model can help me ﬁnd the equivalent fractions. My model can help me understand the regrouping of a whole number into fractional parts or fractional parts into a whole.

After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat • • STEMscopes Tip Interactive Practice games are found in the Elaborate section. Students can use the games not only throughout the scope to reinforce relevant skills and concepts but also throughout the year to review skills and concepts. Interactive Practice games provide students with another opportunity to see the concepts covered in action.

• • •

•

282

DOK-1 What operation did you use to find how many laps or miles were completed in each scenario? Addition DOK-1 Does it matter the order in which you add your fractions or mixed numbers? No, the order in which you add doesn’t matter. This is known as the commutative property. DOK-1 What does the denominator represent in a fraction? The denominator shows the number of equal pieces in a whole. DOK-1 Can you add denominators? Explain. No, the number of fractional pieces in a whole does not change just because you are adding. DOK-2 How do you find the numerator for your answer in an addition problem? You add or join the numerators of your fractions or mixed numbers. If your numerator is greater than your denominator after your addition, then you must regroup by using the denominator to help you figure out how many fractional parts are in a whole. DOK-2 If our answer is an improper fraction, how can I turn that into a mixed number? I can regroup my improper fraction by using the denominator to tell me how many fractional parts make a whole. For example, in scenario 1, my answer 5 was 2 and _3_. I regrouped the fraction by making a group of three fractional parts 2 into a whole. This then created three wholes and left my fraction as _3_. My final 2 answer was 3 and _3_. © Accelerate Learning Inc. - All Rights Reserved

•

Engage

Explore

Explain

Elaborate

Evaluate

DOK-3 How could you solve each addition scenario without a model? I can solve by using equivalent or improper fractions, or I can use the standard algorithm of addition to help me solve. If my answer gives me an improper fraction, then I can use the denominator to help determine how many parts are in my wholes to help me regroup.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Intervention

Acceleration

STEMscopes Tip Within the Teacher Toolbox under the Communicate Math tab is the Communicate Math – Making Connections page. This resource provides teachers with ways to explicitly emphasize connections students can make to help them bridge their knowledge from concept to concept. Possible types of connections are included.

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ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Add and Subtract Fractions and Mixed Numbers Explore 3 – Subtract Fractions and Mixed Numbers with Like Denominators ACTIVITY PREPARATION Students are able to solve problems that involve subtraction of fractions and mixed numbers with like denominators by using a variety of strategies.

Standards for Mathematical Practice • • •

MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Essentials Cards (per group) 1 Set of Rock Climbing Cards (per class) 1 Exit Ticket (per student)

Reusable Part I • • •

6 Sets of fraction circles (per class) 6 Sets of fraction tiles (per class) 1 Paper clip (per group)

Part II • •

6 Sets of fraction tiles (per class) 6 Clear resealable bags (per class)

Preparation • •

Plan to divide the class into 4 to 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student.

Part I • •

For each group of students, print a set of Essentials Cards. The Essentials Cards can be printed on card stock and laminated for durability, if desired. Cut apart the Essentials Cards, and paper clip them together for each group.

Part II • • • •

Print one set of Rock Climbing Cards for the class. The Rock Climbing Cards can be printed on card stock and laminated for durability, if desired. Cut each card apart, and place them around the room as stations. Label each resealable bag with one of the following words: “Fourths,” “Eighths,” “Sixths,” “Tenths,” “Twelfths,” “Thirds.” Gather the six sets of fraction tiles, and separate each size into resealable bags as follows: • • • • • •

• • •

284

Mt. Fangtooth: the fourths from each tile set Mt. Bearclaw: the eighths from each tile set Mt. Crooked Thumb: the sixths from each tile set Mt. Camel’s Back: the tenths from each tile set Mt. Lakeview: the twelfths from each tile set Mt. Pumice Rock: the thirds from each tile set.

Place each ﬁlled bag at the correct Rock Climbing Card. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions by using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles and Fraction Tiles)

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS Part I 1.

2. 3. 4. 5. 6. 7.

Read the following scenario to the class: Some fellow hikers are getting ready to go rock climbing. They have packed some important items for the journey. It is our job to ﬁgure out how much of their essentials remain after their rock climbing adventure. Divide students into 4 groups. Provide each student with a Student Journal. Give a set of Essentials Cards and three sets of fraction circles or three sets of fraction tiles to each group. Have students look at the Water Essentials Card. Read the scenario together. Instruct the students to work together with their groups and to use their fraction circles or tiles to solve the scenario. Notice which groups decide to decompose just one whole and solve that way and which groups decompose all the wholes in order to solve. Choose one group that regrouped one whole and one group that regrouped both wholes, and allow them to share their strategies. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

4 DOK-2 How can you take away _5_ if you only have two wholes? I can 5 4 decompose a whole into _5_ and take _5_ away. I know two wholes is the 10 10 4 , so I can trade in both wholes for ___ and take _5_ away. same as ___ 5 5

Explain how both strategies can be represented with an equation. Have students help write equations to show both strategies, and discuss how the equation represents the strategy. 4

10.

11.

To engage students, demonstrate with bottles of water, similar to the scenarios. Have students discuss what operations should be used.

FACILITATION TIP Have each group discuss and decide the strategy they will use to solve the problem.

DOK-2 How are these strategies similar? How are they different? Both strategies show how one whole can be decomposed into fractional parts so you can subtract from them. The ﬁrst strategy only decomposed one whole, and the other decomposed all the wholes.

__ = ___ – __ = __ = 1__ i. Example: 2 – _5_ = 1_5_ – _5_ = 1_5_ (or) 2 – __ 5 5 5 5 5

FACILITATION TIP

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After groups have shared their strategies, students record their work on their Student Journals. Next, read the Trail Mix Essentials Card with the class. Encourage the groups to work together to solve this scenario using a different strategy than the one they used for the Water Essentials Card. Monitor students as they work to solve the Trail Mix Essentials Card. Remind them that they are trying to use a different strategy in order to solve. Discuss the following questions: a.

DOK-2 What were some strategies other groups mentioned that you can try? Answers may vary. One group decomposed all the wholes into 9 6 3 fractional parts, which gave them _4_ – _4_ = _4_.

DOK-2 Are there other ways that we could represent the wholes or each whole? Answers may vary. Instead of decomposing both the wholes in 1 9 2_4_ into fractional parts to get _4_, you could decompose only one of the 5 wholes to get 1_4_.

FACILITATION TIP Groups with different strategies can provide their equations to other groups.

STEMscopes Tip Each grade level includes a Daily Numeracy program. In it, teachers will ﬁnd an overview of Daily Numeracy and how it can be used in the classroom, a variety of short activities focused on developing students’ mental math strategies and number sense, and resources that supplement the activities to build students’ thinking and reasoning skills.

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Add and Subtract Fractions and Mixed Numbers Explore 3 – Subtract Fractions and Mixed Numbers with Like Denominators c.

STEMscopes Tip Interactive Practice, located in the Elaborate section, involves interactive games that students can access throughout the scope to reinforce skills related to the standard(s) addressed in the scope. Interactive Practice games give students another opportunity to see the concepts learned in action.

12. 13.

2. 3.

Challenge groups to use different strategies than they used in Part I.

DOK-1 Is there a way we could represent decomposing or regrouping with our models? Answers may vary. Yes, we can use diagrams as fraction models where wholes can be decomposed, or partitioned, into fractional parts and fractional parts can be regrouped to represent mixed numbers.

After students have had an ample amount of time to solve, discuss with students which strategy they used and the relationships between their strategies. Once their strategies have been discussed, have students record their models, their work, and their solution statements on their Student Journals.

Part II 1.

FACILITATION TIP

DOK-1 Is there a way we can make equivalent fractions? Answers may 6 vary. If I have an improper fraction, like _4_, and I want to make it a mixed number, I can use division. I know that one whole equals four parts. I can take four parts out of six and make one whole. 6 – 4 = 2, so my 2 mixed number is 1_4_.

5. 6.

Read the following scenario to the class: After gathering the hiking essentials, some friends have decided to hit the trails and go rock climbing. Each friend has chosen a different mountain to climb. Each mountain is a different height. They have rappelled some of the way down, but it is your job to ﬁgure out how much farther they must go to get to the bottom of the mountain. Divide students into six groups, and assign each group a station at which to begin. Explain that students are to use the knowledge they gained from Part I to help them complete the stations in Part II. Encourage students to work together in using the fraction tiles at each station to help them solve. Remind students that they can use any strategy they choose to solve. Students record their work for each station in their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 How do we represent our starting amount? Answers may vary. I use the denominator to make sure I decomposed the whole into the correct number of pieces. I create my model by using the numerator from my fraction and placing that many fraction tiles as my starting amount.

FACILITATION TIP Have students place an X on the fraction model that is being subtracted. The fraction models will assist them in writing the equations.

8. 9.

DOK-2 How do we represent the amount the climber has rappelled down the mountain? I remove the fraction tiles of the fraction or whole number they rappelled down from the fraction tiles of the original height of the mountain.

DOK-2 How can we use the model to help us solve the scenario? My model can help me understand the regrouping of a whole number into fractional parts (and vice versa) in order to take away the amount needed and ﬁnd the remaining amount.

If students show readiness, have them attempt to subtract the fractions without the models. Once students have done a couple of stations, they need only record their equations and regrouping on their Student Journals. Rotate students to each station after giving them enough time to solve and complete their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

286

DOK-3 What connections did you make during this activity? I remembered how to compose and decompose fractions and mixed numbers. This helped me take away fractional parts from a whole when I needed to. © Accelerate Learning Inc. - All Rights Reserved

•

Engage

Explore

Explain

Elaborate

Evaluate

2. 3.

Acceleration

DOK-1 How could you solve each subtraction scenario without a model? I could use the denominator to help determine how many parts are in my wholes to make an equivalent fraction. I could also use the denominator to help regroup a whole into fractional parts. DOK-1 Can you subtract denominators? Explain. No, the denominator just tells you how many pieces it will take to make a whole. It gives you an idea of how big each piece is. This does not change just because you are removing some of the pieces. DOK-1 If our answer is an improper fraction, how can I turn that into a mixed number? I can treat it like a division problem. For example, for Mt. Pumice Rock, I know that one whole equals three parts. I can take three parts out of ﬁve and 2 make one whole. 5 – 3 = 2, so my fractional part is _3_.

Post-Explore 1.

Intervention

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Prior to having students complete this Exit Ticket, determine your criteria for success. Some students may want to just write the answer without showing how they solved the scenario. Students who need support may beneﬁt from having a number line drawn on the space for them.

Notes __________________________________________________________________________________________________________________________________________________

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ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Add and Subtract Fractions and Mixed Numbers Explore 4 – Solve Addition and Subtraction Fraction Problems ACTIVITY PREPARATION Students apply their skills of adding and subtracting fractions and mixed numbers to solve a variety of problems.

Standards for Mathematical Practice • • •

MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Scenario Cards (per pair) 1 Exit Ticket (per student)

Reusable •

• •

1 Set of fraction circles or tiles (optional for students that may need it) 1 Dry-erase board (per pair) 1 Dry-erase marker (per pair)

Preparation • • • • •

•

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Scenario Cards for each group. The Scenario Cards can be printed on card stock and laminated for durability, if desired. Give a set of fraction circles or fraction tiles to each pair if students need concrete manipulatives. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions by using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles and Fraction Tiles)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Assign each group one or two scenarios. Groups can then present their solutions to the class. FACILITATION TIP

288

2. 3.

Read the following scenario to the class: The class took a field trip to Polynesian Park, the nearby water park. Students need to find the details about their trip in order to write a journal entry the next day! Distribute supplies to pairs. Using the dry-erase boards, students should create a diagram to model each problem, develop an equation, and solve by using a strategy of their choice. Students record all of their work on their Student Journals and write a final solution statement to answer the question. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

Print a list of the questions 4a–4e for each group. Group members can take turns answering each question.

What is the question asking you?

What information do you need to answer the question?

FACILITATION TIP

How can we create a model of the situation?

Questions 4a–4e provide good guidance for almost all scenario problems. Consider printing and posting in the classroom where students and teachers can refer to it at any time.

What do you need to do with these values in order to answer the question?

e. Are we joining or separating amounts to ﬁnd the difference? 5.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat DOK-1 What did you notice about some of the problems? Sometimes you do not need all the information. In the ﬁrst problem, we only needed the two fractions that were about riding on the rides. Some problems needed more than one step or operation. • DOK-2 How were your diagrams helpful? They helped us create an equation to solve. It helped me decide which operation to use to answer the question. • DOK-2 What strategies did you use to solve your equations? The denominator tells us what size pieces we can decompose the wholes into. This helped us join or separate fractional parts and ﬁnd a solution. •

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Noticing extraneous information in a scenario is a critical math assessment skill. Students need to be reminded to continue to carefully read all math problems and use the above questions 4a–4e consistently. STEMscopes Tip The Interventions section is found in the Teacher Toolbox. It provides teachers with intervention strategies for students who need support with a variety of roadblock behaviors. Included are detailed methods to help students with their communication, physical, cognitive, social and emotional, and adaptive development.

Notes __________________________________________________________________________________________________________________________________________________

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ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Add and Subtract Fractions and Mixed Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Join and Separate Parts of a Whole Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Add Fractions and Mixed Numbers with Like Denominators Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Subtract Fractions and Mixed Numbers with Like Denominators

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Solve Addition and Subtraction Fraction Problems

Independent practice assignment that gives students an opportunity to demonstrate their learning

290

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Money Monday

Farmer

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

After the Fire

Add and Subtract Fractions with Like Denominators

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Flight Challenge

Fraction Addition and Subtraction Problem Solving – Like Denominators

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Home

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

PhET Interactive Simulation Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

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Students who are still acquiring the concept and need remediation

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

Add and Subtract Fractions and Mixed Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can add and subtract fractions by joining and separating parts of the same whole.

What prompts will be used?

What does mastery look like?

ADD AND SUBTRACT FRACTIONS AND MIXED NUMBERS

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I can use concrete fraction models to add and subtract fractions and mixed numbers.

I can reason about the sizes of fractions and mixed numbers and their relationships in order to add and subtract.

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SCOPE 1

Represent and Compare Decimals Scope Introduction SCOPE SUMMARY Fourth graders are introduced to decimals by reading, writing, and representing fractions with denominators of 10 or 100 in fraction notation to understand decimal notation. Students’ conceptual understanding is extended as they also gain the ability to compare decimals to the hundredths by reasoning about their size. Results are recorded using the symbols >, <, or =. Students justify their conclusions by using visual models. Student Expectations

4.NR.5.2 Represent, read, and write fractions with denominators of 10 or 100 using decimal notation, and decimal numbers to the hundredths place as fractions, using concrete materials and drawings. 4.NR.5.3 Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

First-grade students partition circles and rectangles into two and four equal parts. Second-grade students extend their ﬁrst-grade knowledge by partitioning different shapes into halves, thirds, and fourths. Third grade develops an understanding of fractions as numbers, including fractions greater than one, being composed of unit fractions. They begin to use fractions to solve problems involving equivalence and comparisons of unit fractions, understanding that the size of a fractional part is relative to the size of the whole. Fourth grade prepares students to compare decimals by building on their knowledge of comparing two fractions. In fourth grade, students compare fractions with different numerators and/or different denominators, using models, number lines, and benchmark fractions.

Fifth-grade students read and write decimals to the thousandths, using base-ten numerals, number names, expanded form, and expanded notation. Fifth graders also compare and order decimals to the thousandths place while using place value charts, place value disks, and scaled number lines to help them model the values of decimals. Place value understanding is used to round decimals to any place.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

choose the student who correctly uses symbols, words, or pictorial models.

•

compare two fractions with the same numerator or denominator.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

discuss how to compare a fraction and a decimal.

•

use an array model.

•

use a number line.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 294

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Decimal Notation for Denominators of 10

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, groups of students will construct 10-piece sculptures and determine the fraction and decimal notation for the number of sculptures they create in a determined amount of time. In solving the scenario, students will: •

discuss how to create a model.

•

discuss how to write the number in fractional notation and decimal notation.

In this exploration, students will be tasked with measuring different items in the room using the metric system. Through completing the task, students will: •

measure items using the metric system.

•

write numbers in fraction notation.

•

write numbers in decimal notation.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 3

Decimal Notation for Denominators of 100

REPRESENT AND COMPARE DECIMALS

Home

Represent and Compare Decimals In the last exploration, students will compare statistics about amusement park rides from two different amusement parks. In solving the scenario, students will: •

construct a model of each decimal to the hundredths place using base ten blocks.

•

use models to construct a number line to make a comparison statement using the symbols of <, >, and =.

•

discuss and write a justiﬁcation for each comparison.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

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REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students choose the student who correctly uses symbols, words, or pictorial models to compare two fractions with the same numerator or denominator. This activity is intended to assess mastery of the following standard(s): 4.NR.4.2 Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole.

Materials

Preparation

Printed •

•

1 Slideshow (per student, per group, or per class)

•

Reusable •

Prepare to project the Slideshow for the class, or print a Slideshow for each student or each group. Plan to have students work in groups for this activity (optional).

REPRESENT AND COMPARE DECIMALS

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1 Projector or document camera (per class, optional)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5.

Project the Slideshow for the class, or distribute a Slideshow to each student or group. Instruct students to look at each student’s comparison statement and symbol or pictorial model. Students should choose the comparison they agree with the most. Call on volunteers to justify their choices. Facilitate a class discussion as students provide reasoning for their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. 1

a. I agree with Angel. Four is greater than three, so _4_ would be greater 1 than _3_. 1

b. I agree with Monique. Her picture shows that _4_ and _3_ are exactly the same size. Therefore, they are equal.

FACILITATION TIP Pair students who have different answers, and ask them to explain their thinking to one another. Then, give them an opportunity to change their answers. FACILITATION TIP Set up 3 columns on the board with the names Angel, Monique, and Rocky, and have students draw a tally mark in the column for the comparison they agree with the most.

c. I agree with Rocky. The pieces of _3_ are going to be bigger than the 1 1 1 pieces of _4_, so _4_ is going to be less than _3_. 6.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope. Notes

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REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals Hook – Candy Comparison ACTIVITY PREPARATION Students use decimal notation to compare two decimals to the hundredths by reasoning about their size.

Materials

Preparation

Printed

Part I

•

1 Student Handout (per student)

•

Reusable • • •

Plan to show the Phenomena Video.

Part II

1 Phenomena Video (per class) 1 Projector (per class) 1 Colored pencil (per student)

•

Print a Student Handout for each student.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

2. FACILITATION TIP Project the scenario and read it aloud with students. Have some student volunteers read aloud as you guide students to locate the important math phrases and values.

Use Virtual Manipulatives or other manipulatives as a visual for students.

Read the following scenario to the class: Jim and Tim each got 100 pieces of Halloween candy this year. However, they are both allergic to nuts, so they each had 33

67 had nuts. After they had taken out the candy with nuts, Jim had ____ left and Tim 100 7 had ___ of his candy to eat. Who had to take out the most candy, and who had the 10

most candy left to eat? Discuss the following questions: a.

DOK-1 What do you need to ﬁnd out? I need to know who had to take out the most candy because it had nuts. I also want to know who had the most candy left after the nut candies had been taken out.

DOK-2 What is something you can do to help you compare their candy? If I shade fractions in two wholes that are the same size, I will be able to compare them more easily.

DOK-2 Would making each fraction into a decimal help when comparing the two fractions? I think it would help since the two fractions have different denominators. That makes it hard to compare fractions sometimes.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

298

to take out a fraction of their candy. ____ of Jim’s candy had nuts. ___ of Tim’s candy 100 10

FACILITATION TIP

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas.

DOK-1 What do you need to ﬁnd out? I need to know who had to take out the most candy because it had nuts. I also want to know who had the most candy left after the nut candies had been taken out. © Accelerate Learning Inc. - All Rights Reserved

3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What is something you can do to help you compare their candy? If I shade fractions in two wholes that are the same size, I will be able to compare them more easily.

DOK-2 Would making each fraction into a decimal help when comparing the two fractions? I think it would help since both fractions have different denominators. That makes it hard to compare fractions sometimes.

Intervention

Acceleration

Give each student a Student Handout and a colored pencil. Review the problem, and then allow students to solve it. Discuss the following questions: a.

DOK-1 What fraction and decimal did you write on the two models to represent how much candy they needed to take out due to nuts? The 3 model on the left should show ___ and 0.30. The model on the right 10 33 should show ____ and 0.33. I shaded 3 columns, or tenths, on the ﬁrst 100 model. On the second model, I shaded 33 squares, or hundredths.

DOK-1 What comparison symbol did you write between the models? Who had to take out the most candy? I wrote < between the models. 3 33 I can see ___ < ____ by looking at the area shaded in each model to 10 100 represent the fractions. Jim had to take out the most candy.

DOK-3 Why is 3 tenths written as 0.3 instead of 0.03? If I write 0.03, I have made 3 tenths into 3 hundredths. I wrote 0.3 so that the 3 is in the tenths place.

FACILITATION TIP Have students compare the array models for each fraction. Then, have students shade the amount representing the fraction and decimal.

REPRESENT AND COMPARE DECIMALS

Home

FACILITATION TIP Consider using money as a reference point to help students compare decimals.

DOK-2 Who had the most candy left after getting rid of the candy with nuts? What did your models look like, and how did they help you 67 7 compare? Tim had the most candy left because ___ > ____ and 0.7 > 0.67. 10 100 I looked at the models to compare the two fractions and decimals easily. Notes

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REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals Explore 1 – Decimal Notation for Denominators of 10 ACTIVITY PREPARATION Students write in decimal notation for fractions with a denominator of 10.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • •

• • • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable • • •

100 Craft sticks (per group) 1 Set of base ten blocks (per group) 1 Timer (per teacher)

•

Plan to have students work in groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Bundle 100 craft sticks for each group. For students who need more support in recalling information, please see our Base Tens and Decimal Place Value Mat Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS 1. 2.

Give a Student Journal to each student. Begin the lesson by reviewing the relationships between base ten blocks. a.

Hold up a flat, a rod, and a small unit cube. Discuss the following question: i. DOK-1 If the flat is considered one whole, what are the values of the other pieces? The rod is one-tenth because it takes 10 of them to make the flat. The small cube is one-hundredth because it takes 100 of them to make one flat.

FACILITATION TIP Model the building process for students, and allow each student to practice a few times before beginning the timer.

Pass out a bundle of 100 craft sticks to each group along with a few base ten block flats and rods. Explain that students will be assembling mini-sculptures that can be painted and used to decorate bedrooms, playrooms, offices, and more! Show students how to build one sculpture. Each sculpture should be built from 10 craft sticks and be arranged as shown below, with five layers of two sticks.

Placeholder AW

300

6. 7.

9. 10.

Engage

Explore

Explain

Elaborate

Evaluate

Set the timer for 30 seconds. Instruct student groups to build as many sculptures as they can in 30 seconds. Tell them the whole group must work on one sculpture at a time. When the timer goes off, have students stop building their sculptures. Have students use the base ten blocks to build a model of how many sculptures they were able to build using the ﬂat as one whole. Tell them they can show their models by shading in the amount on their Student Journals. Have students record their number of sculptures as a fraction and as a decimal. Model for students how both ways of showing the number are read the same 4 way. For example, “two and four-tenths” can be written as 2___ or 2.4. 10 Repeat the same process while timing students for 45 seconds. Have students record their work on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • • •

•

DOK-1 How many whole sculptures did your group build? We were able to build two whole sculptures. We didn’t finish building our third one. DOK-1 How much of the last sculpture did you finish? We only put together 4 of the 10 craft sticks. DOK-1 How would you describe this amount as a fraction? We finished two and 4 four-tenths (2___ ) of the sculptures. 10 DOK-2 Let’s talk about another way we could represent this amount. What do you already know about the relationships between place values? When you look at two side-by-side place values, the value on the left is ten times the value on the right. The value on the right is one-tenth the value of the left. DOK-2 What if we wanted to record a number of tenths using a place value instead of a fraction? What would we do? You could record it in the place value to the right of the ones place. That place would be one-tenth of the ones place. DOK-1 Show students how a decimal point is needed to separate the ones place from the tenths place. Allow students to share where they may have seen a number like this before. I’ve seen a decimal used when I look at the price of something. DOK-1 What does the decimal point tell us? It separates the wholes from the parts of a whole. Anything to the right of the decimal is part of a whole.

Post-Explore 1. 2. 3.

Intervention

Acceleration

FACILITATION TIP Inform students that partial sculptures will be counted using fractions.

FACILITATION TIP If needed, follow up this practice in step 8 with some extra individual whiteboard practice. Have students write several equivalent fractions and decimals. FACILITATION TIP

REPRESENT AND COMPARE DECIMALS

Home

Model for students how to use the base ten blocks to convert their sculpture number into a mixed fraction, a decimal, words, and a number line. FACILITATION TIP Be sure that students are using the term tenths. Discuss the difference between tenths and tens. Have students chorally practice saying tenths, hundredths, and thousandths.

FACILITATION TIP Gather some additional real-world applications of decimals. Consider using students’ science and social studies books to ﬁnd ideas.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals Explore 2 – Decimal Notation for Denominators of 100 ACTIVITY PREPARATION Students measure items around the classroom and write the corresponding decimal notation and fraction notation to the nearest hundredth. They also sketch a number line with the measurement.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • • •

1 Student Journal (per student) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

Reusable •

•

2 Metersticks (per group)

Plan to have students work in groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Scenario Cards for each group. Cut the cards apart. For students who need more support in recalling information, please see our Base Tens, Decimal Place Value Mat, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Number Lines)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP

1. 2. 3.

Direct students’ attention to their metersticks. Have students observe the number of centimeters and possibly millimeters on a meterstick. Display on the board a visual of metric system conversion.

Give each student a Student Journal. Give each group a set of Scenario Cards and 2 metersticks. Tell students to look at their metersticks. Allow students to discuss their thinking with their elbow partners before discussing as a whole group. a.

DOK-1 How many centimeters are in a meter? There are 100 centimeters in a meter.

DOK-1 What fraction of a meter is 1 centimeter? 1 cm is ____ of a meter. 100

FACILITATION TIP

Challenge students to use their metersticks to show how tall Sultan Kösen was. Students will need three metersticks to complete the model.

DOK-2 If you wanted to split up a meter into 10 equal parts, how many centimeters would be in each section? How would you ﬁgure that out? Each of the sections would have 10 centimeters; we could divide 100 by 10, giving us 10. DOK-1 What fraction of a meter is 10 centimeters? Every section of 10 1 centimeters is equal to ___ of a meter. 10

e. DOK-1 How could you skip count each section of 10 centimeters? We could count by 10s. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 4.

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Read the following scenario to the class: In 2019, Sultan Kösen was the tallest man in the world. Measuring at 2.46 meters tall, the Turkish man is over 8 feet tall! Today, we are going to see how you measure up in comparison to Sultan Kösen. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

9. 10.

Engage

Explore

Explain

Elaborate

Evaluate

Begin by using Sultan Kösen’s height of 2.46 meters. Discuss the following questions: a.

DOK-1 How many metersticks tall is the world’s tallest man? At least 2

DOK-1 Is he 3 meters tall? How do you know? No; by looking at the decimal, you see there’s a 2 in the ones place, which means he is at least 2 meters but not 3.

DOK-1 Which two whole numbers is Sultan Kösen’s height in between? Between 2 and 3

DOK-1 How would we write his height in fraction form? 2____ 100

Draw a number line on the board. Discuss the following questions: a.

DOK-1 What whole numbers should be on the ends for sketching 2.46 meters? Between 2 and 3

DOK-1 What numbers should be at the hash marks? Answers may vary. By tenths, hundredths, etc.

DOK-1 Where would we mark 2.46? Answers may vary. Between 2.4 and 2.5; between 2.45 and 2.47

Tell students they are going to be working as teams to measure various items around the classroom as noted on each Scenario Card. They should measure to the nearest hundredth of a meter (or centimeter). Once they have measured the item on the Scenario Card, they should ﬁll in their Student Journals with the length written in fraction notation and decimal notation. They should also sketch a number line modeling the length they measured. They should work collaboratively with their groups to complete the action items for accuracy as well as their Student Journals. Walk around the classroom as the students work to ensure there are no misconceptions. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat

Intervention

Acceleration

STEMscopes Tip Bookmarks and Notes, located on the Scopes home page, allow you to bookmark scopes or individual elements for quick and easy access and provide a place to digitally record personal planning notes. You may choose to set up folders by class, term, or semester to help with longterm planning and can alphabetize bookmarks for quick access.

REPRESENT AND COMPARE DECIMALS

Home

FACILITATION TIP Each group member can take turns measuring the items on the Scenario Cards. Demonstrate as needed how to convert the measurement into the fraction notation, the decimal notation, and the number line. FACILITATION TIP Consider helping students create equally spaced tick marks on their number lines. The ﬁrst two scenarios have solutions where the number lines do not necessarily begin at 0.

DOK-1 Where do we start measuring on the metersticks? Why? We have to start at zero to get an accurate measurement. • DOK-2 What is the relationship between the fractions and decimals you are writing? They are read the same way. They both show the same amount in different ways. • DOK-2 How do the place values to the right of the decimal relate to the fractions they represent? The ﬁrst place to the right of the decimal is the tenths place. Whatever digit is there represents how many tenths you have. The next place value to the right is the hundredths place. Whatever digit is there tells you how many hundredths you have. If you have 2 tenths and 5 hundredths, you can say you have twenty-ﬁve hundredths because each tenth is ten hundredths. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Before students complete this Exit Ticket, consider how much support students will need to create an effective number line to show their thinking.

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REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals Explore 3 – Represent and Compare Decimals ACTIVITY PREPARATION Students represent comparisons with decimals to the hundredths using the symbols >, <, and =.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

1 Student Journal (per student) 1 Amusement Park Comparison (per group) 1 Place Value Mat (per group) 1 Exit Ticket (per student)

Reusable • • •

• • • •

•

1 Set of base ten blocks (per group) 1 Sheet protector (per group) 1 Dry-erase marker (per group)

•

Plan to have student work in groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print an Amusement Park Comparison for each group. Print a Place Value Mat, and place it in a sheet protector so students can write on it using the dry-erase marker. The Place Value Mat can be printed on card stock and laminated for durability, if desired. For students who need more support in recalling information, please see our Base Tens, Decimal Place Value Mat, and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Number Lines)

PROCEDURE AND FACILITATION POINTS 1. STEMscopes Tip In the Teacher Toolbox, the Communicate Math – Representations page under the Communicate Math tab features methods to help teachers show students how to select and use representations and to make connections between representations and what is being represented. A variety of possible representations is provided.

Discuss what students may remember about comparing fractional amounts. Use the following scenario to help them think about the need for the whole to be the same when comparing fractional parts. Read the following scenario to the class: Let’s say your mom decided to stop at the bakery on the way home from work. She wanted to reward you and your sibling with some sweet treats to celebrate your excellent grades. She hands you 0.50 of a cupcake, and you are so excited! You look over and notice that she got your sibling 0.50 of an entire cake. Discuss the following questions: a.

DOK-2 Is this an equal amount? Why or why not? No, because they are different sizes. A cupcake is much smaller than a cake.

DOK-2 What is similar about the sweets you both received? They are 5 50 both ___ or ____ of the sweet treat. 10 100

c. 4.

5. 304

DOK-1 So to make a comparison between two things, what has to be the same? The size of the whole has to be the same.

Read the following scenario to the class: Two amusement parks are interested in opening up in your area of town. However, the city says that only one of the parks will be built. Both parks gave your city oﬃcials some statistics about their parks in an effort to be chosen. The city has decided to put it to a vote. Tell students they will be comparing features of both parks and deciding which park they want in their city based on the statistics. © Accelerate Learning Inc. - All Rights Reserved

8. 9. 10.

11.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Give a Student Journal to each student. Give each group an Amusement Park Comparison. Discuss the information. Statistics

Splashing Wild

Screaming Good Time

Distance from city center

2.46 miles

2.36 miles

Entrance fee

$33.25

$33.20

Average ride wait time

1.35 minutes

1.09 minutes

Average ride time

3.2 minutes

3.20 minutes

Have students use their base ten blocks to show the distance from the city center FACILITATION TIP to Splashing Wild on the first row of their Place Value Mats and the distance from Use several different examples to model the city center to Screaming Good Time on the second row. Be sure to check that how to use the flat, the rod, and the unit. students are correctly using the base ten blocks to build the number. One whole For example, use 3.0, 4.5, and 9.85. can be represented using a flat. Have students use the dry-erase markers to write each digit in each place value on their Place Value Mats. Have students shade in a representation of the base ten blocks on the given grids for both distances in their Student Journals. Have students use their Place Value Mats, folded on the dotted line, to compare the numbers. They should look at the wholes first and relate them to the models FACILITATION TIP they built. Discuss the following questions: a.

DOK-1 Which number is greater? Can you tell? Explain. Both of the digits are equal, so right now I can’t tell which number is greater or less. Both models had the same number of wholes.

DOK-1 What process could you follow to compare numbers? We could look at the highest place value ﬁrst and only look at the wholes. If the digits are different, we can tell which number is greater based on that digit. If they are the same, we have to look at the next place value to the right and use those digits to compare.

Next, have students uncover the tenths and hundredths places on their Place Value Mats and relate them to the models they built. a.

DOK-1 Which park is farther away? Splashing Wild

DOK-2 How do you know? They both are a little over 2 miles. Splashing Wild is another forty-six hundredths of a mile away, and Screaming Good Time is only another thirty-six hundredths of a mile away. Fortysix is more than thirty-six, so Splashing Wild is a little farther away. I can see this in my model because there are more pieces shaded for Splashing Wild.

DOK-1 How could we record this comparison using symbols? We could write 2.46 > 2.36.

DOK-1 Is there another way we could write it? Yes, we could write 2.36 < 2.46 because it means the same thing.

REPRESENT AND COMPARE DECIMALS

Home

Have students read the numbers aloud. When reading the decimal, students should use the word decimal instead of point. For example, a student might say, “3.5 is three decimal ﬁve or 3 and ﬁve-tenths.”

STEMscopes Tip A Parent Letter, located in the Home section, provides parents with a breakdown of the concepts being learned in school, as well as a choice board of related activities that students can complete at home. Sending home the Parent Letter at the start of each scope strengthens the family-school connection by keeping parents informed and included in the learning process.

e. DOK-1 How could we read this statement? 2.46 is greater than 2.36; 2.36 is less than 2.46. f.

DOK-1 Draw the following number line on the board, and ask students where these two numbers would fall on the number line.

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Have students record the number comparison using the appropriate symbol on their Student Journals.

FACILITATION TIP After students have written their comparisons, check with groups before students write their justiﬁcations. 305

REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals Explore 3 – Represent and Compare Decimals 13. 14.

Have students compare the rest of the statistics using the same process described above. Have students build each number (as needed), create their visual models, and record the digit in each place value on their Place Value Mats. Students should fold their Place Value Mats and look at wholes ﬁrst. If the wholes are the same, then they should uncover the decimal values to reason through which is greater or less. Then, have students record their work and comparison statements on their Student Journals. Students should use their visual models as support for their reasoning. a.

STEMscopes Tip Students take notes, express ideas, and/or process the information presented in class using the Interactive Notebook element, located in the Explain section of each scope. These cut-and-glue activities provide an interactive way for students to showcase the concepts and skills learned in the Explore activities and can be added to a notebook for future reference.

15.

The goal is for students to be able to compare two numbers without the use of base ten blocks. However, allow students to use the blocks if they are still needed.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How did you know which number was greater or less? We looked at the wholes ﬁrst. If they were the same, we had to move to the right of the decimal point to look at the number of tenths or hundredths we were comparing. If I thought about both as a certain number of hundredths, it was easy to know which was greater or less. Or I could look at the number of tenths to see if they were the same or different. If they were the same, I could look at the number of hundredths. • DOK-1 What tools could help you do this? We could build a number using base ten blocks to compare them or draw a model of them. We could record the number in a place value chart and compare the numbers one place value at a time. • DOK-2 In order to compare two numbers, do the wholes need to be the same size? Why or why not? Yes, they need to be the same size, or it is an unequal comparison. • DOK-1 How would you read this comparison statement? (Choose a few comparison statements, and have students model how to read each statement, including the symbol.) One and thirty-ﬁve-hundredths is greater than one and nine-hundredths. •

Post-Explore 1. 2. 3. 4.

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Represent and Compare Decimals Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Decimal Notation for Denominators of 10 Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Decimal Notation for Denominators of 100 Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Represent and Compare Decimals Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Shelby and the Springﬁeld Sharks

Melvil Dewey

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Mighty Copper

Compare Decimals – Tenths and Hundredths

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

The Artist

Match Decimal Models to Decimal Numbers

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

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Students who are still acquiring the concept and need remediation

REPRESENT AND COMPARE DECIMALS

Represent and Compare Decimals

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can represent, read, and write fractions with denominators of 10 or 100 using decimal notation.

What prompts will be used?

What does mastery look like?

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I can represent, read, and write decimal numbers to the hundredths place as fractions using concrete materials and drawings.

I can compare two decimals to the hundredths place by reasoning about their sizes.

I can recognize that comparisons are only valid when the decimals refer to the same whole.

I can use the symbols >, =, or < to record comparisons, and I can justify why.

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SCOPE 1

Area and Perimeter Scope Introduction SCOPE SUMMARY

Student Expectations

4.GSR.8.3 Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths.

Students build on their prior knowledge of area (the measurement of the space inside an object in square units) and perimeter (the measurement of the space around an object). They solve problems in a variety of contexts, using different strategies to ﬁgure out both perimeter and area. Students begin by using models and concrete objects to determine the areas and perimeters of various rectangles. They extend their knowledge base to determine the formulas for the perimeter of a rectangle (l + w + l + w OR 2l + 2w) and a square (4s) and the formula for the area of a rectangle (l × w) by using models. Students also solve problems for scenarios where the dimensions of a rectangle or a composite ﬁgure are already given, and they have to apply the formulas for area and perimeter to determine a solution.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students also determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Third graders solve for the perimeter of polygons by adding the lengths of all sides when given the numerical values for each side. They can also solve for the length of a missing side when the total perimeter and all other sides are given. Third graders also investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters.

In ﬁfth grade, students learn what volume is, what a cubic unit is, and how a cubic unit is used to determine volume. Students will use familiar and concrete objects and pictorial models to understand and develop formulas for the volumes of various rectangular prisms. Students will extend their knowledge of the area formula to become familiar with the formulas used to calculate volume in a rectangular prism (ll × w × h and Bh). They will also become familiar with the special formula for a rectangular prism that is also a cube (s ( × s × s).

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon.

•

solve problems involving perimeters of polygons.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

will use models to build a fence and determine the formula for the perimeter of a square (P ( = 4s).

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 312

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Area and Perimeter Formulas In this exploration, students will use models to derive the formulas for ﬁnding the perimeter and area of a rectangle. Students will:

Explore 2

Explore 1

EXPLORE ACTIVITIES Apply the Formulas In this exploration, students will apply the formulas for perimeter and area in order to plan a new zoo. Students will:

•

determine the perimeter of frames for art pieces.

•

create a blueprint for the zoo.

•

determine the area for the frames.

•

determine the area and the perimeter of exhibits.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

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After completion of the activity, students share their learning, complete an Exit Ticket; then, revisit the Hook to solve.

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Area and Perimeter Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students choose the statement they think describes a missing length and the perimeter of a polygon when given the remaining side lengths. This activity is intended to assess mastery of the following standard(s): 3.GSR.8.1 Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve problems involving perimeters of polygons.

Materials

Preparation

Printed • •

•

1 Slideshow (per student, group, or class) 1 Answer Card (per student)

Reusable •

AREA AND PERIMETER

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• •

Prepare to project the Slideshow for the class, or print out the Slideshow for each student or group. Print an Answer Card for each student. Plan to have students work in groups for this activity (optional).

1 Projector or document camera (optional) (per class)

Consumable •

1 Piece of scratch paper (per student)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5. 6. 7.

Distribute an Answer Card and scratch paper to each student. Project the Slideshow for the class, or distribute it to students or groups. Read the scenario together as a class, or instruct students to read it by themselves. Have students look at the polygon and read each student’s statement. Give students time to work the problem on their scratch paper. Ask the students to hold up the Answer Card with the student they think is correct pointing up. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a. I think Justin is correct. The lengths of the sides are there; you just need to add them. b. I think Dalia is correct. Niko will need 7 feet of fence because that is how much fence is missing. c. I think Nelly is correct. You have to ﬁnd the missing length ﬁrst and then add all the lengths together.

FACILITATION TIP First, project the Slideshow without displaying any of the student solutions. Second, provide students quiet think time with their scratch paper. Third, display the students’ scenario solution statements and give some think time. Finally, allow students to collaborate with their shoulder partners or table groups before they vote with their Answer Cards (or hand signals).

FACILITATION TIP While students explain their reasoning, listen for accurate use of area and perimeter vocabulary terms and look for misconceptions.

d. I think Ethan is correct. There are two rectangles. You have to ﬁnd the missing length of one of the rectangles by adding the lengths of the opposite sides together. Then, you can add the side lengths of each rectangle, and then add those sums together. 8.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

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Area and Perimeter Hook – Vegetable Garden ACTIVITY PREPARATION Students will use models to build a fence and determine the formula for the perimeter of a square (P (P = 4s).

Materials

Preparation

Reusable • • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 30 Toothpicks or craft sticks (per group) 1 Resealable bag (per group)

Plan to show the Phenomena Video.

Part II • •

Count out 30 toothpicks or craft sticks for each group. Put them into resealable bags. Plan to have students work in groups to complete this activity.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP

Project the scenario and conduct a careful read aloud. Guide students to locate the important math phrases and values. 4.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You have planted a vegetable garden in your yard. You need to build a fence around it to keep out rabbits and other animals. You have 30 feet of fencing you can use. The vegetable garden is shaped like a square. You need to ﬁnd the biggest square-shaped area you can make using the 30 feet of fencing. Discuss the following questions: a.

DOK-1 What do we know? The garden is a square, so all the side lengths are the same. We have 30 feet of fencing to use.

DOK-2 How could you solve a problem like this? We could build a model of the square garden and see if we can use up 30 feet of fencing on it.

FACILITATION TIP In addition to using a model, some students may be ready to solve this problem using mental math, a multiplication algorithm, repeated addition, or other strategies. FACILITATION TIP This Post-Explore might also work as a Pre-Explore depending on your class. Determine ahead of time if you want students to think they need to use all of the fencing to make a perfect square. Some students may consider cutting the craft sticks to accommodate that constraint if you allow it.

Part II: Post-Explore 1. 2.

3. 4.

5. 316

Move on to complete the Explore activities.

After students have completed all the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do we know? The garden is a square, so all the side lengths are the same. We have 30 feet of fencing to use.

DOK-2 How could you solve a problem like this? We could build a model of the square garden and see if we can use up 30 feet of fencing on it.

Give each group a bag of toothpicks or craft sticks. Instruct the students to arrange the cubes into a fence that is shaped like a square. They should be ﬁnding the biggest square they can make with their 30 pieces of fencing. Tell students each toothpick represents 1 foot of fencing. As they are working, remind students to think about a formula they could use to ﬁnd the perimeter of any square. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Discuss the following questions:

Intervention

Acceleration

STEMscopes Tip

DOK-1 What was the side length of the fence you ended up with? It was 7 feet.

DOK-1 What was the perimeter of the fence? It was 28 feet.

DOK-1 What formula did you use to ﬁnd the perimeter? We used P = 4 × s (or P = s + s + s + s).

DOK-2 How would you find the AREA inside the fence? You would multiply the side length by itself. You would get 7 × 7 = 49 square feet.

Students work collaboratively on a Problem-Based Task, located in the Elaborate section, to apply the knowledge and skills they have learned to an open-ended, real-world challenge. These tasks provide a more rigorous opportunity for students to practice their mathematical thinking and problemsolving skills within a real-world context.

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Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Area and Perimeter Explore 1 – Area and Perimeter Formulas ACTIVITY PREPARATION Students use models to derive the formulas for ﬁnding the perimeter and area of a rectangle.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials Printed • • •

1 Student Journal (per student) 1 City Art Collection (per group) 1 Exit Ticket (per student)

Reusable • • • •

Preparation • • • •

1 Ruler (per group) 6 Colored tiles (per group) 1 Quart-size resealable bag (per group) 4 Containers (per class)

• • • •

Consumable • • •

1 Glue stick (per group) 66 Inches of framing material (per group) Suggested materials are as follows: • • •

Ribbon Colored strips of paper Chenille stems

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a City Art Collection for each group, and cut out the paintings. The City Art Collection can be printed on card stock and laminated for durability, if desired. Cut the following pieces of framing material. The suggested material for the framing material is ribbon, colored strips of paper, or chenille stems. The amount listed represents the amount needed for each group. Once the pieces are cut, combine all of the pieces of the same size into a container, and label the length. Place the containers in a central location for easy student access.

• • • •

Four 3″ pieces Eight 4″ pieces Two 5″ pieces Two 6″ pieces

For Part I, gather a ruler and glue stick for each group. For Part II, prepare a quart-size resealable bag with 6 colored tiles for each group. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used for support in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS

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FACILITATION TIP

Part I: Framing Material

Prior to completing these two Explore activities, take time to carefully define and model the difference between area and perimeter for students. These two geometry terms can continue to confuse students well into junior high. Post them on your word wall, have students state the definitions out loud, and find a way to use physical responses for each word.

Read the following scenario to the class: The local university has just donated their collection of paintings created by former art students, some of whom have become successful artists, to the city. The square and rectangular art pieces need to be framed before the city opens an art gallery that will display all the art. They have asked you to help them determine the size of frame and backing material each piece of art needs as well as the total amount of framing and backing materials they will need to purchase. Discuss the following questions: a.

DOK-1 What does the city want to do? It wants to open an art gallery to display art.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What shapes are the art pieces that need to be framed? They are squares and rectangles.

DOK-1 What do we know about the sides of a square? They are all equal in size.

Intervention

Acceleration

e. DOK-1 What do we know about the sides of a rectangle? Opposite sides are equal in size. 3. 4. 5.

6. 7. 8.

10.

Give a Student Journal to each student. Give a set of art pieces, a ruler, and a glue stick to each group. Tell students their ﬁrst task is to provide frames for the art pieces. Show students where they can get the framing materials. They will need to know what pieces they need before taking them. This will require students to measure the sides and choose which container to take pieces from. Once students have found the pieces needed for one art piece, they should record the total amount of framing supplies needed for that piece. When students are done, discuss how the frames were built in order to develop the formula for perimeter. Discuss the following questions: a.

DOK-1 When you were figuring out the total amount of framing material needed for an art piece, were you finding the area or perimeter? We were finding the perimeter because we were finding the distance around the shape.

DOK-2 What could you do to ﬁnd the perimeter of a rectangle? We could add up the length of each side to ﬁnd the total.

Explain that when you have a process like this, you create a formula to follow. What students just said is their formula. Show students how to write the formula for perimeter: P = l + l + w + w. Students should record the formula on their Student Journals. Discuss the following questions: a.

DOK-3 Think about the sides of a rectangle and what pieces you had to take from the containers. What do you notice about the sides of a rectangle? Opposite sides are congruent. If we measured the length of one side, we needed to get two framing pieces that were that length to cover both sides.

DOK-3 Is there a way we could use this information to ﬁnd the perimeter more quickly? Yes! We could double the length, double the width, and add those together to ﬁnd the perimeter.

Show students how to write this formula for perimeter: P = 2l + 2w.. Students should record the formula on their Student Journals. Discuss the following question: a.

DOK-3 Why could we use either formula? They are calculating the same thing. Instead of adding the length twice, we are ﬁnding the length times two. This is just a different way to ﬁnd the same solution.

Part II: Backing Material 1. 2.

Tell students that they will now figure out the total amount of backing material the city needs to purchase to cover the back side of each art piece. Give a bag of six colored tiles to each group. Tell students each piece is 1 square inch. The online store sells the backing material for 1 dollar per square inch, so they need to communicate the dimensions and the total number of square inches in order to submit the order. Allow students to use the ruler, the colored tiles, or both to figure out the total number of square inches needed to cover each piece of art. Students intentionally don’t have enough colored tiles so that they will not simply cover the shape and count the tiles. Students should use the length and width to find the number of square inches.

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FACILITATION TIP Preview the Student Journal with students and note that it includes “number sentences.” Consider changing number sentences to “equations” if time allows. FACILITATION TIP If time is limited, have students sketch the frames rather than build them all. Alternatively, have students select just one of the color City Art Paintings to frame. They can create and glue a frame for it to keep as a model.

FACILITATION TIP Clarify that this formula is special for rectangles. Perimeter formulas for irregular quadrilaterals, triangles, and other ﬁgures will vary.

FACILITATION TIP Many students will not have seen a factor in front of a variable before. Slow down to teach students about coeﬃcients when you introduce the 2< and 2w in this equation. FACILITATION TIP This Explore activity might work well if it is split into two different class sessions; one for Part I and one for Part II.

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Area and Perimeter Explore 1 – Area and Perimeter Formulas 4.

5. 6.

Once students have found the dimensions and amount of backing material needed for one art piece, they should record the information on their Student Journals. When students are done, discuss how they found the total amount of backing material in order to develop the formula for area. Discuss the following questions:

STEMscopes Tip Decide and Defend, located in the Evaluate section in Grades 2-5, is an open-ended formative assessment in which students make a mathematical decision and justify their reasoning using any combination of written text, visual models, expressions, and equations.

DOK-1 When you were figuring out the total amount of backing material needed for an art piece, were you finding the area or perimeter? We were finding the area because we were finding the amount of space covered by the shape.

DOK-2 What could you do to ﬁnd the area of a rectangle? We could multiply the length and width to ﬁnd the total number of square units.

Explain that when you have a process like this, just like with perimeter, you create a formula to follow. What students just said is their formula. Show students how to write the formula for area: A = l × w.. Students should record the formula on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What did you notice about the formula for area? I noticed you are multiplying the length and width, which is just like multiplying the rows and the number of columns in an array. It can tell us how many square units there are in a space. • DOK-2 What did you notice about the formulas for perimeter? I learned that there are two different formulas we can use for perimeter, but they are both helping us ﬁnd the same thing. • DOK-3 In what scenarios is it best to use the area formula to solve? We can use the area formula to solve when the scenario needs us to determine how much space, or square units, the inside of a shape covers. • DOK-3 In what scenarios is it best to use the perimeter formula to solve? We can use the perimeter formula to solve when the scenario needs us to determine the length around the outside of a shape. •

FACILITATION TIP Take time to gather several relevant realworld examples of when students and adults need to accurately calculate area and perimeter. Use digital images related to familiar careers.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP This Exit Ticket could be used as a Preassessment for some students who may be ready for enrichment or acceleration.

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Explore

Explain

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Evaluate

Intervention

Acceleration

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Area and Perimeter Explore 2 – Apply the Formulas ACTIVITY PREPARATION Students apply the formulas for perimeter and area in order to plan a new zoo.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Zoo Spaces (per group) 1 Exit Ticket (per student)

Reusable •

•

1 Quart-size resealable bag (per group)

Plan to have the students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Zoo Spaces, on card stock for durability, for each group. Cut out each Zoo Space, and place the cards in a quart-size resealable bag for each group. For students who need more support in recalling information, please see our Grid Paper and Base Tens Supplemental Aids elements in the Intervention section.

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Be prepared for students to ask about other constraints. They may be curious about how much total area they can use, how long the shape of the whole zoo is allowed to be, and can they create their own exhibit sizes and more. STEMscopes Tip Student Goal Setting, located in the Essentials section of the Teacher Toolbox can be used by students to self-evaluate. Included in this section is a student goal-setting sheet on which students identify a math goal, write or draw “I can” statements, describe what they will do to reach the goal, and evaluate whether they have met their goal.

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2. 3. 4.

Read the following scenario to the class: Congratulations! You are on the design team to plan out the new zoo in your city! There are many animal exhibits you would like to have included at the zoo, but because of the limited land space, you will need to make tough decisions on which exhibits to include and which exhibits to exclude. You and the rest of your design team will need to determine how much ground cover and how much fencing material will be used for each animal exhibit you would like to include at your zoo. You will need to create a blueprint of the new zoo that meets the following criteria: a.

It must include at least ﬁve exhibits. One of them must be a square. It must include the hippos and zebras exhibits.

You must label the length and width of each exhibit.

Direct students’ attention to the ﬁrst page of their Student Journals and the Zoo Spaces. Tell students the space on the ﬁrst page of their Student Journals is where they will create the blueprint of their zoos. Explain to the class that they will use the Zoo Spaces to trace each exhibit space on their blueprint and label each space with its name, length and width, area, and perimeter. Encourage the students to examine the hippos and zebras exhibits that must be included in their zoos and ask the following questions: a.

DOK-1 What do you notice about the hippos and zebras exhibits? Answers may vary. I noticed that they are not rectangles or squares. I noticed that they are irregular or composite shapes. I noticed that they are made of two rectangles put together.

DOK-2 How do you think we can determine the area of the hippos and zebras exhibits? I think we can decompose the whole shape into two smaller shapes. We can ﬁnd the area of each decomposed shape and then add those products together. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 Does breaking it apart change the total area of the exhibit? How do you know? It does not change. We are still determining the area of both parts of the shape, so the whole shape is still being calculated. We are just breaking the whole shape into smaller pieces in order to ﬁnd the area more easily.

DOK-2 How do you think we can determine the perimeter of the hippos and zebras exhibits? We can still add all the sides together. We just have to make sure we include all the lengths of the sides given.

Allow students to begin working. Students will work with their group design teams to collectively create one blueprint per group. They will decide which exhibits they want to include in the new zoo and work together to calculate the ground cover and fencing materials of each exhibit by applying the formulas for perimeter and area and record their work on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What do you notice about the different zoo spaces? Some are rectangles, and some are squares. They each mark the space for a different animal. Each zoo space includes a length and width for that animal exhibit.

DOK-3 How do you think these exhibits will be built? They will need fences or walls around them. Some will need a rocky floor, and some will need a grassy floor, while others will need a tile floor so they can hold water.

DOK-3 When building a ground cover for each exhibit, will we need to determine the area or perimeter of that zoo space? Explain. We will need to determine the area because we will need to ﬁnd out the number of square units that are needed to cover the ground.

DOK-1 What is the formula for area? The formula for area is length × width.

e. DOK-3 How is the area formula different when you need to decompose the shape into two smaller areas? The formula is different because we will need to ﬁnd the area of both decomposed shapes and then add the two areas together. The formula would be (l × w) + (l × w). f.

DOK-3 When building a fence or wall around a zoo space, will we need to determine the area or perimeter of that zoo space? Explain. We will need to determine the perimeter because we will need to ﬁnd the total distance around the outside of the zoo space.

DOK-1 What is the formula for perimeter? The formula for perimeter is length + length + width + width.

DOK-3 How is the formula for perimeter different when you need to determine the perimeter for the hippos and zebras exhibits? The formula for perimeter is different because we will need to add on two more sides to our formula, or a length and a width. The formula could be length + length + length + width + width + width.

i. DOK-3 How did you determine how to break down the area of the hippos and zebras exhibits? Was there more than one way? Answers will vary. Yes, there were multiple ways of breaking down the dimensions. It would make more sense to break apart the number I am not so familiar with when multiplying. This will help make the process of calculating an answer easier because I’m using different numbers. 7.

Intervention

Acceleration

AREA AND PERIMETER

Home

FACILITATION TIP For this type of activity, it might work best to allow students to work independently or select their own partners to create their blueprint.

STEMscopes Tip The Career Connections element is available to students in Grades 3–5. Located in the Elaborate section of each scope, its videos and slideshows introduce students to careers that use the mathematical concepts students are learning and the 21st century skills needed to be successful in those careers. After viewing and discussing the video or slideshow, students complete a related activity that includes math concepts from the scope.

FACILITATION TIP Take time to teach students that sometimes lengths can have different values and so can widths (unless it is a rectangle or square).

FACILITATION TIP Finding the area and perimeter of complex ﬁgures may require guided support. Consider calculating the hippo and zebra exhibits together before students begin collaborating.

Allow students enough time to complete their zoo blueprint and determine the area and perimeter of each zoo space they chose. Students will then work together with their groups to answer the reﬂection questions on their Student Journals.

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AREA AND PERIMETER

Area and Perimeter Explore 2 – Apply the Formulas 8.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat STEMscopes Tip The Communicate Math – Representations page under the Communicate Math tab of the Teacher Toolbox provides teachers with strategies for modeling and using pictorial representations and for demonstrating connections between the representations and the content to help support student learning. A variety of possible representations is provided.

FACILITATION TIP This Exit Ticket could be used as a Preassessment for some students who may be ready for enrichment or acceleration.

DOK-2 When you found the amount of ground cover needed, were you finding the area or perimeter of the space? Explain. We were finding the area because we were finding the amount of space on the inside of a shape. • DOK-2 When you found the amount of fencing material needed, were you finding the area or perimeter of the space? We were finding the perimeter because we were finding the distance around a shape. • DOK-2 How did you find the area or perimeter of the space? We multiplied the length by the width to find the area of each exhibit. Sometimes we had to decompose the exhibit into smaller parts to determine the area of the whole exhibit. We added up the lengths of all the sides to find the perimeter of the space. • DOK-3 Why is it important to know the difference between area and perimeter? It is important to know the difference between area and perimeter because both formulas determine different values. Area determines the amount of space inside of a shape, and perimeter determines the distance around the outside of the shape. We must know what the scenario is asking us to determine so we can apply the correct formula to the problem. •

Post-Explore 1. 2. 3. 4.

324

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

AREA AND PERIMETER

Home

325

AREA AND PERIMETER

Area and Perimeter Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Area and Perimeter Formulas Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Apply the Formulas Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

326

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Ralph the Rock Collector

Podiatrist

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Raising Animals for Show

Problem Solving with Area and Perimeter

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

PhET Interactive Simulation

Animal Rescue Farm

Student activities using the PhET Interactive Simulations from the University of Colorado Boulder

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

AREA AND PERIMETER

Home

327

AREA AND PERIMETER

Area and Perimeter Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

328

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

What prompts will be used?

AREA AND PERIMETER

Home

What does mastery look like?

I can solve problems involving the area of composite rectangles.

I can solve problems involving the perimeter of composite rectangles.

329

SCOPE 1

Angles Scope Introduction SCOPE SUMMARY

Student Expectations

4.GSR.7.2 Measure angles in reference to a circle with the center at the common endpoint of two rays. Determine an angle’s measure in relation to the 360 degrees in a circle through division or as a missing factor problem.

Students understand that the vertex of an angle is located at the center of a circle; it is from this point that two rays can create angle measurements. They are introduced to a new type of measurement when learning to measure angles. Students learn that angles 1 are measured by the “turning distance” between two rays, which use increments of ____ 360 of a circle, or a 1° (degree) angle. In addition, students practice measuring angles using a protractor. This includes aligning the vertex, the zero edge, and the ray properly to tell the degrees of an angle. Fourth-grade students learn to read, document, and draw angles in the proper mathematical format, using manipulatives and a protractor. They also learn to represent a fractional model with a division and multiplication equation to ﬁnd the solution for missing angle measures in relation to a circle.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students brieﬂy have an interaction with the concept of angles, speciﬁcally right angles. Students begin to identify right angles while also identifying perpendicular line segments and parallel line segments. Third graders extend this knowledge by analyzing problems to identify these parallel and perpendicular line segments, as well as right angles, within polygons. However, students do not encounter the deeper concepts of angles prior to fourth grade.

As students delve into ﬁfth-grade mathematical concepts, they will apply their concept knowledge of angles as they classify two-dimensional ﬁgures into categories based on their properties. An example of this would be “all rectangles have four right angles, and squares are rectangles, so all squares have four right angles.” Students begin to move from the analytic level of thinking in geometry to the more abstract.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

use attributes to identify and draw quadrilaterals.

•

listen to quadrilateral riddles.

•

use the attributes described to determine whether the quadrilateral is a parallelogram, rhombus, rectangle, square, or trapezoid.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

determine the angles.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ANGLES

Home

Angles as Fractions of a Circle In this exploration, students will begin exploring angles by analyzing and classifying angles for a quilt design. With participation in this exploration, students will: •

draw the angles.

•

classify angles.

•

explain reasoning for classiﬁcations.

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, students will use manipulatives to determine an angle’s measure in relation to the 360 degrees of a circle through division or a missing factor problem. Students will: •

determine the correct fraction circle wedge to use to create the play set for a toy design.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 3

Determine the Angle Measure

Measuring Angles In this exploration, students will be tasked with solving a real-world problem about identifying the direction of a robot pathway. Through completing this exploration, students will: •

measure angle sizes.

•

use a protractor.

•

name angles.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

331

ANGLES

Angles Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

332

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ANGLES

Home

ACCESSING PRIOR KNOWLEDGE Students listen to quadrilateral riddles and determine the quadrilateral that matches based on attributes. This activity is intended to assess mastery of the following standard(s): 3.GSR.6.1 Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve problems involving parallel line segments, perpendicular line segments, and right angles.

Materials

Preparation

Printed • •

1 Set of Quadrilaterals (per class) 1 Quadrilateral Riddles (per class)

• • •

Print one set of Quadrilaterals for the class. Cut the quadrilateral pictures apart on the dotted lines, and tape them around the room. Prepare to read each riddle on Quadrilateral Riddles aloud to the class.

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5.

Show the students the quadrilateral pictures around the room. Read aloud the name of each quadrilateral as they are shown to the students. Read the riddles one at a time to the class. Challenge students to walk to and stand by a quadrilateral that matches the description from each riddle. Some riddles have multiple quadrilaterals that match them. Invite students to share with the class how they knew the pictures they selected matched the riddles. Facilitate a class discussion about their choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. a. Riddle 1: I knew it had to be a trapezoid because it is the only quadrilateral that has one pair of parallel lines. All of the others have two or no pairs of parallel lines.

Alternatively, provide each student with a set of riddle cards, and have the students tape each card next to a shape that matches its description.

b. Riddle 2: The rhombus is correct because it has 4 congruent sides and no right angles.

STEMscopes Tip

c. Riddle 3: The rectangle is the quadrilateral that matches since it has 4 right angles and opposite sides that are congruent, not 4 congruent sides. d. Riddle 4: The reason we are in different spots is because both the rectangle and the square have 4 right angles, so the matching quadrilateral can be either one. e. Riddle 5: The match has to be the kite since it is the only one without pairs of parallel lines. f. Riddle 6: The only quadrilateral that has 4 right angles and 4 equal sides is the square. g. Riddle 7: It has to be the parallelogram since it does not have right angles or 4 equal sides, but it does have two pairs of parallel lines. h. Riddle 8: We are all in different places since the square, parallelogram, rectangle, and rhombus all have two pairs of parallel lines. All of these quadrilaterals are parallelograms. i. Riddle 9: All of the ﬁgures around the room have 4 sides and 4 angles. That is what makes a ﬁgure a quadrilateral. All the pictures match the riddle. 6.

FACILITATION TIP

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

The Assessment Builder, accessed under Assessments along the menu bar, allows you to build a customizable assessment. Choose to create a printable and/or digital assessment item bank. Search for English and Spanish items by standard, lesson, key words, topic, grade level, and question type. Assessments are saved in your private account for you to access or edit at any time. FACILITATION TIP As students describe the shapes, kinesthetic learners may beneﬁt from whole-body physical movements to model deﬁning attributes. For example, students could point both arms out in front of them to model parallel lines or stretch out their arms in different positions to represent acute, right, and obtuse angles. 333

ANGLES

Angles Hook – Ride the Wheel ACTIVITY PREPARATION n

Students measure and draw angles within a circle. They will recognize the angles as fractions of the circle, ____ . 360

Materials

Preparation

Reusable • • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Protractor (per student) 1 Ruler (per student)

Part II • • •

Consumable •

Plan to show the Phenomena Video.

1 Round paper plate (per student)

Cut off the curved edge of the paper plates so you have ﬂat circles. Mark the center of each circle. Plan to have students work in groups of 6 to complete this activity.

PROCEDURE AND FACILITATION POINTS

STEMscopes Tip Use the Communicate Math – Discourse page, found under the Communicate Math tab in the Teacher Toolbox, to learn strategies that can be used to model expectations and appropriate interactions students need to follow during productive math discussions with partners, in small groups, or with the whole class.

Part I: Pre-Explore 1.

4. 5.

FACILITATION TIP Display images of bicycle wheels or wagon wheels. Have students recall information about fractions.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You are designing a new Ferris wheel for the state fair. You need to tell the builders how many cars your Ferris wheel will have and what angles are between the spokes on the wheel. The number of cars on your Ferris wheel will differ. Your Ferris wheel will have 4, 5, 6, 8, 9, or 10 cars. Explain that the spokes are evenly spaced around a Ferris wheel. That means all the angles between the spokes are the same. Discuss the following question:

DOK-2 How could we ﬁgure out the angle measurements between the spokes for each car on the Ferris wheel? We could build a model and measure it based on how many cars our Ferris wheel has.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following question: a.

FACILITATION TIP Monitor students as they draw the lines. The lines need to intersect at one point in the center and be as equal as possible. 334

3. 4. 5.

DOK-2 How could we ﬁgure out the angle measurements between the spokes for each car on the Ferris wheel? We could build a model and measure it based on how many cars our Ferris wheel has.

Give a paper plate, a ruler, and a protractor to each student. Divide the class into groups of 6. Tell students they will need to decide how many cars they want on their Ferris wheel. Each person in their group should have a different number of cars. They should have 4, 5, 6, 8, 9, or 10 cars. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Tell students they can each use their paper plate to build a model of their Ferris wheel. Students can draw lines with their rulers. Tell the students to think of the circle as their whole and the spokes partitioning the whole into equal parts. Give students time to solve the problem. Gather students in a whole group, and discuss the following questions: a.

DOK-1 How many degrees are in a whole circle? There are 360 degrees in a whole circle.

DOK-2 How many equal angles make up your circle on your Ferris wheel? Answers will vary. I had 6 cars, so I knew that I needed to think of dividing the whole into 6 equal parts. I knew that 36 ÷ 6 = 6, and so I knew that 360 ÷ 6 = 60 degrees. I used a protractor to measure 60 degrees from the center point. I used a ruler to make the lines and had six 60-degree angles.

DOK-2 What did you need to do in order to get the circle partitioned into equal angles? We had to divide 360 by the number of spokes or angles we had on our Ferris Wheel.

DOK-2 There are two scales on the protractors, the inner scale and the outer scale. How did you know which scale on your protractor to use? The direction the bottom ray is pointing will be 0, so you count up from there. I also thought about what type of angle I needed. If I needed a right angle, it had to measure 90 degrees. If I needed an acute angle, I knew it had to be less than 90 degrees. If I needed an obtuse angle, it had to be greater than 90 degrees.

Intervention

Acceleration

ANGLES

Home

FACILITATION TIP Monitor students as they draw the lines. The lines need to intersect at one point in the center and be as equal as possible.

STEMscopes Tip Key Concepts, located under the Home tab, are “I can...” statements that describe what students will know and be able to do when they have mastered the standard(s) of the scope. During each Explore lesson, it is helpful to post these statements for students to reference at the start and end of the activity.

335

ANGLES

Angles Explore 1 – Angles as Fractions of a Circle ACTIVITY PREPARATION Students use manipulatives to illustrate that the measure of an angle is a fraction of a circle with the center at the vertex of the angle and that the space between the rays that create angles is measured in degree units.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • •

• • •

1 Student Journal (per student) 1 Exit Ticket (per student)

• • • •

Reusable • •

1 Pair of scissors (per student) 1 Ruler (per student)

Consumable • •

Plan to have students work in groups of 4 or 5 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Gather the following materials so that each student will have one of each item:

•

1 Box of colored markers (per student) 1 Paper plate (per student)

•

Pair of scissors Ruler Box of colored markers Paper plate

For students who need more support in recalling information, please see our Fraction Circles Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used for support in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles)

PROCEDURE AND FACILITATION POINTS Part I: The 360 1. FACILITATION TIP

Consider using the Foundation Builder as a refresher for geometric shapes, numbers of sides, and angles.

FACILITATION TIP

Display the Picture Vocabulary to assist students. Discuss how the unit used when measuring angles is degrees. FACILITATION TIP Model for students how to cut and fold the plate. Be prepared with extra plates for students. 336

Tell students you were watching a dance competition show on TV last night. You noticed that the dancers did a lot of 360s. Elicit ideas from students about what a 360 might be. Tell students that a 360 is a full turn all the way around. It’s called a 360 because going around in a full circle means you spin 360 degrees. Have students stand up and model doing a 360. Discuss the following question:

Give a Student Journal, paper plate, box of markers, and pair of scissors to each student. Discuss the following question: a.

DOK-1 Where else have you seen something doing a 360? Answers may vary. A top spinning, a car, a dog chasing his tail, etc.

DOK-1 How would you show 360 degrees on this plate? Going all the way around the plate is 360 degrees.

Have students fold the paper plate in half twice to ﬁnd the center and then open the plate back up.

11.

Explore

Explain

Elaborate

Evaluate

Tell students the center point of the 360 circle is called the vertex. Have students label the center point “Vertex” with a colored marker. Students should also label the vertex point of the circle on their Student Journals. Have students use their ﬁngers to model going 360 degrees around the plate. Then, have students draw a circle all the way around the plate with a different colored marker. Students should label this “360.” Explain to students that we use units called degrees to measure angles. An angle that makes one complete circle around is called a 360-degree angle. We use a small circle following the number to represent the word degrees degrees. Demonstrate how to write the symbol for degrees beside 360. Have students write a ° symbol beside the number 360 on their plate. Discuss the following question: a.

10.

Engage

DOK-2 Why do you think this symbol was chosen for degrees? It looks like a little circle, which is like going all the way around or going 360 degrees.

Have students draw around the circle on their Student Journals with the colored marker and label it “360°.” Students should write “1 circle” on their Student Journals to show this is the measurement of one whole circle. Have students cut along one of the folds across the plate. Discuss the following questions: a.

DOK-1 What did we do to the circle? We cut it in half. It is now two equal parts. Like fractions, there are two parts to the whole of 360 degrees.

DOK-1 If it takes 360 degrees to go all the way around the circle, how could we ﬁnd out how many degrees it takes to go halfway around the circle? We could divide 360 by 2.

12.

Students should turn one of the paper plate halves over and divide 360 by 2. Discuss the following question:

13.

Have students turn the paper plate half back over and draw an arc with a different colored marker (a third color) from the edge on the right to the edge on the left. Students should label this “180°.” Have students trace along the straight edge of the paper plate half. Tell students that 180-degree angles are also called straight angles.

14. 15.

16.

17.

Acceleration

STEMscopes Tip Virtual Manipulatives are located under the Explore tab. Unlike concrete manipulatives, these digital manipulatives require no setup and are easily accessed online at any time. Students can interact with a variety of virtual manipulatives to explore mathematical concepts anytime, anywhere.

DOK-1 How many degrees is half a circle? It is 180 degrees.

Have students use a ruler to draw a straight horizontal line through the vertex of the circle on their Student Journals with the third colored marker and label the 1 top half “180°.” Students should write “_2_” and “straight angle” to show that this is the measurement and name of half of the circle. Have students cut along the remaining fold line on the other half of the paper plate. Discuss the following questions: a.

DOK-1 What did we do to the half of the circle? We cut it in half. It is now two equal parts.

DOK-1 If it takes 180 degrees to go halfway around the circle, how could we ﬁnd out how many degrees each of these pieces is? We could divide 180 by 2.

Students should turn one of the paper plate quarters over and divide 180 by 2. Discuss the following question: a.

Intervention

ANGLES

Home

DOK-1 How many degrees is each of these pieces? Each is 90 degrees.

FACILITATION TIP Model drawing a straight line and labeling the plate for students.

FACILITATION TIP Every time the plate is divided, write each equation on the board along with a divided plate drawing.

337

ANGLES

Angles Explore 1 – Area and Perimeter Formulas 18.

Have students turn the paper plate a quarter back over and draw a right angle symbol ( ) with a fourth colored marker. Students should label this “90°.” Have students trace the 90-degree angle with their ﬁngers. Discuss the following questions:

STEMscopes Tip The Skills Quiz, located in the Evaluate section, is a short standardsbased assessment where students demonstrate their computational ﬂuency. These assessments include a variety of question types and can be used to formatively evaluate students’ knowledge about topics covered in the scope or to review the content.

19.

DOK-1 What do you notice about the vertex of this angle? It looks like a perfect corner.

DOK-1 What does that tell you about an angle that measures 90 degrees? It makes a perfect corner, like on a sheet of paper.

Tell students 90-degree angles are also called right angles. Discuss the following questions: a.

DOK-1 If we cut the other paper plate half on the fold line, how many pieces of the paper plate would we have? Four

DOK-1 How many right angles would we have? Four

DOK-1 What fraction of the circle is one of the paper plate pieces? _4_

d. 20.

21.

DOK-1 How many degrees does _4_ of a circle represent? 90 degrees

Have students use a ruler and a colored marker to draw a straight vertical line from the vertex to the edge of the circle on the bottom half of the circle on their Student Journals. Students should write the right angle symbol in one section 1 and then label it “90°.” Students should write “_4_” and “right” in the section to show this is the measurement and name of one-fourth of the circle. Discuss the following question: a.

DOK-1 What point do each of these angles have in common? They all start at the vertex. The corner points to the vertex.

b. Explain how an angle is made of two rays (shown by arrows, representing a line segment with one endpoint) that both start at the center of the circle or vertex. This can be related to cutting a slice of pie. Part II: Dance Moves 1. STEMscopes Tip The Standards list is located along the menu bar. Here, a keyword can be entered to locate each standard. The search will result in a list of standards and direct links to the scopes where those standards appear. The standards are organized by grade level as well. Clicking on a standard within a grade level will also provide direct links to the scopes.

3. 4. 5.

Students will work together with their groups using their paper plate pieces to design a dance. For example, students may place a 180° piece, a 90° piece, a 90° piece, and a 180° piece and then place two 180° pieces together to create a 360° piece. Students will practice their dance. Students should change direction for each new piece. In the above example, students would spin 180° clockwise, then 90° counterclockwise, then 90° clockwise, then 180° counterclockwise, and then make one full turn clockwise. Have students draw their dance on their Student Journals. They should label each piece with the degree measurement. If time permits, allow student groups to demonstrate their dances for the class. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

DOK-2 What right angles do you see in this room? The bookcase against the wall, the corner of a book, etc. DOK-3 Where do you think angle measurements are used in real life? They are used to build buildings, to make objects, to design dance moves, to tell someone to turn a certain way, etc.

Post-Explore 1. 2. 3. 338

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ANGLES

Home

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

339

ANGLES

Angles Explore 2 – Determine the Angle Measure ACTIVITY PREPARATION Students use manipulatives to determine an angle’s measure in relation to the 360 degrees of a circle through division or a missing factor problem.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Toy Design Cards (per group) 1 Exit Ticket (per student)

Reusable • • •

1 Set of fraction circles (per class) 1 Pair of scissors (per class) 1 Quart-size resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of the Toy Design Cards for each group. The Toy Design Cards can be printed on card stock and laminated for durability, if desired. Place cards inside of a quart-size resealable bag.

•

__, __, __, and __ fraction circle wedge from a set of fraction circles Remove a __ 3 4 6 8 for each group. Label and place the fraction circle wedges into the quart-size resealable bag with the Toy Design Cards. Gather 4 paper plates and a pair of scissors for each group. For students who need more support in recalling information, please see our Fraction Circles Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used for support in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles)

• •

Consumable •

• • •

4 Paper plates (per group)

•

1 1 1

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Project this scenario for students to read along with you.

FACILITATION TIP Consider the thickness and type of paper plates before having student cut into them with school scissors.

2. 3. 4.

Read the following scenario to the class: There is a local toy company in your town that builds customized wooden toys for their customers. Some of these toys include wooden food play sets that kids can pretend to cut and serve to their parents or friends. Customers can order different pizza, cake, or pie play sets and customize the number of pieces in each set. You just so happen to be a master woodworker, and this toy company has hired you to cut the pieces in each of these orders so each play set has equal-sized pieces in each play set. It is up to you to determine the angle measure of each food play set so the toy is designed just right. Give a Student Journal to each student. Distribute 4 paper plates, a pair of scissors, and a bag of Toy Design Cards and fraction raction circle wedges to each group. Explain to the class that they will be working with their groups to read each Toy Design Card in order to determine the correct fraction circle wedge to use to create the play set. Each paper plate represents a toy play set they will be creating for each customer. Encourage students to quickly examine their cards, and discuss the following questions: a.

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Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 How many degrees does it take to go all the way around the circle? It takes 360°.

DOK-2 What would happen if we cut the food play set in half? We would be dividing 360 by 2, which means each half of the circle is 180°.

DOK-3 How can we use the information given in the Toy Design Card and fraction circle wedge to create the play set using the paper plate? I can read the Toy Design Card to determine how many pieces the play set will be cut into. I can then mark the center of the plate and place the correct fraction circle wedge on that point and mark off each piece of the play set that needs to be cut.

Challenge students to mark the center of each of their paper plate toy play sets. They will then use this center to place the correct fraction circle wedge from their bag and create the correct number of pieces needed to be cut to design the play set. We want each piece in a toy play set to be the same, so it is important that each angle is cut correctly. Students will use their scissors to cut the pieces.

Explain to students that they will then solve using a division equation to determine the angle measure of each piece and then label each piece with that angle measure. They can then use multiplication to check their work. Students then label the angle measure on each piece of their paper plates.

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What information is given to you about the wooden play set? Answers may vary. I am told how many pieces the play set will be separated into.

DOK-2 How can we use our fraction circle wedges to model this scenario? Answers may vary. We can ﬁnd the fraction circle that 1 represents _8_ to model that the play set will be divided into 8 pieces. I will place that fraction circle wedge on my paper plate and use it to help me cut my paper plate into 8 equal pieces.

DOK-2 How can we use our model to help us ﬁnd the angle measure of each piece? Answers may vary. I know that the denominator of each fraction circle is 8. I also know that a circle measures 360°. If I divide the whole circle of 360° by the 8 pieces, then I can determine the angle measure of each piece.

DOK-3 How can we use a division equation to represent this problem to ﬁnd the solution? Answers may vary. I will divide 360° by 8 to determine the angle measure of each piece.

e. DOK-3 How can we use a multiplication equation to represent this problem to ﬁnd the solution? Answers may vary. I can multiply the missing factor by 8 knowing that when I multiply 8 by the product, it will equal 360°. f.

DOK-2 When using the equations, what did you determine to be the angle measure of each piece? Answers may vary. I found that the angle measure was 45°.

DOK-3 What did you notice about the solution to the division and multiplication problem? Explain. I noticed that the answers for the division and multiplication problem were the same. In order to ﬁnd the unknown angle measure, or missing factor, we needed to divide 360° by 8, which gave us the value of 45°. I checked my division work using multiplication and found that 8 × 45° equals 360°.

Intervention

Acceleration

ANGLES

Home

FACILITATION TIP Help students ﬁnd the center of the paper plates by making a few gentle folds that create a center point. (Alternatively, premark the plates with center points beforehand). FACILITATION TIP For students who may struggle to precisely trace and cut the wedges, consider providing support from older students or adults. Alternatively, have students just draw the angles and shade with a pencil rather than cutting.

STEMscopes Tip Career Connections is found in the Elaborate section of Grades 3–5. This element features a STEM career video or slideshow to showcase how the math concepts students are learning are applied in real-world work settings and what 21st century skills are needed to be successful. A followup activity related to the career that highlights the math concepts from the scope is also included.

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ANGLES

Angles Explore 2 – Determine the Angle Measure h. DOK-2 How can we use our solution to label each piece of our toy play set? Answers may vary. Since I determined that each piece was 45°, I will label each piece of the play set with “45°.” 8. 9. 10.

Have students record their model with labels, equations, and solution statements on their Student Journals. Once students have completed every problem on their Student Journals, have them answer the reﬂection questions that follow. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP Print and project the Math Chat questions to guide your class discussion. Record appropriate student responses. STEMscopes Tip Each scope includes a Home section accessed along the scope’s menu bar. Here you will see student expectations as well as key concepts and fundamental questions. Each Home tab includes drop-down options to access the Scope Overview, Content Support, Content Unwrapped, Materials List, and Parent Letter pages.

DOK-3 How is the angle measure of a piece of the circle related to the measure of the whole circle? The measure of a whole circle is 360°. When I’m determining the angle measure of a piece of the circle, it represents the measure of that piece of the whole circle. • DOK-2 What do you notice about the measure of each angle when a circle is divided into equal pieces? I notice that the angle measure of each piece is the same when they are divided into equal pieces. • DOK-3 How can we use division or multiplication to determine the measure of an angle within a circle? If we are dividing the circle into equal parts, we can take the total degrees of the circle, which is 360°, and divide it by the given number of parts to determine the degrees of each angle. We can check that by multiplying the angle measure by the number of equal parts to ﬁnd that it equals 360°. •

Post-Explore 1. Have students complete the Exit Ticket to formatively assess their understanding of the concept. 2. Complete the Anchor Chart as a class. 3. Have each student complete their Interactive Notebook. Notes

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Explain

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ANGLES

Home

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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ANGLES

Angles Explore 3 – Measure Angles ACTIVITY PREPARATION Students use manipulatives to explore and measure angle sizes.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Robot Pathways Cards (per group) 1 Exit Ticket (per student)

•

Reusable • • •

•

1 180° protractor (per student) 1 Ruler (per student) 1 Quart-size resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of the Robot Pathways Cards for each group. The Robot Pathways Cards can be printed on card stock and laminated for durability, if desired. Place cards inside a quart-size resealable bag. For students who need more support in recalling information, please see our Fraction Circles Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used for support in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. STEMscopes Tip The Engage section, located along the scope menu, is designed to activate student interest in the learning topic. Within the Engage section, activities to access students’ prior knowledge about the topic, to build a strong foundation to bridge any gaps in understanding before diving into the new content, and to set the purpose for learning a new skill are included.

4. 5.

6. 344

Give a Student Journal to each student. Give a set of Robot Pathways Cards to each group. Read the following scenario to the class: You and a team of robot designers are coding your robots to follow a certain pathway to get from a starting point to an endpoint. This code will tell your robot how far to travel on a given path and what angle measure in which to turn when it comes time to change directions. In order to write this code, it is important to know the degree of each angle so your robot can follow the pathway correctly. Explain to the class that they will be working with their groups to determine the measurement of each angle in order to code their robots correctly. Discuss the following questions: a.

DOK-1 When we want to ﬁnd the exact measurement of something, what do we do? We use a measurement tool such as a meterstick or a scale to ﬁnd the exact measurement.

DOK-1 Angles can be many different sizes. How do you think we can ﬁgure out the exact measurement of an angle? Accept all answers. For example: We can use a ruler to measure how “open” it is.

8. 9.

10.

11. 12.

14.

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Give each student a protractor. Have student pairs put two protractors together to form a circle. Discuss the following questions: a.

DOK-1 What do you notice about the protractors when they are together? They form a circle.

DOK-1 What is the measure of a circle in degrees? A circle is 360 degrees.

DOK-1 How are the numbers arranged on one protractor? The top row goes from 0 to 180, and the bottom row goes from 180 to 0.

DOK-1 What is 180 plus 180? It is 360.

Allow students to discuss why they think there are two sets of numbers on the protractor and then share their ideas with the class. Explain that a protractor has two sets of numbers because sometimes the angle is open to the right and sometimes the angle is open to the left. These two sets of numbers, called number scales, make it easier to measure any angle, regardless of the direction of the angle. Have students look at the protractor numbers again. Discuss the following questions: a.

DOK-1 How many lines are there between the numbers? There are 10 lines.

DOK-1 What do you think those lines represent? Each line is a degree.

DOK-1 If an angle measured 5 lines past 40, what would the measurement of the angle be? It would be 45 degrees.

STEMscopes Tip Located along the scope menu is the Explore section. One to ﬁve inquirybased Explore activities are designed to be hands-on, teacher-facilitated lessons in which students collaborate to build conceptual understanding and reason mathematically. This section also contains Skill Basics lessons in Kindergarten through Grade 2 and Virtual Manipulatives.

Tell students that the protractor uses the vertex and the sides, or rays, of an angle to measure the size of the angle. Show students where the vertex of an angle should be placed on the protractor. Have students look at the angle made with the ﬁrst turn of robot 1 ( ABC). Students should take turns following these steps: a.

Place the midpoint of the protractor on the vertex of the angle. (Some protractors have a hole where the vertex should be.)

The ﬂat edge of the protractor is called the zero line. Line up one side of the angle with the zero line of the protractor (where you see the number 0 in the number scale).

Explain that if a line is too short and does not cross the angle measurements on the protractor, you should line up the edge of the protractor to the ray and draw the extension so you are able to measure the angle more easily.

d. 13.

Engage

ANGLES

Home

Count the degrees, starting from 0, until you get to where the other side of the angle crosses the number scale.

Students should determine this angle’s measurement and record it on their Student Journals, along with the direction of the turn. Students may need assistance with naming the angles. a.

If needed, draw an angle on the board. Demonstrate how to write A on one side of the angle, B at the vertex of the angle, and C on the other side of the angle, just like the ﬁrst turn of each robot.

Explain to students that they read this angle as, “angle ABC” or “angle CBA.” Show students this angle would be written as ABC or CBA.

STEMscopes Tip The Explain section, located along the scope menu, has a variety of elements designed to solidify students’ understanding of the content presented in the Explore section. Each scope’s Explain section includes a Picture Vocabulary, independent practice assignments, anchor charts, journal prompts, and interactive notebook activities.

Have each student in each group take a card and measure the angles for the pathway. Students will exchange cards until they have measured the angles for each pathway.

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ANGLES

Angles Explore 3 – Measure Angles 15.

16. 17.

STEMscopes Tip Located along the scope menu is the Elaborate section, where engaging activities that extend student learning and solidify their understanding of math concepts are found. Included are hands-on and virtual games; a math review and math story; a problembased task; proﬁles of careers and everyday life situations where math is used, and in the primary grades, a discussion of a data set.

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you ﬁnd that angle’s measurement? I put the protractor on the vertex. I put one side of the angle on the zero line. I looked at where the other side of the angle crossed the number scale.

DOK-1 How did you name the angles? I used the three points on the angle’s rays and listed them in order with the vertex point being in the middle.

Students should compare their measurements. If there is a discrepancy, have them remeasure the angle and come to an agreement. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-1 What do you need to do to get an accurate measurement when using a protractor? We need to make sure the vertex is on the correct spot on the protractor. We need to line one side up with the zero line. We need to make sure we are using the correct number scale. • DOK-2 Why do we name angles? We name angles so people can know which angle we are talking about. Naming angles helps us see each angle in a shape or pathway and make sure we are talking about the same angle. • DOK-3 In what situations would measuring angles be helpful? You are building a house and need to cut boards correctly. If you were making a cover for something, you may need to measure the angles of the corners to make the cover ﬁt. •

Post-Explore 1. 2. 3. 4.

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Intervention

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Home

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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ANGLES

Angles Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Angles as Fractions of a Circle Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Determine the Angle Measure Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Measure Angles Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

348

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ANGLES

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Fun Times at the County Fair

Orthopedic Doctor

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Why Do Different Areas Have Different Climates?

Problem Solving with Angles

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task Protect This City Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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ANGLES

Angles Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ANGLES

Home

What prompts will be used?

What does mastery look like?

I can measure an angle in reference to a circle with the center at the common endpoint of two rays.

I can determine an angle’s measurement in relation to the 360 degrees in a circle through division or a missing-factor problem.

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SCOPE 1

Points, Lines, and Angles Scope Introduction SCOPE SUMMARY Students are expected to understand the concepts of and be able to draw points, lines, line segments, lines of symmetry, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. When given two-dimensional shapes and various images and representations, students are able to investigate, identify, and draw each of these attributes that are unique to the shape. Student Expectations

4.GSR.7.1 Recognize angles as geometric shapes formed when two rays share a common endpoint. Draw right, acute, and obtuse angles based on the relationship of the angle measure to 90 degrees. 4.GSR.8.1 Explore, investigate, and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, parallel lines, and lines of symmetry. Identify these in two dimensional ﬁgures.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students make generalizations about properties that are shared between categories of 2-D shapes, such as parallel line segments, perpendicular line segments, right angles, and lines of symmetry. Third-grade students mainly focus on identifying quadrilaterals and subcategories of quadrilaterals, but they also classify, compare, and contrast various polygons up to 6 sides and 3-D solids.

Students will continue enhancing their knowledge and application of this standard. Fifth-grade students use the geometric properties of sides, angles, and symmetry to classify polygons, quadrilaterals, and triangles in categories and subcategories. For example, they conclude that squares are parallelograms because they are quadrilaterals with opposite sets of parallel and congruent sides. Students use deductive reasoning to justify their thinking about the categories into which shapes are sorted while gaining a deeper understanding of “if …, then …” relationships. For example, if a shape is a parallelogram, then it must also be a quadrilateral.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to:

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to:

•

identify parallel lines.

•

identify two-dimensional ﬁgures.

•

identify parallel lines.

•

determine if statements describing attributes of shapes are true or false.

•

identify perpendicular lines.

•

identify lines on a navigation map.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 352

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Investigate and Draw Points, Lines, Rays, and Angles In this exploration, students will work collaboratively to solve a scenario in which they help a local science museum create a model of a newly discovered constellation. In solving the scenario, students will: •

identify points, lines, and rays of real-world objects.

•

understand points, lines, and rays of real-world objects.

•

understand geometric attributes.

Explore 2

Explore 1

EXPLORE ACTIVITIES

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Investigate and Draw Types of Angles In this exploration, groups will help determine if a ﬁsherman’s idea that the greater the angle the line and the rod make when the line is cast, or thrown into the water, the more ﬁsh you will catch is true. As students solve the scenario, students will: •

classify the angle as acute, right, or obtuse angle.

•

measure angles of different boat designs and classify the angles as acute, right, or obtuse.

•

measure pole angles using a protractor.

POINTS, LINES, AND ANGLES

Home

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Investigate and Draw Types of Lines In the ﬁnal exploration, students are tasked with solving a real-world scenario where they imagine they are helping build a new track and four-square court for their school’s playground. In solving the scenario, students will: •

explore perpendicular and parallel lines.

•

identify perpendicular and parallel lines within their environment.

•

identify attributes of two-dimensional shapes.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

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POINTS, LINES, AND ANGLES

Points, Lines, and Angles Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students answer either true or false to statements about different types of quadrilaterals. This activity is intended to assess mastery of the following standard(s): 3.GSR.6.1 Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve 3.GSR.6.1 problems involving parallel line segments, perpendicular line segments, and right angles.

Materials Printed • • •

POINTS, LINES, AND ANGLES

Home

Reusable

1 Slideshow (per class) 1 Set of True/False Cards (per class or per student) 1 True/False Statements (per teacher)

• 1 Projector or document camera (per class)

Preparation • • •

Prepare to project the Slideshow. Print one set of True/False Cards to hang on opposite sides of the classroom, or print one set of True/False Cards (front and back) per student. Print a True/False Statements for the class.

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5.

6. 7.

Hang True/False Cards on opposite sides of the classroom. If you prefer for students to do this activity individually from their desks, then print the True/False Cards double-sided for each student. Project the ﬁrst slide on the screen for each student to see. Read each statement from the True/False Statements. Ask students to go to the side of the classroom and stand near the answer with which they agree. Alternatively, students can answer individually from their seat by holding up either the True side or the False side of the card. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Repeat steps 2–5 for slides 2–4. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Ask students if they can name each figure. If so, have them write the name of each figure on the displayed copy. FACILITATION TIP If time allows, try the following extension activity: Display all the figures. Invite one student to describe a shape they are thinking of and to call on their classmates to guess the shape. For example, a student may say, “I am thinking of a shape that has more than 3 vertices and only one line of symmetry,” and their classmates may guess Figure 3.

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POINTS, LINES, AND ANGLES

Points, Lines, and Angles Hook – Lead the Way! ACTIVITY PREPARATION Students identify parallel lines, perpendicular lines, and angles on a map and in 2-D ﬁgures.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Part I

Reusable • •

Plan to show the Phenomena Video. Print a Student Handout for each student.

•

1 Phenomena Video (per class) 1 Projector (per class)

Plan to project the Student Handout.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You made a map of your hometown for a new student. You know your way around town, but you can’t remember the names of the streets. You will need to use the clues I give you to ﬁll in the street names on the map before giving it to your new friend. Project the Student Handout for the class. Discuss the following questions: a.

DOK-1 What is an intersection? It is where two streets meet or cross on a map.

FACILITATION TIP

Guide the students to number the intersections from left to right going down each street.

DOK-1 How many intersections do you see on this map? I see 17 intersections.

DOK-1 Does an intersection have to make a perfect corner, or can the crossing streets be at different angles? They can be at any angle.

DOK-2 Are there any streets that can never cross even if they keep going in the same direction off the edge of the map? Yes, streets that are next to each other will never cross.

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Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Give a Student Handout to each student. Discuss the following questions: a.

DOK-1 What is an intersection? It is where two streets meet or cross on a map.

DOK-1 How many intersections do you see on this map? I see 17 intersections.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 Are there any streets that can never cross even if they keep going in the same direction off the edge of the map? Yes, streets that are next to each other will never cross.

Read the clues one at a time slowly, and repeat each one a few times before moving on to the next clue. Give students some time to write the street names. You can also have them turn and talk to see if they agree by explaining their thinking to each other. a.

The northernmost street that runs east to west is called Nickel Way.

The closest parallel street to Nickel Way is called Tangent Lane.

FACILITATION TIP Consider printing the street name clues with space to write the names. Students can then transfer the names to the maps.

POINTS, LINES, AND ANGLES

Home

c. Trapezoid Avenue intersects Tangent Lane but is NOT perpendicular to it. d.

Quotient Row is the westernmost street that is perpendicular to Tangent Lane.

e. Angle Drive is the southernmost street that is perpendicular to Quotient Row. f.

Perimeter Lane is perpendicular to Angle Drive and is next to the sports ﬁelds.

Protractor Way is parallel to Angle Drive.

h. Sum Avenue is perpendicular to Protractor Way. 4.

Gather students in a whole group, and discuss the following questions: a.

DOK-1 What are two lines that cross called? They are called intersecting lines.

DOK-2 What are some intersecting roads on this map? Answers will vary. Examples include Nickel Way and Trapezoid Avenue, Quotient Row and Tangent Lane, etc.

DOK-2 How do streets that intersect and are perpendicular look different from streets that are not perpendicular? The streets that intersect and are perpendicular have right angles (perfect corners) at the intersections. The streets that intersect and are not perpendicular have intersections that are acute or obtuse angles.

DOK-2 How many perpendicular intersections are there on this map? There are 12 perpendicular intersections.

e. DOK-2 How many obtuse angles are at intersections on this map? I counted 8 obtuse angles at intersections on this map. I know that obtuse angles are greater than right angles. I looked for any intersections that made angles larger than a perfect square. f.

DOK-2 How many acute angles do you see in the intersections on the map? I counted 8 acute angles. I looked for any angles that were less than a right angle.

DOK-2 What streets are parallel in the trapezoid area created by the streets around the city park? Tangent Lane and Protractor Way are parallel in that trapezoid area of the map.

h. DOK-2 What streets are parallel in the square area around the post oﬃce? Nickel Way and Tangent Lane and Quotient Row and Sum Avenue are parallel. i. DOK-1 What are the angles at each intersection called? They are called right angles. I know they are right angles because they each create a perfect square.

FACILITATION TIP Generate hand gestures to represent perpendicular and parallel lines.

FACILITATION TIP Use physical response to have students model acute and obtuse angles with arms, hands or ﬁngers. STEMscopes Tip The Intervention section of each scope is found along the scope menu. If the assessments revealed that some students have not reached mastery of the content, the Intervention section has Small-Group Intervention and Supplemental Aid resources to help those students who need reteaching and additional support.

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Points, Lines, and Angles Explore 1 – Investigate and Draw Points, Lines, Rays, and Angles ACTIVITY PREPARATION Students experience real-world objects as they investigate the points, lines, rays, and angles on each one.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Constellation Cards (per group) 1 Exit Ticket (per student)

•

Plan to divide the class into groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Constellation Cards for each group. These can be printed on card stock and laminated for durability, if desired. For students who need more support in recalling information, please see our Geoboard Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Project this scenario and read it along with students. Project visual images of stars, constellations, and astronomers to connect with students. Ask students about their experiences with the night sky.

2. 3.

Read the following scenario to the class: You are planning to join a group of astronomers who identify new constellations. Constellations can be described using various geometric attributes. To join the group of astronomers, you must ﬁrst go through extensive training with identifying geometric attributes in known constellations. Today, we are about to start your training! It’s time to identify the attributes of some constellations. Divide the class into groups. Distribute Constellation Cards to each group. Discuss the following question: a.

FACILITATION TIP Consider labeling the points on the constellations together as a whole class. With common points labeled you can all discuss line segments, rays, lines, and angles on each ﬁgure. If all students have different labels, it may be diﬃcult to clarify.

FACILITATION TIP Consider providing some constraints on where students will locate the rays on the constellations.

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DOK-1 What do you notice about the constellations on the cards? The constellations are made up of several points, line segments, angles, etc.

Explain to students that they will work in groups to draw each constellation, label the points using letters, and ﬁnd two examples of each attribute on their Student Journals. Model for students how to use geometric notation for points, lines, line segments, rays, and angles. Students will use these notations to distinguish between the different attributes they ﬁnd on their constellations. The Libra constellation can be completed as a class before they begin work in their groups on the other constellations. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Why do you think it is important to label the points on your drawn constellations? The points and the labels help us identify the different attributes that make up the constellations.

DOK-2 What makes a ray different from a line? A line goes on forever in both directions. A ray has one endpoint and only goes on forever in one direction.

DOK-1 How will you identify examples of rays and lines on your constellations? We will draw imaginary lines and rays that extend from line segments on our constellations. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Allow students enough time to complete their drawings for each constellation and to ﬁnd two examples of each attribute on their Student Journals. Students can answer the questions at the bottom of their Student Journal pages after they have completed all of the work for their Constellation Cards. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What makes a line segment different from a line? They both are straight. Lines go on forever in both directions, and line segments are a piece of a line. • DOK-1 Where in our classroom do you see examples of line segments? The edges of our bulletin board are made of line segments. My pencil is an example of a line segment. • DOK-2 What is the relationship between a ray and an angle? An angle consists of two rays with a common endpoint. • DOK-1 Where in our classroom do you see examples of angles? I see an angle made when I open my scissors. There is an angle on our clock made by the two hands. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Intervention

Acceleration

FACILITATION TIP Project these Math Chat questions to guide your discussion. Post examples and deﬁnitions for each math term included in this Explore activity on your word wall.

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Points, Lines, and Angles Explore 2 – Investigate and Draw Types of Angles ACTIVITY PREPARATION Students use manipulatives to investigate, classify, and measure angle sizes.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of Fishing Angles (per group) 1 Exit Ticket (per student)

• •

Reusable • • •

•

1 Protractor (per student) 1 Ruler (per student) 1 Pair of scissors (per class)

•

Consumable • •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Fishing Angles for each group. These can be printed on card stock and laminated for durability, if desired. Cut the paper plate into fourths (to create four right angles) for each group. For students who need more support in recalling information, please see our Angles Supplemental Aids element in the Intervention section.

1 Paper plate (per group) 1 Sheet of chart paper (per class)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Post the theory on the board as this is the question that the students are trying to answer with the Explore activity.

FACILITATION TIP Have students write “90 Degrees” on each piece of the plate pieces. Later, students can write “Right Angles” on the plates.

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Part I: Angler Theory 1.

2. 3.

Read the following scenario to the class: It’s almost time for the annual Angler Fishing Tournament! You love to fish, so you have entered the contest for the first time. You have watched other anglers fish in the contest for years, and you have a theory that the greater the angle the line and the rod make when the line is cast, or thrown into the water, the more fish you will catch. Give each student a Student Journal and a ruler. Give groups the Fishing Angles. Students should use their plate pieces to measure the angles and sort them into groups of angles that are exactly 90 degrees, greater than 90 degrees, and less than 90 degrees. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How do you know this angle is greater than 90 degrees? The angle is bigger than my 90-degree angle on my plate piece.

DOK-1 How did you measure this angle? I put my 90-degree piece against one side of the angle. If I could see the other side of the angle, I knew the angle was greater than 90 degrees. If I couldn’t see the other side of the angle, I knew the angle was less than 90 degrees. If it matched my 90-degree piece, it was a 90-degree angle. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Once students have sorted the angles into three piles, have them estimate the measure of each angle based on how close it is to 90 degrees (or 180 degrees). Students should draw each angle and write the estimate on their Student Journals. Make sure students are drawing and naming the angles appropriately. Review with students that 90-degree angles are called right angles and 180-degree angles are called straight angles. Explain to students that angles that are less than 90 degrees are called acute angles, and angles that are greater than 90 degrees but less than 180 degrees are called obtuse angles. On the chart paper, draw an example of each type of angle, and write its name. Have students add the names of each of the angles to their Student Journals. Challenge students to determine whether their theory is correct that the greater the angle the line and the rod make when the line is cast, or thrown into the water, the greater number of ﬁsh are caught by looking at the total number of ﬁsh caught in each of their sorted categories.

Intervention

Acceleration

FACILITATION TIP Students can create each angle measurement using their hands. Have students repeat to the class each angle type.

POINTS, LINES, AND ANGLES

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Part II: Angler Reality 1.

Discuss the following questions: a.

DOK-1 How can we know the exact measure of each of these angles? We can use a protractor to measure the size of the angle.

DOK-1 What units does a protractor measure? Degrees

Have each student in the group take a ﬁshing angle and measure the angle. Have students then record the measurement of the angle on their Student Journals. Students will exchange ﬁshing angles until they have measured and recorded all eight angles. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you ﬁnd that angle’s measure? I put the protractor on the vertex. I put one side of the angle on the zero line. I looked at where the other side of the angle crossed the number scale.

DOK-1 Is that an acute, right, or obtuse angle? Answers will vary. It is an obtuse angle.

DOK-1 What makes an angle obtuse? The measure of the angle is greater than 90 degrees but less than 180 degrees.

DOK-1 What makes an angle acute? The measure of the angle is less than 90 degrees.

FACILITATION TIP Model how to use the protractor and the have students write and say the unit of “degrees” when collaborating. FACILITATION TIP Using a protractor may be a new skill for many students. Students will need practice. If available, use clear protractors and large boldly drawn angles as practice before this Explore activity.

e. DOK-1 What would an angle that measures 179 degrees be called? It would be called an obtuse angle. 4.

Students should compare their measurements. If there is a discrepancy, have them remeasure the angle and come to an agreement.

Part III: The Perfect Boat 1.

Read the following scenario to the class: The Angler Fishing Tournament is fast approaching, and you need a good ﬁshing boat! Your boat needs to have obtuse angles so you can easily move around, but it also needs acute angles so it glides smoothly and quietly through the water. The boat store has all different kinds and sizes of boats. It’s up to you to pick the one you think will be the best! Draw a triangle on the board. Discuss the following questions: a.

DOK-1 How many angles does a triangle have? A triangle has three angles.

DOK-1 How might you measure these angles? I can use a protractor and place the zero line on one side of the triangle and the vertex in the correct place and then measure where the other side crosses the number scale. I can do this for all three angles.

FACILITATION TIP Allow students to correct their measurements and ﬁgure out what their errors in measurement were.

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Points, Lines, and Angles Explore 2 – Investigate and Draw Types of Angles

FACILITATION TIP Model with another polygon on the board how to measure each angle, write the angle measurement, and identify the type of angle.

3. 4. 5. 6.

FACILITATION TIP Have the groups discuss the Reﬂection question and develop one cohesive explanation.

DOK-1 If the sides of the angle are too short and don’t reach the top of the protractor, what can you do? We can place one side against the protractor’s zero line and then lay a ruler on top of the protractor along the other side so the ruler crosses the number scale. We could use a straightedge to draw longer sides so they cross the number scale.

DOK-1 Which number scale on the protractor should you use? It depends on the way the angle is facing. I always need to make sure I am starting the measurement at 0.

Point out that there needs to be proper notation when naming each angle. For example, students need to write “ ABC = _____.” Have students look at the four polygons on their Student Journals. Explain that these are the ﬁshing boats that are for sale. Students should work together to measure the angles of each ﬁshing boat and identify them as acute, right, or obtuse. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you measure ABC? I put the protractor on the vertex, which was B. I made sure the side AB was on the zero line of my protractor. The number on the number scale where the side BC crossed the protractor was the measurement of the angle.

DOK-1 What did you do when the sides of the angle were too short? We drew longer sides; we placed one side against the protractor’s zero line, and then we laid a ruler on top of the protractor along the other side. The number where the ruler crossed the protractor on the number scale was the measurement of the angle.

DOK-1 How do you know if this angle is acute or obtuse? I measured the angle using a protractor and saw it was greater or less than 90 degrees.

When student groups ﬁnish measuring the polygon angles, have them compare their measurements with another group. If there is a discrepancy, have them remeasure the angle and come to an agreement. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 What connections did you make during this activity? We were comparing numbers to 90 to see if they were greater or less than 90. We were measuring angles using a protractor, which we have done before. • DOK-2 Why do we name angles using the points on the rays? We name angles using the points on the rays so people can know which angle we are talking about. Naming angles helps us see each angle in a polygon and make sure we are measuring each one. • DOK-1 How can you quickly classify angles? If the angle appears to be smaller than a perfect corner, then it is probably smaller than 90 degrees and is acute. If it looks larger than a perfect corner, then it is probably greater than 90 degrees and is obtuse. •

FACILITATION TIP Before students complete this Exit Ticket, consider your criteria for success. The angle on this Exit Ticket measures 88°, some students may come very close and think it is a 90° angle.

Post-Explore 1. 2. 3.

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Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

POINTS, LINES, AND ANGLES

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Points, Lines, and Angles Explore 3 – Investigate and Draw Types of Lines ACTIVITY PREPARATION Students explore perpendicular lines, parallel lines, and lines of symmetry and investigate them within their environment and as attributes of two-dimensional shapes.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • • •

1 Student Journal (per student) 1 Set of Playground Track Options (per group) 1 Exit Ticket (per student)

Reusable •

•

1 Ruler (per group)

Consumable • •

•

5 Rolls of painter’s tape (per group) 1 Piece of sidewalk chalk (per teacher)

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Playground Track Options for each group. The ﬁrst two parts of this activity should be done outside on a hard surface. A grassy area could work, but the results will not be ideal. If weather is an issue, this activity could be done in the classroom, but students will have to make much smaller models. A large hallway or gymnasium are also options. Students will be working outside, so they should bring their binder, a clipboard, or something else hard to write on. For students who need more support in recalling information, please see our Math Shapes and Tangrams Supplemental Aids elements in the Intervention section.

PROCEDURE AND FACILITATION POINTS Part I.a: Create Perpendicular Lines FACILITATION TIP Prior to going outside, ensure that students are familiar with the game Four Square. Show students a video clip of the game being played or a photograph of the court. FACILITATION TIP

1. 2.

Unless students use a ruler, they may ﬁnd it diﬃcult to draw an exact square. Ask students whether their courts are in the shapes of rectangles or squares and how they know. 4. 5. 6. 7. 364

Take students outside to an area with a hard surface. Give each student a Student Journal and a roll of painter’s tape. Tell students to spread out with their groups and create a four-square court. Tell them to use their tape to mark off the area for their court. Listen to conversations as students create their four-square court. Have students draw a model of their court on their Student Journals. Have groups walk around to each other’s courts. Discuss the following questions: a.

DOK-1 What shape is the court? It is a square.

DOK-1 What shapes are the courts divided into? They are divided into squares.

DOK-2 Describe the lines. They are straight. They make a perfect T.

Explain to students that lines such as the ones in the middle of the court are called perpendicular lines. Perpendicular lines create four right angles. Give each group time to go back to their courts and check to make sure the angles created by their perpendicular lines are right angles. Model how to use the corner of their Student Journals to check this. Label the interior lines on one group’s court with points using sidewalk chalk. Tell students they are going to practice naming the lines and comparing them using symbols. Call on volunteers to name each interior line segment of the court. Write each of these on the hard surface. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Show students how to write the symbol for perpendicular lines ( ) in between line segments that are parallel (for example, AB CD). Explain that the order of the line segments does not matter as long as they are identifying them as being perpendicular. Discuss the following questions: a.

DOK-2 Why must the lines of the four-square court be perpendicular? They must be perpendicular because they create four smaller squares that are equal in size.

DOK-2 What would happen if the lines were not perpendicular? (Allow students to rotate one of the lines if they are unsure.) The boxes would not be equal in size. Some boxes might be bigger than others, and that would not make the game fair.

Intervention

Acceleration

FACILITATION TIP Prompt students to record this symbol in the margins of their Student Journals.

POINTS, LINES, AND ANGLES

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Have students answer the questions on the ﬁrst page of their Student Journals.

Part I.b: Create Parallel Lines 1. 2.

After students have completed their reﬂection questions, tell them to remove the tape from the hard surface. Tell them their next task will be to create a two-lane racetrack. Tell students to spread out with their groups and create their racetracks. Have them use their tape to mark off the lanes. Listen to conversations as students create their tracks. Have students draw a model of their track on their Student Journals. Have groups once again walk around to each other’s models. Discuss the following questions: a.

Lines such as the ones that make the tracks are called parallel lines. They can go on and on and will never intersect (or run into each other). a.

8. 9.

10.

DOK-1 Are these lines still parallel? How do you know? No, they are not because even though they do not touch right now, they will eventually touch each other if we extend the lines.

Move one line farther away from another line, keeping them parallel but adding a bigger space between them. Discuss the following questions: a.

DOK-2 Why must lines on a racetrack be parallel? If the lines touched, there would not be lanes. The racers would crash into each other. They wouldn’t have a lane to run in.

Model how to move the lines on one of the tracks. Carefully lift the tape from one lane of a group’s racetrack, and move it to a new location where the lines still do not touch but are not parallel. Discuss the following question: a.

DOK-1 Describe the lines used to make the tracks. They are straight. They do not touch. There is equal space between them.

DOK-1 Are these lines still parallel? How do you know? Yes, they are because even though they are far apart, they still will never touch if they are extended.

Label the lines on one group’s racetrack with points using sidewalk chalk. Tell students they are going to practice naming the lines and comparing them using symbols. Call on volunteers to name each line segment of the racetrack. Write each of these on the hard surface with chalk. Show students how to write the symbol for parallel lines (II) in between line segments that are parallel (for example, AB II CD). Explain that the order of the line segments does not matter as long as they are identifying them as being parallel. Have students answer the remaining questions for Part I on their Student Journals.

FACILITATION TIP Prompt students to draw arrows at the end of each piece of tape to indicate that the lines could extend forever without intersecting. FACILITATION TIP To help illustrate this concept, invite two students to walk directly on one set of racetrack tape. Have them extend an arm out to show that the pieces are a certain distance apart; then, have them slowly walk forward, demonstrating that they remain the same distance apart as the lines extend.

STEMscopes Tip The STEMscopes Teacher Toolbox, located under the Scopes tab on the menu bar, features a variety of resources and tools to help teachers get the get most out of their STEMscopes experience, including essentials like lesson-planning documents, intervention strategies, monitoring tools, mathematical discourse strategies, and data resources.

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Points, Lines, and Angles Explore 3 – Investigate and Draw Types of Lines Part II: Lines Are All around Us 1. 2.

Before heading back to the classroom, take a short walk around the building or playground. With their groups from Part I, students should look for two examples of perpendicular lines, two examples of parallel lines, and two examples of lines that are neither perpendicular nor parallel. Have them draw and label each example in the chart in Part II of their Student Journals. As a whole group, discuss the attributes of each example and how they are similar and different.

Part III: A New Track FACILITATION TIP

Project the scenario and the design constraints 1a–1d for students to reference as they collaborate.

2. 3.

Read the following scenario to the class: Our school wants to build a new track on the playground! There are certain criteria that must be met for the design to be accepted by the school. It is your job to evaluate each design option and determine if it meets the criteria. The track must do the following: a.

Contain at least 2 sets of parallel sides

Contain no acute angles

Contain at least one set of perpendicular sides

Contain at least one line of symmetry

Pass out the Playground Track Options to each group. Tell students before they get started that there is one more line type they must discuss. Instruct students to look at the ﬁrst Playground Track Option. Discuss the following questions:

FACILITATION TIP

Students should be familiar with lines of symmetry from prior standards, but take time to review and clarify.

DOK-1 What is the type of line that divides a shape into two congruent halves? It is called a line of symmetry.

DOK-2 How can I determine if the ﬁrst track has a line of symmetry? We can fold the shape in half to see if the halves match up perfectly.

Allow groups time to determine the number of lines of symmetry the ﬁrst track has. Discuss the following question: a.

5. STEMscopes Tip A link to the list of standards is located on the menu bar. Here, standards can be accessed using two methods: click on the expandable list to see standards organized by grade level, or locate speciﬁc standards using the key word search. Either method will result in locating standards with direct links to the scopes in which they appear.

Students will work together to ﬁll out the report by checking off different criteria on their Student Journals and answering the reﬂection questions at the end. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

• •

•

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DOK-1 How many lines of symmetry does the track have? The ﬁrst track is a parallelogram and has no lines of symmetry.

DOK-3 What connections did you make during this activity? I was able to use what I know about angles to help determine which track meets the criteria. I recognized some of the shapes of the track options. I remembered their names. DOK-1 Which track option ﬁt all the criteria? Track 2 DOK-1 How did you know if the track contained parallel or perpendicular sides? I could use a ruler to extend opposite sides and see if they would run into each other. If they are always the same distance apart, they are parallel. If two sides make a right angle, they are perpendicular. DOK-1 How did you know if the track contained any acute angles? I looked at each angle inside the track. If any of the angles were smaller than a perfect corner (or 90-degree angle), then I knew it was acute. DOK-1 How did you know if the track contained a line of symmetry? I folded the track in different ways to see if it contained two congruent halves.

Engage

Explore

Explain

Elaborate

Evaluate

Post-Explore 1. 2. 3. 4.

Intervention

Acceleration

FACILITATION TIP

When you preview this Exit Ticket with students, clarify that it is two sided. Struggling students may need help examining Shape B for lines of symmetry.

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Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Points, Lines, and Angles Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Investigate and Draw Points, Lines, Rays, and Angles Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Investigate and Draw Types of Angles Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Investigate and Draw Types of Lines Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Peppy’s Pizza Parlor

Land Surveyor and Cartographer

A quick story to engage student interest along with four problems covering previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Looking through Lenses

Deﬁne Geometric Attributes

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

POINTS, LINES, AND ANGLES

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Problem-Based Task X Marks the Spot Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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Students who are still acquiring the concept and need remediation

POINTS, LINES, AND ANGLES

Points, Lines, and Angles

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

What prompts will be used?

What does mastery look like?

POINTS, LINES, AND ANGLES

Home

I can recognize angles as geometric shapes formed when two rays share a common endpoint.

I can draw right, acute, and obtuse angles based on the relationship of the angle measure to 90 degrees.

I can explore, investigate, and draw points, lines, line segments, rays, angles, perpendicular lines, parallel lines, and lines of symmetry in two-dimensional ﬁgures.

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SCOPE 1

Properties of Two-Dimensional Figures Scope Introduction SCOPE SUMMARY

Student Expectations

4.GSR.8.2 Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicular line segments, or the presence or absence of angles of a speciﬁed size and based on side lengths.

Students classify and sort shapes based on parallel lines, perpendicular lines, side lengths, and angle types. They classify and identify various two-dimensional shapes, such as quadrilaterals, triangles, and pentagons, based on the attributes of their sides and angles. Students use side lengths to identify and construct equilateral, isosceles, and scalene triangles, and they use angle sizes to identify and draw right, acute, and obtuse triangles. They fold shapes to determine lines of symmetry, and they notice patterns regarding the number of lines of symmetry in various types of polygons. Students cross-classify triangles (for example, a right isosceles triangle). They use deductive reasoning to justify their thinking about the categories into which shapes are sorted while gaining a deeper understanding for “if …, then …” relationships. For example, if a shape is a triangle, then it must have three sides.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students make generalizations about properties that are shared between categories of shapes, such as parallel line segments, perpendicular line segments, right angles, and lines of symmetry. Third-grade students mainly focus on identifying quadrilaterals and subcategories of quadrilaterals, but they also classify, compare, and contrast various polygons and 3-D solids.

In fifth grade, students understand that attributes belonging to a category of two-dimensional figures also belong to subcategories. Fifth graders classify two-dimensional figures, such as polygons, quadrilaterals, and triangles, into various categories and subcategories based on properties, such as sides, angles, and symmetry.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

•

look at a composite shape and determine how many twodimensional shapes make up that shape. determine the number of rectangles in a composite shape.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

compare 2-dimensional ﬁgures.

•

determine which shape has the most lines of symmetry.

•

draw lines of symmetry after they identifying whether a shape is symmetrical.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 372

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Classify Shapes by Lines and Angles In this exploration, students will classify two-dimensional ﬁgures based on the presence or absence of parallel or perpendicular lines or the presence or absence of certain types of angles. In solving the scenario, students will: •

classify different two-dimensional ﬁgures.

•

collaboratively solve a scenario where they help an artist repair a broken mosaic.

Explore 2

Explore 1

EXPLORE ACTIVITIES Identify Types of Triangles In the ﬁnal exploration, students participate in solving a scenario to learn how to construct and classify triangles based on angle size and side length. Through completing this exploration, students will: •

create models of different triangles and attributes.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students look at a composite shape and determine how many two-dimensional shapes make up that shape. This activity is intended to assess mastery of the following standard(s): 3.GSR.6.2 Classify, compare, and contrast polygons, with a focus on quadrilaterals, based on properties. Analyze specific 3-dimensional figures to identify and describe quadrilaterals as faces of these figures.

Materials

Preparation

Printed • •

• •

1 Student Handout (per student or per pair) 1 Set of colored pencils (per pair, optional)

Print a Student Handout for each student or each pair. Plan to have students work in pairs for this activity.

PROCEDURE AND FACILITATION POINTS 1. 2. 3. 4. 5.

Distribute a Student Handout to each student or each pair. Give students time to determine how many rectangles make up the composite shape. Encourage students to use colored pencils if they want to color each rectangle that they ﬁnd. After each pair of students has had enough time to come up with an answer, have one person from each pair write their answer on the board. Facilitate a class discussion about their answers. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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FACILITATION TIP Post a similar image on the board and challenge students to determine the number of rectangles or other shapes.

FACILITATION TIP Have students share their answers with other classmates and discuss their differences.

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PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures Hook – Symmetry Challenge ACTIVITY PREPARATION Students determine whether a shape is symmetrical and then draw lines of symmetry. Students compare two-dimensional ﬁgures and determine which shape has the most lines of symmetry.

Materials

Preparation

Printed •

•

1 Student Handout (per student)

Part II

Reusable • •

Plan to show the Phenomena Video.

•

Print a Student Handout for each student.

1 Phenomena Video (per class) 1 Projector (per class)

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1. 2.

FACILITATION TIP

Project this scenario and have students read it along with you. Guide students to ﬁnd the math phrases and terms. FACILITATION TIP As you are reading the scenario and showing the video, post the Picture Vocabulary - Lines of Symmetry to provide a visual for students.

FACILITATION TIP Teacher can provide a few examples of congruent from the classroom, on the board, or as manipulatives.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Your teacher asks you to describe what symmetry is. You tell her that it is when an object can be divided in half and each side of the object is exactly the same size and shape so that if you fold the shape along the line of symmetry, the sides match exactly. Then, your teacher asks you, “Which shape has the most lines of symmetry: a square, an irregular pentagon, or an equilateral triangle? How many lines of symmetry does each shape have?” Project the Student Handout. Discuss the following questions: a.

DOK-1 What is symmetry? Symmetry occurs when one shape is exactly like another shape when it is moved in some way. For two halves or two objects to be symmetrical, they must be congruent, which means they are both the same size and the same shape.

DOK-1 How can you tell if a shape is symmetrical? The shape can be folded along a line of symmetry to see if the two sides match up exactly.

DOK-1 Can a shape have more than one line of symmetry? Yes, many shapes have more than one line of symmetry, such as horizontal, vertical, and diagonal.

DOK-1 Do all shapes have a line of symmetry? Not all shapes are symmetrical. Some shapes have no lines of symmetry.

Move on to complete the Explore activities. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Show students the Student Handout. Discuss the following questions: a.

3. 4. 5.

DOK-1 How can you tell if a shape is symmetrical? The shape can be folded along a line of symmetry to see if the two sides match up exactly.

DOK-1 Can a shape have more than one line of symmetry? Yes, many shapes have more than one line of symmetry, such as horizontal, vertical, and diagonal.

DOK-1 Do all shapes have a line of symmetry? Not all shapes are symmetrical. Some shapes have no lines of symmetry.

Review the problem, and allow students to solve it. Give each student a Student Handout. Instruct students to determine whether a shape is symmetrical or not. a.

6. 7. 8. 9. 10.

STEMscopes Tip The Home section of each scope contains a Scope Overview. Here, teachers can access a colorful flowchart to see the overall flow of the scope. Each of the 5E lessons and their activities are listed. In addition, the flowchart shows paths to take for students needing more support as well as for students who have mastered the content.

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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If a shape is symmetrical, they should draw all possible lines of symmetry on it.

Students record the total number of lines of symmetry under each shape. After evaluating each shape, students should award first, second, and third place to the square, pentagon, and equilateral triangle based upon which has the most to fewest lines of symmetry. Give students about 5–10 minutes to identify symmetrical and asymmetrical shapes, to draw all possible lines of symmetry, and to rank the shapes in order of most to fewest lines of symmetry. Using a show of hands, find out which shape was awarded first place, which shape won second place, and which shape came in third place. Gather students in a whole group, and discuss the following questions: a.

DOK-2 Based on your drawing lines of symmetry, which shape had no lines of symmetry? Why? The irregular pentagon had no lines of symmetry. There was no way to divide the pentagon that would make congruent halves that folded onto each other and matched up exactly.

DOK-2 What properties does this irregular pentagon have? It has ﬁve sides, three acute angles, and one obtuse angle.

DOK-2 Is there any type of pentagon that would be symmetrical? Yes, a regular pentagon would. (Other pentagons may also work.)

DOK-2 Which shape had the second-most lines of symmetry? How many lines of symmetry does it have? The equilateral triangle has three lines of symmetry.

e. DOK-2 What other properties does the equilateral triangle have? It has three congruent sides and three congruent acute angles. f.

DOK-2 Which shape had the most lines of symmetry? How many lines of symmetry does it have? The square came in ﬁrst place. It has four lines of symmetry.

DOK-2 What other properties does a square have? It has four congruent sides, four congruent/right angles, four sets of perpendicular lines, and two sets of parallel lines.

FACILITATION TIP Have students share with 2 other students their results and allow them to come to an agreement.

h. DOK-2 Besides folding (or ﬂipping) shapes across a line of symmetry, can you think of any other ways you could move shapes to see if they are symmetrical? Sliding or rotating © Accelerate Learning Inc. - All Rights Reserved

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PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures Explore 1 – Classify Shapes by Lines and Angles ACTIVITY PREPARATION Students classify two-dimensional shapes based on lines of symmetry and the presence or absence of parallel or perpendicular lines, congruent sides, congruent angles, and certain types of angles.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Shapes (per class) 1 Exit Ticket (per student)

Reusable • •

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print each page of Shapes on a different-colored sheet of card stock. Cut out all of the shapes on each page. Assemble ﬁve resealable bags or envelopes with the following number of shapes in each one: • • • •

1 Pair of scissors (per teacher) 5 Resealable bags or envelopes (per class)

•

Four pentagons Four rhombuses Four parallelograms Five rectangles

• Five trapezoids • Three right triangles • Three equilateral triangles

For students who need more support in recalling information, please see our Angles Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Post the Picture Vocabulary for each line and angle description on the board for students to use as a reference. FACILITATION TIP Have students write each category title and draw an image on sticky notes. Students can use the sticky notes to sort the ﬁgures.

Part I: Classifying Shapes 1. 2. 3.

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Read the following scenario to the class: An artist at a local museum creates colorful mosaics out of various shapes. At a recent art showing, one of the mosaics was accidentally broken. Using your knowledge of two-dimensional shapes and their lines and angles, help the artist put the broken mosaic back together. Tell students that they will use what they already know about lines and attributes of geometric shapes to classify shapes and then assemble a broken mosaic.

Tell students that their ﬁrst task will be to classify the mosaic pieces by their properties (lines and angles). Divide students into ﬁve groups. Give each group a bag or envelope of shapes and each student a Student Journal. Have students look at the table on Part I of their Student Journals. Tell them they will be sorting the shapes in their bags based on the properties in the table. Have students take the shapes out of their bags. Remind students that the tick marks on the shapes show whether lines and angles are congruent. If lines or angles have the same number of tick marks, they are congruent. If lines or angles have a different number of tick marks, they are not congruent. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Have students classify the shapes. Tell them a shape might belong to more than one category, and that is OK, as that is why students have multiple cutouts of the same shape. Tell them they should start by ﬁnding all the shapes with one or more lines of symmetry. Then, have them move to the next column in the table. Tell students each category should not have repeating shapes in it. Discuss the following questions: a.

DOK-2 How did you determine which shapes had at least one line of symmetry? Answers may vary. I folded the shape and saw that each half was exactly the same as the other half, so I knew the shape had at least one line of symmetry.

DOK-2 Do any of these shapes have all congruent sides and all congruent angles? Yes, the triangle that has three acute angles has all congruent sides and all congruent angles.

c. DOK-2 Which shapes have both acute and obtuse angles? The pentagon, trapezoid, parallelogram, and rhombus have both acute and obtuse angles. d.

DOK-3 Do you think all shapes that have perpendicular lines will always have a right angle? Explain. All shapes that have perpendicular lines will always have a right angle. For lines to be perpendicular, they have to intersect at a 90-degree angle, which forms a right angle.

Intervention

Acceleration

FACILITATION TIP Have different groups share their results and discuss which category was the most challenging. STEMscopes Tip The Math Chat provides a forum for students to collaboratively discuss the concepts taught in the Explore lesson. This rich discussion helps students develop their number sense, mathematical vocabulary, and math thinking skills. A Math Chat is located at the end of each part of the Explore lesson and is also available in printable form.

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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Part II: Mosaic Reassembly 1. 2. 3. 4.

Have students use the clues on Part II of their Student Journals to reassemble the artist’s broken mosaic. Remind students that more than one shape can have the same property. Therefore, their mosaic might not look exactly like another group’s mosaic. Have students draw and color a model of the mosaic they reassembled on their Student Journals. Discuss the following questions: a.

DOK-2 Did any shapes have at least one line of symmetry and at least one set of parallel lines? Yes, the rectangle, rhombus, pentagon, and trapezoid have at least one line of symmetry and at least one set of parallel lines.

DOK-2 Which shape or shapes did you use the most? Why? Answers will vary. I used the rectangle the most because it matched the most clues.

DOK-2 Why didn’t everyone have the same mosaic? Answers will vary. There were several shapes with the same property. For example, I used 6 rectangles and 1 right triangle for the seven shapes with right angles, but someone else might have used 3 rectangles and 4 right triangles.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 If two or more lines that were on opposite sides continued in both directions indeﬁnitely, what would eventually happen? The lines would eventually meet, the lines will keep going without touching, nothing will happen, etc. • DOK-1 Were there any triangles that could be classiﬁed as right, acute, or obtuse? (Review question from prior topic.) Yes, we had a right triangle and an acute triangle. • DOK-1 Were there any shapes that had obtuse, acute, or right angles? Yes, all the shapes had different angles. Some had two acute angles and one obtuse; or one right, one acute, and two obtuse; and so on. • DOK-2 What is the difference between perpendicular and parallel lines? The difference between the two types is that perpendicular lines intersect at a right angle, and parallel lines do not intersect at all. •

FACILITATION TIP Discuss with the class different strategies to create the mosaic using the ﬁgures.

FACILITATION TIP Before beginning the Math Chat, conduct a Gallery Walk of the different mosaic designs.

FACILITATION TIP Do a quick check to assess student knowledge about obtuse, acute, right, parallel, and perpendicular. Consider using physical responses. 379

PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures Explore 1 – Classify Shapes by Lines and Angles •

FACILITATION TIP On this Exit Ticket, help struggling students to focus by looking at each property one at a time and check each figure for that specific property. For example, looking for all perpendicular lines first may support success.

DOK-1 How can we classify two-dimensional shapes? We can look at the relationships between their sides and the types of angles they have and use those characteristics to classify the shapes.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures Explore 2 – Identify Types of Triangles ACTIVITY PREPARATION Students construct and identify triangles based on angle size and side length.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • •

• • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable • • •

1 Set of geoboards with rubber bands (per group) 3 Equal-length craft sticks or toothpicks (per group) 1 Ruler (per group)

•

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Angles and Geoboard Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Geoboard)

PROCEDURE AND FACILITATION POINTS Part I: Identifying Types of Triangles FACILITATION TIP

Project this scenario and have student volunteers read it aloud with you. Guide students to look for the math phrases and words. 2. FACILITATION TIP Do a quick check with physical responses. Have students show triangles and speciﬁc angle measures with ﬁngers, arms, or their whole body.

3. 4.

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Read the following scenario to the class: The music teacher needs your construction team to build three different triangle-shaped roofs for each house prop in the Three Little Pigs school play. When your team asked her what type of triangle she wants each roof to look like, she had no idea there were so many ways to build it! Your construction team will create models of different triangles and use this information in addition to attributes provided by the music teacher to help her decide which triangle to use on which pig’s house in the upcoming play. Explain to students that each group needs to help the music teacher by showing all the different types of triangles they could build for her so she can pick the one she likes best for each pig’s roof. The construction team needs to know the difference between triangles that are right, acute, and obtuse. They also need to know the difference between triangles that are equilateral, isosceles, and scalene. Give three craft sticks to each pair of students. These should be equal lengths so students can use them to construct equilateral triangles; however, do not tell students this is the type of triangle they are constructing just yet. Encourage students to build a triangle using their craft sticks, and, after students have shared their observations with their partners, have them discuss what they notice about their triangles using the following guiding questions: a.

DOK-1 What shape did you construct? Triangle

DOK-1 What are some of the attributes of this shape? 3 sides, 3 angles

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 What do you notice about the angles of your shape? Are they equal to 90 degrees, smaller than 90 degrees, or larger than 90 degrees? All three angles are smaller than 90 degrees. All angles are congruent or equal. They are all acute.

e. DOK-1 Does your shape have any parallel or perpendicular lines? No f.

5. 6. 7.

Explain to students that this is called an equilateral triangle because all sides and angles are congruent or equal. To be even more speciﬁc, this is called an acute equilateral triangle. Students should see that all three angles in an equilateral triangle are acute. Challenge students to use the same craft sticks to now build an optional triangle for the music teacher that has at least one obtuse angle. Discuss the following question: a.

12. 13.

DOK-2 Can you build an equilateral triangle with an obtuse angle? No, because the third side would need to be longer to connect to the two sides that form the obtuse angle.

FACILITATION TIP Use Picture Vocabulary and have students sketch and label the different types of triangles on their Student Journals. FACILITATION TIP Before giving this challenge, provide some constraints for students about the craft sticks. Students may wonder if they can break the sticks or overlap them.

Challenge students to use the same craft sticks to now build an optional triangle for the music teacher that has at least one right angle. Discuss the following question: a.

9. 10. 11.

DOK-1 Do you know the name of this type of triangle? Some students might not know the name, but others might suggest this is called an equilateral triangle.

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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DOK-2 Can you build an equilateral triangle with a right angle? No, because the third side would need to be longer to connect to the two sides that form the right angle.

Students will record their equilateral triangle model on their Student Journals. Distribute geoboards, rubber bands, and rulers to students. Invite students to now make a triangle with at least two equal sides. If needed, students can use the ruler to measure and check their side lengths. Encourage them to discuss what they notice about their triangles. After students have shared their observations with their partners, use the following guiding questions. In addition, allow groups to share their different triangles. a.

DOK-2 How is the shape you made similar to another group’s model? Both shapes have 3 sides, they are triangles, and they each have at least two congruent sides.

DOK-2 How is the shape you made different from another group’s model? Answers will vary. Some triangles might have exactly 2 equal sides, or some might have 3 equal sides.

DOK-1 What are some of the attributes of this shape? At least 2 equal sides, 3 sides, 3 angles, different-sized angles, a possible set of perpendicular lines (if students constructed a right angle)

DOK-1 What do you notice about the sides of your shape? Two sides are congruent or equal, and one side is shorter or longer than the congruent sides. All sides are equal.

FACILITATION TIP If time allows, provide a limited time for students to make any shapes they can with the geoboards before directing them to create triangles. Set clear expectations around the use of the rubber bands and rulers.

e. DOK-1 What do you notice about the angles of your shape? Answers will vary. Students should notice that this type of triangle has at least 2 acute angles, and the third angle is either right, obtuse, or acute.

14.

DOK-1 Does your shape have any parallel or perpendicular lines? Answers will vary. A triangle with one right angle will have one set of perpendicular lines.

DOK-1 Do you know the name of this type of triangle? Some students might not know the name, but others might suggest this is called an “isosceles triangle.”

Explain to students that this is called an isosceles triangle because it has at least two sides that are congruent.

FACILITATION TIP Project the Picture Vocabulary for isosceles triangle. 383

PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures Explore 2 – Identify Types of Triangles 15.

16. FACILITATION TIP Before students record their triangles on their Student Journals, take time to clarify expectations about the geometric notations for labeling lines and angles (congruent, right).

17. 18. 19.

STEMscopes Tip Fluency Builders are hands-on games that motivate students to practice the concepts from the scope. Located in the Elaborate section, these studentled games include printable studentfriendly instruction sheets detailing how the games are played as well as all the materials needed for game play.

Discuss with students how there can be an acute isosceles triangle with more than 2 equal sides, which is also known as an equilateral triangle. Equilateral triangles are a special type of isosceles triangle. Challenge students to make three other types of isosceles triangles with each of the different types of angles (right, acute, and obtuse). Students should discuss with their groups and help each other as they are working. Students’ work should be recorded on their Student Journals. Ask students to now make a triangle with sides that are each a different length. If needed, students can use the ruler to measure and check their side lengths. After students have shared their observations with their partners, encourage them to discuss what they notice about their triangles using the following guiding questions. In addition, allow groups to share their different triangles. a.

DOK-2 How is the shape you made similar to another group’s model? Both shapes have 3 sides, they are triangles, and they all have 3 different side lengths.

DOK-2 How is the shape you made different from another group’s model? Answers will vary. Some triangles might have one right angle, some might have all acute angles, or some might have one obtuse angle.

DOK-1 What are some of the attributes of this shape? 3 sides, 3 angles, different-sized angles, a possible set of perpendicular lines (if students constructed a right angle)

DOK-1 What do you notice about the sides of your shape? All sides are a different length.

e. DOK-1 What do you notice about the angles of your shape? Answers will vary, but students should notice that this type of triangle does not have 3 equal angles. DOK-1 Does your shape have any parallel or perpendicular lines? Answers will vary. A triangle with one right angle will have one set of perpendicular lines.

DOK-1 Do you know the name of this type of triangle? Some students might not know the name, but others might suggest this is called a scalene triangle.

FACILITATION TIP

20.

Project the Picture Vocabulary for scalene triangle.

21.

FACILITATION TIP

22.

Consider whether you want students to continue to use the geoboards for Part II; collect supplies if not.

Part II: Choosing the Best Triangle 1.

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Explain to students that this is called a scalene triangle because it has three sides of different lengths. Challenge students to make two other types of scalene triangles with each of the different types of angles (right, acute, and obtuse). Students should discuss with their groups and help each other as they are working. Students’ work should be recorded on their Student Journals.

Read the following scenario to the class: Now that you have shared all the different types of triangles with the music teacher, she came back to you with her final prop requests. Read each request, and draw a model of a triangle to represent the roof on each pig’s house. These drawings will help your team prepare to construct the final props for the play! Students will look at the three requests on their Student Journals. They will read each request and use their findings from Part I to draw a triangular roof on top of each pig’s house. They will identify each roof type by right, acute, or obtuse and equilateral, isosceles, or scalene. Discuss the following questions:

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 How did you know which type of triangle this is? Answers will vary. The description said there was one right angle, so I knew this was a right triangle. The description also said there were two congruent sides. The type of triangle with two congruent sides is an isosceles triangle, so this triangle type has to be a right isosceles triangle.

DOK-3 Why couldn’t the triangle for pig 1’s triangle roof be an equilateral triangle? An equilateral triangle has equal side lengths and equal angle sizes. Pig 1’s house has one right angle, so the other two angles have to be acute. That means this type of triangle has one angle that is not the same size as the other two. A right triangle has one side length that is longer than the other two. That means this type of triangle has one side that is not the same length as the other two.

• • •

•

• •

•

DOK-1 What type of triangle does the music teacher want your team to build for pig 1’s house? Right isosceles triangle DOK-1 What type of triangle does the music teacher want your team to build for pig 2’s house? Acute equilateral triangle DOK-1 What type of triangle does the music teacher want your team to build for pig 3’s house? Obtuse scalene triangle DOK-2 Can you make a triangle with two obtuse angles? Try it with your geoboard or craft sticks. No. Once you make one obtuse angle, you can’t make another obtuse angle and close the triangle. You would need to add a fourth side. DOK-2 Can you have two right angles in a triangle? Try it with your geoboard or craft sticks. No. Once you make one right angle, you can’t make another right angle and close the triangle. You would need to add a fourth side. DOK-2 Does an isosceles triangle always have to be an acute triangle? No, it could be right, obtuse, or acute. DOK-2 Does an equilateral triangle always have to be an acute triangle? Yes. If you try to make one angle right or obtuse, the third side isn’t long enough to close the triangle. DOK-3 How are equilateral triangles and isosceles triangles similar? An equilateral triangle is a special type of isosceles triangle. They both have at least two equal sides.

2. 3. 4.

FACILITATION TIP Before the Math Chat, provide some additional real-world images about the uses of triangles. (For example: trusses, pyramids, old sun dials) STEMscopes Tip In Grades 2–5, a Standards-Based Assessment can be found in the Evaluate section. This assessment is designed to allow students to demonstrate their mastery of the standards. Multiple-choice and gridded response questions reﬂect the formats found on state tests. The assessment can be administered and scored multiple ways: digitally, printed, or edited to meet students’ needs.

FACILITATION TIP

Post-Explore 1.

Acceleration

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

Intervention

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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When previewing this Exit Ticket with students, consider having them fold it in half and only examine the vocabulary ﬁrst. Some students may be able to sketch an image below the words without looking at the matches. Struggling students will need read aloud support.

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Properties of Two-Dimensional Figures Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Classify Shapes by Lines and Angles Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Identify Types of Triangles Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Candy Bar Fundraiser

Graphic Designer

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

Playing with Geometry

Match Attributes to 2-D Figures

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

PROPERTIES OF TWO-DIMENSIONAL FIGURES

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Problem-Based Task The Robot Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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Students who are still acquiring the concept and need remediation

PROPERTIES OF TWO-DIMENSIONAL FIGURES

Properties of Two-Dimensional Figures

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can classify, compare, and contrast two-dimensional ﬁgures based on lines of symmetry.

What prompts will be used?

What does mastery look like?

PROPERTIES OF TWO-DIMENSIONAL FIGURES

Home

I can classify, compare, and contrast two-dimensional ﬁgures based on the presence of parallel or perpendicular lines and angles of speciﬁed size and based on side lengths.

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SCOPE 1

Measurement Scope Introduction SCOPE SUMMARY

Student Expectations

4.MDR.6.1 Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with like denominators, and also problems that require expressing measurements given in a larger unit in terms of a smaller unit, and expressing a smaller unit in terms of a larger unit based on the idea of equivalence.

Students select and use appropriate tools to measure attributes of objects by using metric measurements, including centimeters, meters, kilometers, grams, kilograms, milliliters, liters, seconds, minutes, and hours. They convert within a single system of measurement, and they apply what they know about measurement to solve single and multistep real-world problems involving any of the four operations. These problems may require expressing measurements given in a larger unit in terms of a smaller unit, as well as expressing a smaller unit in terms of a larger unit based on the idea of equivalence. Students also build on their prior knowledge of telling time, the four operations (+, –, ÷, ×), and problem solving to tackle problems that deal with intervals of time and elapsed time. Knowing which operation or operations to choose to correctly represent the problem and determine the solution is vital. Understanding what the question is asking is the ﬁrst step. Students read problems regarding time and elapsed time, determine what the question is asking, formulate a strategy to solve the problem, ﬁgure out the solution, and check answers for reasonableness.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students generate data by measuring with rulers marked with halves and fourths of an inch, and they display and analyze the data, using a model of their choice. Third graders also estimate and measure liquid volumes, the weights of objects, and the lengths of objects to solve problems, using the customary system. Third-grade students use an analog clock to tell and write time to the nearest minute and estimate time to the nearest ﬁfteen minutes. They also solve problems involving elapsed time, including intervals of time to the hour, half hour, and quarter hour where the times presented are only on the hour, half hour, or quarter hour within a.m. or p.m.

In ﬁfth grade, students use their knowledge of place value and the relationship between units to convert units of measure of different sizes within both the customary and metric systems. Fifth graders convert units of measure in relation to length, weight and mass, liquid volume, and time. They reason that changing the form of a measurement does not change the size or amount of the quantity being measured. Students decide and explain if a converted amount will be more or less than the original unit before making the actual conversion. Visual models, such as a table or diagram, are tools used to reason about the conversion of units. Once students understand the relationships between units and how to convert between units, they solve multistep problems that involve the conversion and renaming of units.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students ability to: •

estimate and measure liquid volumes, lengths and masses of objects using customary units.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

solve a problem involving elapsed time to the nearest minute.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 390

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

In this exploration, students will convert measurements and solve problems that deal with measurements of length within the metric system. Students will: •

Explore 3

Explore 2

Length

explore the relationships between measurements of length using tools of measurement.

In this exploration, students will convert measurements and solve problems that deal with measurements of mass within the metric system. Students will: explore some of the relationships between measurements of weight and mass.

As students are working, the teacher monitors and adjusts, leads a discussion about the students’ ﬁndings, and has students complete an Exit Ticket to assess learning.

After students have solved the scenario, the teacher guides students in color coding, sharing, and discussing ﬁndings; then the activity ends with a discussion over learning and Exit Ticket.

Liquid Volume

Intervals of Time

In this exploration, students will convert measurements and solve problems that deal with measurements of liquid volume within the metric system. Students will: •

explore the relationships between units of liquid volume.

In this exploration, students will understand the relationships within units of time and can convert units of time. Students will: •

explore the relationships between units of time.

After students have solved the scenario, they share and discuss their ﬁndings; then their learning is assessed via an Exit Ticket.

As students solve the scenario, they discuss their learning with the class and conclude with an Exit Ticket for assessment.

Explore 5

Mass

•

Explore 4

Explore 1

EXPLORE ACTIVITIES

MEASUREMENT

Home

Elapsed Time In this exploration, students will explore elapsed time in real-life situations using schedules. Students will: •

use the ﬂight schedule to help them solve each scenario.

After solving the scenario, students discuss learning with the class, complete an exit ticket for assessment; then, revitist the hook to solve.

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MEASUREMENT

Measurement Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

392

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE

MEASUREMENT

Home

Students choose which statement about measurements of liquid volume or weight they agree with most. They also identify the correct tool to use when measuring liquid volume or weight. This activity is intended to assess mastery of the following standard(s): 3.MDR.5.5 Estimate and measure liquid volumes, lengths and masses of objects using customary units. Solve problems involving mass, length, and volume given in the same unit, and reason about the relative sizes of measurement units within the customary system.

Materials

Preparation

Printed •

•

1 Slideshow (per student, group, or class)

•

Reusable •

Prepare to project the Slideshow for the class, or print out a copy for each student or group. Plan to have students work in groups for this activity (optional).

1 Projector or document camera (per class, optional)

PROCEDURE AND FACILITATION POINTS 1. 2.

3. 4.

Project the Slideshow for the class, or distribute it to students or groups. Instruct students to read the scenario and the two children’s statements. They should choose the statement they agree with most and identify what measurement tool would be appropriate to use. Have students turn to their closest neighbors to discuss and support their choices. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a. I agree with Serena. The water cooler company will need to find the liquid volume of the jug. A measuring cup is the measurement tool they could use. b. I agree with Serena’s brother. The water cooler company will need to find the weight of the jug not filled with water and filled with water. A scale is the measurement tool used to measure weight.

FACILITATION TIP After students read the statements on their own, invite some volunteer students to read aloud Serena’s and her brother’s statements. Read the scenario through more than once to support reluctant readers. FACILITATION TIP Discuss the difference between liquid volume and weight. Record student ideas on a T-chart. For each type of measurement, list some of the standard and metric units used and real-world examples of objects that are measured with these units. More speciﬁc information can be added to this list as the scope progresses.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

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MEASUREMENT

Measurement Hook – Grandma’s Arrival ACTIVITY PREPARATION Students solve a problem involving elapsed time to the nearest minute.

Materials

Preparation

Reusable • •

• •

1 Phenomena Video (per class) 1 Projector (per class)

Plan to show the Phenomena Video. Plan to have students work in pairs to complete this activity.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP In addition to this scenario, consider asking sharing some other events in your life when being on time was very important. Invite students to share appropriate time dependent scenarios as well.

FACILITATION TIP Students may be curious about military time vs a.m./p.m. 5. 6.

Introduce this activity toward the beginning of the scope. The class revisits the activity and solves the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: You are picking up your grandmother at the airport. You know her ﬂight lands at 2:15 p.m. and it will take her about 30 minutes to get off the plane and claim her luggage. You want to be there by the time she has claimed her luggage! It will take you 20 minutes to drive to the airport, and it is now 11:30 a.m. How much time do you have before you need to leave for the airport? Discuss the following questions: a.

DOK-1 What operations will you use to ﬁgure out the start and end times? We will use addition (counting forward) and subtraction (counting backward).

DOK-2 How is adding and subtracting time different from adding and subtracting regular numbers? You can’t just subtract the numbers. You have two sets of 12 hours in a day, so regular subtraction doesn’t work. For example, an hour after 12 noon is 1 p.m.; if you subtracted, it would mean there were 11 hours between the two times, which isn’t true.

Explain that students need to be able to ﬁgure out problems like this. They may need to actually pick up their grandma from the airport on time one day! Move on to complete the Explore activities. Notes

394

Engage

Explore

Explain

Elaborate

Evaluate

Part II: Post-Explore 1. 2.

3. 4.

After students have completed all the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What operations will you use to ﬁgure out the start and end times? We will use addition (counting forward) and subtraction (counting backward).

DOK-2 How are adding and subtracting time different from adding and subtracting regular numbers? You can’t just subtract the numbers. You have two sets of 12 hours in a day, so regular subtraction doesn’t work. For example, an hour after 12 noon is 1 p.m.; if you subtracted, it would mean there were 11 hours between the two times, which isn’t true.

Allow students time to work with a partner to solve the problem. Discuss the following questions: a.

DOK-2 What process did you use to solve the problem? We created a number line to help us figure out what time Grandma would be done picking up her luggage. Then, we had to figure out what time we needed to leave the house to get there at that time. After that, we figured out how much time there was between 11:30 and our leave time.

DOK-3 Allow multiple groups to share their strategies, and facilitate a discussion on the similarities and differences between the strategies.

Intervention

Acceleration

FACILITATION TIP This scenario offers a good opportunity to connect fractions and angles of circles to the measurement of time. If time allows, ask students how minutes are like fractions out of 60, and/or how a quarter hour on an analog clock is like an angle.

MEASUREMENT

Home

STEMscopes Tip Small-Group Intervention is found in the Intervention section. This handson lesson is used to build student understanding of the concepts covered throughout the scope. The lesson includes Teacher Checklists to help monitor students’ progress and Student Handouts. A short assessment to determine whether students have attained mastery of the skills and concepts being retaught is available in Grades 2-5.

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MEASUREMENT

Measurement Explore 1 – Length ACTIVITY PREPARATION Students convert measurements and solve problems that deal with measurements of length within the metric system.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Event Cards (per class) 1 Exit Ticket (per student)

Preparation • • •

•

Reusable • • •

4–5 Centimeter rulers (per group) 1 Meterstick or metric tape (per group) 1 Roll of repositionable painter’s/ masking tape (per group)

Plan to divide students into 8 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. You need to measure a large distance ahead of time. If there is not enough room in the classroom, this can be done in a hallway or outside with sidewalk chalk.

• •

•

Measure 10 meters on the ﬂoor with masking tape. Label the tape “KILOMETER.” Label one meterstick “100 meters,” and leave the meterstick beside the tape on the ﬂoor.

Print the Event Cards, and cut them out. Create stations with each card representing one station. Prepare the measurement tools and the masking tape for each group; each group should have a meterstick, rulers, and a measuring tape. Tools can be shared between groups, if needed. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS Part I: Find the Relationship 1. 2. FACILITATION TIP

Have students brainstorm some items from the classroom that they could measure the lengths of.

4. 396

Explain to students that they are going to explore the relationships between measurements of length using tools of measurement. Give a set of tools to each group of students. Allow groups a few moments to discover the tools and discuss the tools’ similarities and differences. Tell students to use the tools to find how many of one, two, and three units are equal to another unit. Explain that some units are very big, such as kilometers. For these comparisons, they measure a scaled model within the classroom. Show students the premeasured tape on the floor. Show the students the meterstick labeled “100 meters.” Explain that this one meterstick is going to represent 100 meters for the sake of the scaled model. Ask students how they could find the actual distance using the scaled model. Students should come to the conclusion that they need to count how many metersticks the measured tape is equal to and multiply that number by 100. Do not provide the answer. Students complete this process within their groups when the activity begins.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What is length? It is a measurement of how long something is.

DOK-1 How do we measure it? We use various tools, such as rulers and metersticks. We can also measure length using objects and their relative size.

DOK-1 What are some different units of length? Answers will vary but could include centimeters, meters, and kilometers.

DOK-2 Are all units of length the same? No. Some units are very small, and some are large.

MEASUREMENT

Home

FACILITATION TIP Some rulers have both the standard system and the metric system. Direct students’ attention to the rulers and metersticks, and have them identify which type of unit should be used to measure.

e. DOK-1 Look at each of your rules for the tables. What do you notice? One rule was always using division, and one rule was always multiplying. f.

DOK-1 What process do we use for converting a large unit into a smaller unit? We use multiplication.

DOK-1 What process do we use for converting a small unit into a larger unit? We use division.

h. DOK-1 Which rule could we use to determine how many centimeters are equal to 2 meters? Number of meters × 100 = number of centimeters Solve. 2 meters × 100 centimeters = 200 centimeters i. DOK-1 Which rule could we use to determine how many meters are equal to 2,000 centimeters? Number of centimeters ÷ 100 = number of meters Solve. 2,000 centimeters ÷ 100 = 20 meters j. DOK-3 How is using the table helpful? It can help you ﬁnd a pattern and a rule. Then, you can apply the rule to change the units of something. 6.

Students should evaluate the pattern within the tables to ﬁnd the rule for converting units both ways (larger to smaller and smaller to larger).

Part II: Who Will Win at Field Day? 1.

3. 4.

Read the following scenario to the class: The annual school Field Day is coming soon, and Coach Manning needs a lot of help. Many of the games planned for Field Day include activities in which the winner of the game is determined by measuring length. Your job is to help Coach Manning calculate the results so a winner can be announced! Explain to students that they rotate through the stations and use tools as well as the tables they created in Part I to ﬁgure out the winning team for each of the events on the Event Cards. Students should complete the appropriate section of their Student Journals during each rotation. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What is the question asking? Answers will vary. The problem is asking us a couple of things—we need to ﬁnd the winning team and how much farther the toy hoop traveled than the other team’s hoop.

DOK-2 How many steps do you have to take to solve the problem? Answers will vary. We will have to convert the measurements to one unit and then subtract one team from the other to ﬁnd the result.

DOK-2 What operations are you using? How do you know? Answers will vary. We will have to use multiplication to convert the measurements and then subtraction to ﬁnd the difference.

FACILITATION TIP Before students move to Part 2, ensure their conversion tables are correct. The tables will be used in Part 2. STEMscopes Tip Math Today, found in the Acceleration section, is designed to engage students using real-world videos, photos, or articles provided by the Associated Press in exploring the connections between the current events and math as well as other cross-curricular content. Used as a review or a formative assessment, this activity includes a printable Student Handout and Answer Key.

FACILITATION TIP Have students take turns identifying the variables, converting the variables to one unit, and adding each team’s totals.

FACILITATION TIP Challenge students who ﬁnish early to convert the ﬁnal measurement into a mixed fraction or a larger unit: 300 cm = 3 m.

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MEASUREMENT

Measurement Explore 1 – Length 5.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • STEMscopes Tip

•

The Visual Glossary, located under the Scopes tab, provides a variety of instructional resources. Browse topics alphabetically in English or Spanish. Each topic includes a visual and/or video featuring key vocabulary and concepts. The visuals include text and a speech button with narration. The videos, featuring real-world examples, are 3–15 seconds in length.

•

• FACILITATION TIP Reassure students that the metric system is the most common system for all other countries. Almost all scientists use metric measurements. Since most students will have limited experience with the metric system, consider using some acronyms and visual charts (like King Henry Doesn’t Usually Drink Chocolate Milk). Use total physical responses to model the sizes (a cm is about the width of a pinky, a m is about waist high).

•

DOK-1 What do the results reveal? Which team won each of the events? (Call on different groups to review answers from their Student Journals.) DOK-2 What patterns or discoveries did you make? I noticed that in the metric system, there were groups of 100 in 1 meter, so it was easier to convert centimeters and meters. I found the “rules” for each conversion that will help me solve any type of problem involving those units. I noticed that I have to multiply when I am converting a larger unit into a smaller unit, and I have to divide when I am converting a smaller unit into a larger unit. DOK-3 What process did you develop to convert between units of length? I used multiplication when I was trying to go from a larger unit, such as meters, to centimeters. Since 100 centimeters are in 1 meter, I would multiply by 100 to find out how many centimeters were in so many meters. I would divide in groups of 100 to when trying to go from a smaller unit to a larger unit such as centimeters to meters. DOK-2 Why are the rules for converting units either multiplication or division? Changing units involves equal groups. A larger unit is a group of a certain number of smaller units. For example, a meter is a group of 100 centimeters, so I would need to multiply the number of meters by 100 to figure out how many centimeters there are. DOK-3 How would you explain the process of conversion to a friend? I would tell them that after learning the basic unit of length in each of the systems, they just have to remember that when changing a smaller unit (such as centimeters) to a larger unit (such as meters), they should divide to find how many groups of the smaller unit they can make. When changing from a larger unit to a smaller unit, they should multiply to find how many total smaller units they have by combining each group of smaller units. DOK-2 If we could add the word convert to our word wall, what definition would you give for this word? It should be simplified to “to change.”

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

398

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

MEASUREMENT

Home

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MEASUREMENT

Measurement Explore 2 – Mass ACTIVITY PREPARATION Students convert measurements and solve problems that deal with measurements of mass within the metric system.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

Reusable • • • •

2 Balance scales (per class) 1 Set of gram weights (must total at least 1,000 grams) (per class) 1 Kilogram weight (per class) 1 Quart-size resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. For Part I, place the materials in bags or bins at an accessible location in the classroom for easy distribution and cleanup. Prepare multiple sets so fewer students are working with the same materials, depending on availability and the size of the class. •

•

Materials: A set of gram weights (there must be enough to total 1,000 grams or more), a 1-kilogram weight, and balance scales

For Part II, print the Scenario Cards, and cut along the dotted lines. Place these cards in a quart-size resealable bag. There needs to be a full set for each group of students. Allow the materials for Part I to be available for Part II in case students need to revisit certain units or relationships. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Part I: Find the Relationship

The difference between mass and weight is that weight includes the gravitational force, and mass is the amount of matter in an object. Use the moon as an example; a 1 student would weigh about _6_ of their weight on the moon; however, their mass would not change.

1. 2.

FACILITATION TIP Since most students will have limited experience with the metric system, consider using some acronyms and visual charts (like “King Henry Doesn’t Usually Drink Chocolate Milk”). Use familiar references to connect to their real world (For example, a gram is about the mass of a raisin, a kg is about a cantaloupe). 400

3. 4.

Tell students they are going to explore some of the relationships between measurements of weight and mass. Review units and tools used to measure weight and mass: a.

DOK-1 What are weight and mass? Weight is a measurement of how heavy something is. Mass is a measurement of how much matter is in an object.

DOK-1 How do we measure them? We use various tools, such as scales or triple beam balances.

DOK-1 What are some different units of weight and mass? Student answers should include grams and kilograms.

DOK-2 Are all units of weight and mass the same? No. Some units are very small, and some are large.

Demonstrate to students the tools they are to use. Each group should begin at one of the two stations. Explain that for the purposes of this Explore activity, students will only be working with units of mass. In future grades, they will work with units of weight, as well. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Tell students they will use tools to ﬁnd the relationships between different units of mass by determining how many of one unit make up another unit within that same measurement system. Given a set of gram weights and the 1 kg weight, students ﬁnd how many grams it takes to balance the kilogram weight. Students should use this relationship to complete the table and write rules for converting grams to kilograms and kilograms to grams. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Look at each of your rules for the tables. What do you notice? One rule was always using division, and one rule was always multiplying.

DOK-2 Why do you think we are using multiplication and division? Each larger unit is a group of smaller units. The relationship shows how many groups of smaller units it takes to make one group of larger units.

DOK-1 What process do we use for converting a large unit into a smaller unit? We use multiplication.

DOK-1 What process do we use for converting a small unit into a larger unit? We use division.

Intervention

Acceleration

FACILITATION TIP Monitor groups as the students complete the tables. Before progressing to Part II, ensure the class has the correct conversions.

MEASUREMENT

Home

STEMscopes Tip Fact Fluency activities, located in each grade level under the Scopes tab, help develop students’ addition and subtraction fact fluency in all grades and multiplication and division fact fluency in grades 3–5. Activities include mini-lessons, stations, games, and assessments to help address common fact-fluency groupings and strategies.

Allow suﬃcient time for students to complete the relationship with their groups and write down the relationships between units on their Student Journals.

Part II: Farmers’ Market 1.

2. 3.

Read the following scenario to the class: The Country Village Farmers’ Market meets every Saturday at the town center. Your family owns a small ranch outside of town, and every Saturday, the family brings a wide variety of fruits and vegetables to sell at the market. Give a set of Scenario Cards to each group. Explain to students that they will work cooperatively to solve each Scenario Card. They need to convert the units of a particular type of produce within the metric measurement system. Students solve the scenarios by creating tables and applying the rules they found in Part I. They show their work in the boxes on Part II of their Student Journals. a.

FACILITATION TIP Have students identify the equalities provided in each scenario by underlining or highlighting them. Students can then convert the units using information from Part I.

If extra space is needed, students can show their work on pieces of scratch paper.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-1 How were units of mass helpful at the Country Village Farmers’ Market? The amounts of fruits and vegetables needed to be measured. Units of mass were used to tell how much they had. To convert metric units, you use base-ten understanding, which is easy to convert if you know place value and that each digit is ten times greater than the digit to its right. DOK-3 Explain how to ﬁnd unit conversions using only a table. I could continue adding on to my table and use the skip counting method for the smaller units until I reached the number of kilograms the problem is asking about. DOK-2 What are some of the different strategies you used to convert units? I used division or multiplication to apply the rule I found in the table. I created a table, skip counted, used repeated addition or subtraction, used place value understanding, etc.

FACILITATION TIP Consider providing students with a premade conversion chart with KHDUDCM (Kilo, Hecto, Deka, Unit, Deci, Centi, Milli) to refer to.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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MEASUREMENT

Measurement Explore 3 – Liquid Volume ACTIVITY PREPARATION Students convert measurements and solve problems that deal with measurements of liquid volume within the metric system.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials Printed •

1 Student Journal (per student)

• 1 Set of Station Cards (per class)

Reusable •

1 Set of liquid volume measurement tools that include 1 L graduated cylinder or pitcher, 1 100 mL graduated cylinder and a dropper with mL markings (per group)

• 1 Exit Ticket (per student)

• 1 Medium-size funnel (per group) • 1 Five-gallon bucket ﬁlled with water (per group) • 1 Plastic tray (per group, optional)

Consumable •

1 Roll of paper towels (per class, for cleanup)

Preparation • •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student.

Part I •

•

For each group, ﬁll a 5 gal. bucket with water. Omit if the classroom is very near a water source or if you are able to do this activity outside. If implementing this lesson outside, ensure that a water source and a site for disposing of the used liquid are readily available. Each group needs a set of measuring containers. It might be helpful to put them on a plastic tray to contain any spilled water, but it is not necessary. Each group needs a container for the following measurements: •

•

1 L graduated cylinder or pitcher

• 100 mL graduated cylinder

• Dropper with mL markings

If containers measuring the exact capacities listed above cannot be found, use any clear containers that can hold these capacities. You need to measure out these amounts ahead of time, and make a mark on each container at the point at which students should stop ﬁlling. Label all containers with the following units: milliliter and liter.

Part II • •

402

Print the Station Cards on white card stock, and cut them apart. This part of the lesson is done as a rotation, so there is one card at each table. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS

MEASUREMENT

Home

Part I: Find the Relationship 1. 2.

4. 5.

Tell students they are going to explore the relationships between units of liquid volume. Review capacity and measurements of capacity: a.

DOK-1 What is liquid volume? It is a measurement of how much liquid a container can hold.

DOK-1 How do we measure it? We use various tools, such as containers, cups, pots, and medicine cups.

DOK-1 What are some different units of liquid volume? Answers may vary but should include milliliters and liters.

DOK-2 Are all units of liquid volume the same? No. Some units are very small, and some are large.

Demonstrate to students the tools they are to use. Allow students a few minutes to discuss the tools’ similarities and differences. Each group should begin at one of the six stations. Explain to students they use the tools to ﬁnd the relationships between different units by determining how many of one unit it takes to equal another unit. This would be a good time to discuss how to carefully pour water from one container to another without making a mess. Show students how they begin with milliliters. Fill up the 100 mL graduated cylinder. Empty it into the liter container. Ask students if it is full. They should see that a liter is larger than a milliliter. Students should keep ﬁlling the100 mL graduated cylinder and pouring it into the liter container, making sure to keep track of how many pours are made. The milliliter dropper is provided to each group so they can see just how small 1 milliliter is. Tell students that milliliters are usually used to measure liquid medicines. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Look at each of your rules for the tables. What do you notice? One rule was always using division, and one rule was always multiplying.

DOK-1 What process do we use for converting a large unit into a smaller unit? We use multiplication.

DOK-1 What process do we use for converting a small unit into a larger unit? We use division.

FACILITATION TIP Provide tubs or trays on desks for students to collect spills. Discuss the safety protocols for large spills if you have a tiled ﬂoor. FACILITATION TIP Model for students how to get at eye level with the graduated cylinders to read the measurements. Have each student note the level of the liquid. Some students may need some support locating the numbers in between (Smaller cylinders will have more precise lines).

Part II: Smoothie Sam’s 1.

2. 3. 4.

Read the following scenario to the class: Smoothie Sam’s is a smoothie hut in our community. Today, you will be gathering some data related to its smoothies and sales. Give a Station Card to each group. Explain to students that they work together to read about the situation and answer the questions on their Student Journals. Give groups time to work through each problem. When students have ﬁnished, you can either rotate the cards or have the students rotate to the next table with a new card. Students repeat this process until they have solved the problem at each station.

FACILITATION TIP Consider breaking this Explore activity into two different class sessions to allow for clean up of Part I hands-on supplies before completing Part II.

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MEASUREMENT

Measurement Explore 3 – Liquid Volume 5.

Students solve the scenarios by creating tables and applying the rules they found in Part I. They show their work in the boxes on Part II of their Student Journals. a.

If extra space is needed, students can show their work on a piece of scratch paper.

After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP During this Math Chat, provide some real-world images of metric volume measurements. Images of petrol prices, menus, and recipes from English-speaking countries in Europe might be good sources for examples.

•

DOK-3 Explain how to find unit conversions using only a table. I could continue adding on to my table and use the skip counting method for the smaller units until I reached the number of units the problem is asking about. DOK-3 What process did you use to change, or convert, from one unit to another? I first looked at the original unit and then decided if that unit was smaller or greater than the unit I was supposed to convert to. For example, if I was changing milliliters to liters, I knew that milliliters were smaller than liters, so to find out how many milliliters were in a liter, I divided the total number of milliliters by 1,000 to get the total number of liters. DOK-3 How can you check your measurements? I can work backward – for example, if I converted from milliliters to liters and used division, I would do the opposite and multiply liters by 1,000 milliliters to get the total number of milliliters.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

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Measurement Explore 4 – Intervals of Time ACTIVITY PREPARATION Students understand the relationships within units of time and can convert units of time.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Game Cards (per class) 1 Exit Ticket (per student)

•

Reusable • • •

1 Stopwatch (per group) 10 Plastic or paper cups (per group) 1 Geared clock (per group)

•

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Game Cards on white card stock and cut them apart. This part of the lesson is done as a rotation in Part II. Place cards on tables around the room. For students who need more support in recalling information, please see our Analog Clock and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Clock and Number Lines)

PROCEDURE AND FACILITATION POINTS Part I: Find the Relationship 1. 2.

FACILITATION TIP Compile a list on the board that is sequenced from seconds to days. Have students provide the correct amount of time to convert to the next unit. For example: 60 seconds = 1 minute. FACILITATION TIP Students will need to practice the stopwatches several times: Start, Stop, Reset. Practice the stopwatch without cups ﬁrst. Next, plan some extra time for students to practice stacking the cups and using the timer.

3. 4.

5. 6.

Tell students they are going to explore the relationships between units of time. Discuss what they know about units of time: a.

DOK-1 How do we measure time? We use various tools, such as stopwatches, wristwatches, wall clocks, clocks on appliances or phones, etc.

DOK-1 What are some different units of time? Answers may vary but should include seconds, minutes, and hours.

DOK-2 Are all units of time the same? No. Some units are very small, and some are large.

Tell students they are going to have a competition. Explain that students have one minute to work together to create the highest tower of cups they can possibly create. Distribute 10 cups and a stopwatch to each group. Show students how to properly work the stopwatch. Explain that when you say “go,” one student needs to press the start button on the stopwatch, and they only work for one minute. Make sure all students are able to see the stopwatches in their groups, and challenge students to stop the stopwatches at exactly one minute. Once students are ready to work, say “Go!,” and allow students to work together to build their towers of cups. After each group has completed the activity, discuss the following questions: a.

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c. 7.

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Explore

Explain

Elaborate

Evaluate

DOK-1 How did you know when it had been one minute? The stopwatch changed to a new column, and after 60 seconds, there was 1 minute on the stopwatch. DOK-1 How many seconds did it take for the stopwatch to say 1 minute? 60 seconds

Give a geared clock to each group, and instruct students to collaborate to ﬁgure out how many minutes there are in one hour. Explain that they complete Part I of their Student Journals as they explore each relationship. They create conversion tables and writing rules for their tables, just like in the previous Explore activities. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you know when one hour had passed on your clock? When the hour hand had moved from one number to the next

DOK-1 How many minutes did it take to move the hour hand from one number to the next? 60 minutes

Intervention

Acceleration

FACILITATION TIP Use the same type of stopwatch for each group. Demonstrate how to read the stopwatch as needed.

MEASUREMENT

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Part II: Family Reunion Fun! 1.

2. 3.

5. 6.

Read the following scenario to the class: The Denson family has gathered for their annual family reunion. One of the things everyone looks forward to at these reunions are the fun games that are played, boys vs. girls. There are all ages on each boy and girl team, and the goal is to be the fastest team to complete each game. At the end of the games, one team will be declared a winner. Your job is to calculate the results so a winner can be announced! Divide the class into six groups so there is a group at each station. Students should rotate from station to station on your cue. Instruct students to use the Game Cards to help ﬁnd out who is the winner in each round of the activity by determining if the boys’ team or the girls’ team was the fastest at ﬁnishing the game. The task is to be able to determine if the measurements given are in the same units; if they are not, students should develop a process or system for changing one or both of the units so they can be compared and a winner determined. They can also use their results from Part I as a reference tool to convert units. They should draw tape diagrams or number lines to show their conversions on their Student Journals. Students should complete the appropriate section of their Student Journals during each of the rotations. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

• •

DOK-1 What do the results reveal? Which team won each of the events? Call on different groups to review answers from their Student Journals. DOK-2 What do you notice about both the relationship between seconds and minutes and minutes and hours? When you convert hours to minutes or minutes to seconds, you multiply by 60. To convert seconds to minutes or minutes to hours, you divide by 60. DOK-1 Which team won the most events at the family reunion? The girls’ team DOK-3 What process did you develop to convert between units of time? I used multiplication when I was trying to go from a bigger unit to a smaller unit, such as minutes to seconds. I would multiply by 60 to ﬁnd out how many seconds were in so many minutes. DOK-2 What patterns or discoveries did you make? I noticed that the rule for each set of conversions was to multiply the larger unit by 60 to equal the smaller unit. DOK-2 Why are the rules for converting units using multiplication? Changing units involves equal groups. A larger unit is a group of a certain number of smaller units. For example, an hour is a group of 60 minutes, so I would need to multiply the number of hours by 60 to ﬁgure out how many minutes there are.

FACILITATION TIP Have students convert each time unit on the table ﬁrst. Then, model for students how to convert using a number line model. The number line for the larger time unit should be the top line. FACILITATION TIP Students should be able to explain that when converting from a larger to a smaller measurement, multiplication is used. When converting from a smaller to a larger measurement, division is used. FACILITATION TIP As groups begin to write the rules for converting, guide students to use the number line.

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MEASUREMENT

Measurement Explore 4 – Intervals of Time Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

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Measurement Explore 5 – Elapsed Time ACTIVITY PREPARATION Students explore elapsed time in real-life situations using schedules.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• • • • •

1 Student Journal (per student) 5 Flight Schedules (per class) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print 5 Flight Schedules. Print a set of Station Cards on white card stock, and cut them apart. Set up ﬁve stations in the room, with one ﬂight schedule and one station card at each station. For students who need more support in recalling information, please see our Analog Clock and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Clock and Number Lines)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Before giving each student a Student Journal about ﬂight times, introduce some additional relevant real-world reasons why people need to be skilled with calculating elapsed time using schedules.

1. 2.

Give each student a Student Journal, and assign each group of students a station to start with. Discuss the Flight Schedule that is available to students at each station. Discuss the following questions: a.

DOK-2 What do you notice? I see ﬂight times. I see that some times are missing. I see the times ﬂights departed and arrived.

DOK-1 What does departure mean? Would this be the start or end time of a ﬂight? Departure means when the plane leaves the airport. This is the start time for a ﬂight.

DOK-1 What does arrival mean? Would this be the start or end time of a ﬂight? Arrival means when the plane lands. This is the end time for a ﬂight.

FACILITATION TIP Select one of the ﬂights to use as an example to complete together before students begin rotating to stations. This activity can also be done at student desks or table groups as the supplies are minimal.

FACILITATION TIP Take time to preview the unique locations and names on the scenario cards with students before they begin collaborating.

4. 5. 6.

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Explain to students that they will be reading their Station Cards and solving two scenarios. They will need to use the Flight Schedule to help them solve each scenario. They will solve each scenario by using jumps on an open number line. Students may break the time apart and make jumps on their number line however they see ﬁt. Students will answer the short reﬂection questions before moving on to the next station. Give students about 10 minutes at each station. After the Explore activity, invite the class to a Math Chat to share their observations and learning. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat DOK-1 How did you know which piece of information the questions were looking for? I thought about what was happening in the scenario. I determined the two known times, and it helped me figure out the missing time. • DOK-2 How is this activity similar to real life? Schedules help us every day. They help us plan our day and determine how long activities are and when we need to get where we are going. • DOK-2 How does knowing a flight time help you plan your trip? We can figure out how long we will be on a plane. We can schedule activities for after our landing time. •

Post-Explore 1. 2. 3. 4.

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MEASUREMENT

Measurement Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Length Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Mass Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Liquid Volume

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Intervals of Time

Independent practice assignment that gives students an opportunity to demonstrate their learning

Show What You Know, Part 5 Elapsed Time Independent practice assignment that gives students an opportunity to demonstrate their learning

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

MEASUREMENT

Home

Can be done independently

Spiraled Review

Career Connections

The Superior Sandbox

Carpenter

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

The Time-Eﬃcient Family

Equivalent Measurements – Metric and Customary

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task Race to the Finish Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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MEASUREMENT

Measurement Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER

MEASUREMENT

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Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions

What prompts will be used?

What does mastery look like?

I can use the four operations to solve real-world problems that involve elapsed time to the nearest minute.

I can use the four operations to solve real-world problems that involve intervals of time.

I can use the four operations to solve real-world problems that involve measurements of liquid volumes, lengths, distances, and masses of objects.

I can convert measurements within the metric system.

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SCOPE 1

Represent Measurement with Line Plots Scope Introduction SCOPE SUMMARY Students collect data by accurately measuring objects to an eighth of an inch. They represent the measured data by creating a line plot. Students create the line plot with corresponding fractions of a unit to show multiple data points for each measurement. The data displayed on a line plot is used to solve problems that involve addition and subtraction of fractions. Student Expectations

4.MDR.6.2 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life. 4.MDR.6.3 Create dot plots to display a distribution of numerical (quantitative) measurement data.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students collect, organize, and represent data by using tables, pictographs, and bar graphs. They interpret the data, and they use the data to solve addition and subtraction problems. In third grade, students collect, organize, and represent numerical data by using tables, line plots, pictographs, and bar graphs. They interpret these types of graphs, and they solve one- or two-step problems.

In ﬁfth grade, students collect, represent, and interpret numerical data by using tables, bar graphs, and line plots. They solve real-world problems in relation to the data collected, and they consider the distribution of data by determining and analyzing measures of mode, median, mean, and range.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

make a line plot that displays a data set of measurements in fractions of a unit.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

make a line plot to display a data set of measurements in fractions.

•

solve problems involving addition and subtraction of fractions using information from the line plot.

Students move onto the Explore activities and come back at the end of the explorations to complete the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. Notes

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Create Line Plots to Display Data In this exploration, groups of students will complete data sets about arm length and hand length. In completing the exploration, students will: •

use their data to create line plots to represent each set of data.

•

title and label the line plots.

Explore 2

Explore 1

EXPLORE ACTIVITIES Problem Solve Using Line Plots In the ﬁnal exploration, students will work in groups to solve a scenario where they are data consultants and must help generate a ﬁnal report using a variety of data Through completing the scenario, students will: •

solve problems using line plots in a circuit activity.

Students conclude the exploration with an Exit Ticket and revisit the Hook to solve using their learning from the explorations.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Notes

REPRESENT MEASUREMENT WITH LINE PLOTS

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REPRESENT MEASUREMENT WITH LINE PLOTS

Represent Measurement with Line Plots Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students make line plots that display a data set of measurements in fractions of a unit. This activity is intended to assess mastery of the following standard(s): 3.MDR.5.1 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Materials Printed •

Reusable

1 Slideshow (per group)

•

Consumable

1 Projector or document camera (per class)

•

1 Piece of scratch paper

Preparation • • •

Prepare to project the Slideshow for the class. Plan to have students work in groups to complete this activity. Print a Slideshow for each group.

REPRESENT MEASUREMENT WITH LINE PLOTS

Home

Procedure and Facilitation 1. 2. 3. 4. 5.

Project the ﬁrst slide of the Slideshow, and have students read and discuss it. Instruct students to create line plots on their scratch paper and to plot the data as a group. Give students time to discuss each of the choices on slides 2–5 of the Slideshow as you project them. Challenge each group to identify the line plot they think is correct and to be ready to defend their answer. Facilitate a class discussion about each of the line plots. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a. The line plot on slide 2 is incorrect because it shows that there is one pencil for each of the measurements on the line plot. However, no one 1 had a pencil measuring 2 inches or 3_2_ inches. b. The line plot on slide 3 is incorrect because it incorrectly plots the two 1 measurements of 2_2_ inches at the 2 inch mark.

FACILITATION TIP Students experience with line plots in third grade was most likely limited. Be prepared to review or use the Foundation Builder prior to starting this scope.

FACILITATION TIP Number each data representation, and have students list the corresponding numbers on their papers so they can record thoughts and keep track of whether they agree or disagree with each model.

c. The line plot on slide 4 is incorrect because it shows that there is only 1 one 2_2_ inch pencil instead of 2. It also incorrectly shows that there is 1 one pencil that measures 3_2_ inches. 1

d. The line plot on slide 5 correctly displays 2 pencils that measure 2_2_ inches each, 1 pencil that measures 3 inches, 1 pencil that measures 4 1 inches, and 1 pencil that measures 4_2_ inches. 6.

If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope. Notes

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REPRESENT MEASUREMENT WITH LINE PLOTS

Represent Measurement with Line Plots Hook – Grow, Grow, Grow ACTIVITY PREPARATION Students create a line plot to display a data set of measurements in fractions. Students solve problems involving addition and subtraction of fractions by using information in the student-created line plot.

Materials

Preparation

Printed •

•

1 Student Handout (per pair)

Part II

Reusable • •

Plan to show the Phenomena Video.

•

1 Phenomena Video (per class) 1 Projector (per class)

•

Plan to have students work in pairs to complete this activity. Print a Student Handout for each pair of students.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1.

FACILITATION TIP Coordinate with a science teacher to plant some seeds to create a cross-curricular lesson.

DOK-1 What do we know? We will be creating a line plot to represent the classroom’s plant growth data.

DOK-1 What will we need in the data for you to create a line plot? We would need to know how many inches each plant grew at the end of the 3 weeks.

DOK-2 Would each plant grow an exact number of inches? No, some plants will be in between inches. I think they will grow half inches and maybe quarter inches, too. Our line plot will probably have fractions on the number line in order to represent the data given.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

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Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: A class is doing a unit on plants. Students planted several seeds in soil. The class is going to observe the plants for 3 weeks. At the end of the 3 weeks, students will measure each plant to see how many inches each one has grown. You will take their data and represent it on a line plot. You will be solving problems and analyzing the data from the plant growth. Discuss the following questions:

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What do we know? We will be creating a line plot to represent the classroom’s plant growth data.

3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

Give each pair of students a Student Handout. Review the problem, and then allow students to solve it. Have students work together to ﬁll in the rest of the number line. a.

DOK-2 Have students turn and talk about what fractions they think belong on each line based on the data they received. Tell them to ﬁll in 1 1

the number line and put dots on the line plot. I think the fractions _4_, _2_, 3

and _4_ will be on the number line since each whole is partitioned into 4 2

Intervention

equal parts. _4_ is equivalent to _2_, so _2_ will go in the middle of each whole.

Gather students in a whole group, and discuss the following questions: a.

FACILITATION TIP To help groups begin, model for students how to make a line plot. Students can write the measurements on a sticky note, then organize the sticky notes on the desk before making a line plot.

DOK-1 How many inches did most plants grow? 2_4_ in. Since there were more dots above that fraction, that means most of the plants grew that many inches. 1 3

DOK-1 How many inches did the least plants grow? _2_, _4_, and 2_4_ had the least plants. I saw only 1 dot above each of these fractions. At ﬁrst, I looked at the fractions that had 0 dots above them. I then realized that if there were 0 dots, no plants grew that many inches.

DOK-2 What is the difference between the greatest amount of growth 3 1 and the least growth in inches? 2_4_ in. was the greatest growth and _4_ 3 3 1 1 1 in. was the least growth. I subtracted _4_ from 2_4_; 2_4_ – _4_ = 2_2_ inches difference.

DOK-2 If you add the heights that had 3 plants grow that height, what 3 1 would the total number of inches be? _4_ in. and 1_4_ in. had 3 plants grow 3_ _1_ 4_ _ _ that height. I added 1 4 + 4 = 1 4 or 2 inches total.

STEMscopes Tip

REPRESENT MEASUREMENT WITH LINE PLOTS

Home

Fluency Builders, located in the Elaborate section, are partner or smallgroup student-led games that engage students in practicing the skills and concepts addressed in the scope. These games come with studentfriendly instruction sheets. All the materials used in the games are found in the print ﬁles on the right side of the screen.

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Represent Measurement with Line Plots Explore 1 – Create Line Plots to Display Data ACTIVITY PREPARATION Students gather sets of data using measurement and represent the data on a line plot.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Data Display Chart (per group) 1 Exit Ticket (per student)

• •

Reusable • • • • •

•

1 Flexible tape measure (per group) 1 Ruler (per group) 1 Sheet protector (per group) 1 Dry-erase marker (per group) 30 Two-color counters (per group)

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Data Display Chart for each group, and place each in a sheet protector. Cut a meter strip of masking tape for each group, and gather other materials. For students who need more support in recalling information, please see our Assorted Number Lines and Open Number Line Supplemental Aids elements in the Intervention section.

Consumable •

1 Meter of masking tape (per group)

PROCEDURE AND FACILITATION POINTS Part I: Arm Length STEMscopes Tip If students are not ready to move on to the next concept, use Small-Group Intervention, located in the Intervention section, to revisit the conceptual foundation of the scope’s concepts and to build student understanding. Here, you will ﬁnd a hands-on reteach activity, Teacher Checklists for monitoring student progress, and supplemental Student Handouts. A student Checkup is provided in Grades 2-5.

FACILITATION TIP Use string to mark the length of the arms. Then, measure the length of the string with the ﬂexible tape measure. 422

1. 2. 3. 4.

Give each group a number 1–5. Have a student write their group number at the top of their group’s Data Display Chart. Give a ﬂexible tape measure, a Data Display Chart, and a dry-erase marker to each group. Choose a volunteer to come to the front of the classroom to show students how they should be measuring their arm. a.

Demonstrate for students that they will be measuring starting on top of their shoulder all the way down to their longest ﬁnger and taking the measurement that lands on the end of their longest ﬁnger. Measure the 1 student’s arm to the nearest _8_ of an inch, and encourage the volunteer to look at the measurement and tell the class. Students may need guidance to realize halves and fourths are also eighths of an inch.

Explain to students that they should be helping each other measure just as you helped the volunteer measure their arm.

6. 7. 8. 9. 10.

11.

Engage

Explore

Explain

Elaborate

Evaluate

Each student’s data should be recorded on the group’s Data Display Chart and on their Student Journal. Groups should rotate to the other 4 groups (leaving their data chart at their table) so they can record measurements for the whole class. Students should now complete the questions over the data they have recorded on their Student Journals. At this time, the students should return to their original group. Hand out masking tape and two-color counters. Invite the students to create a line plot as a group using the data they collected. The masking tape can be used as the number line, and the two-color counters can represent data points. Students can write on the table with dry-erase markers to label the intervals. If writing on the table is not an option, sticky notes can be used to label their lines. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What is the shortest arm length in the class? Answers will vary according to class data collected.

DOK-1 What is the longest arm length in the class? Answers will vary according to class data collected.

DOK-2 How can we use the shortest and longest lengths to create a line plot? The shortest length will be the ﬁrst measurement listed on our line plot, and the longest length will be the last measurement on our line plot because there are no measurements before or after.

DOK-2 How will you know what measurements to write in between the shortest and longest lengths? We will partition it as if it were a number line and write the intervals between each measurement.

e. DOK-2 What do you do if an interval is not represented in your data display? Students may decide not to record a missing value on the interval of the number line. Be sure students understand that the numbers must be in progression, and any values not represented will simply be blank. 12.

Allow students to rotate to see each table’s line plot and check it with their own work. a.

Students should draw a model of the line plot they drew as a group on their Student Journals and answer the questions.

Part II: Hand Length 1. 2. 3.

Students will repeat the same process, except this time they will measure the length of their hand from their wrist to the tip of their middle ﬁnger using a ruler. Students will record the data, gather data for the whole class, create a line plot to represent it, and answer the questions on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

FACILITATION TIP Instruct students to use the US Customary 1 system and to measure to the nearest _8_ of an inch.

FACILITATION TIP Show some images of simple line plots. Demonstrate with a sample set how to plot data on a line plot.

FACILITATION TIP

REPRESENT MEASUREMENT WITH LINE PLOTS

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One option is to have students ﬁrst collect all the data and place it on a poster. The other groups can then rotate to each poster to write down the data.

Math Chat DOK-2 What connections did you make during this activity? I’ve measured the length of objects before. I noticed equivalent fractions when I was measuring. I’ve made line plots before; we just included more fractional parts this time. • DOK-3 Why is it helpful to represent data this way? It makes it easier to see which lengths happened most often or not at all. It makes it easier to see the highest and lowest amounts. • DOK-1 What do you know about the measurement(s) on your line plot with the most dots? I know that/those measurement(s) occurred the most. • DOK-1 What do you know about the measurement(s) on your line plot with the fewest dots? I know that/those measurement(s) occurred the least or not at all. •

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Represent Measurement with Line Plots Explore 1 – Create Line Plots to Display Data • FACILITATION TIP When previewing this assessment Exit Ticket with students, model how to lightly cross out data as you record or tabulate it. Students are sometimes tempted to heavily cross out the numbers, and then can’t go back to double check. Struggling readers may need masking cards to focus their attention.

DOK-1 How did you use your line plot to ﬁnd out how many students participated in the data collection? I counted the number of dots in my line plot, and there were _____ students.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Represent Measurement with Line Plots Explore 2 – Problem Solve Using Line Plots ACTIVITY PREPARATION Students solve problems using line plots in a circuit activity.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems, and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print one set of the Station Cards per class, and laminate them, if desired. Hang the Station Cards around the room. For students who need more support in recalling information, please see our Assorted Number Lines and Open Number Line Supplemental Aids elements in the Intervention section.

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Explain to students that a data consultant is a career that analyzes and researches data like diseases, video gaming, test scores, and prices. Consider your students’ interests and connect data analysis to their lives.

2. 3.

FACILITATION TIP Use sentence stems like: “The title of this line plot is..... The unit is..... The highest value is......”

FACILITATION TIP

Math Chat

Have students share the strategies they used to analyze the data. Ask students, “What kind of data could we analyze in your lives like video gaming or sports?”

FACILITATION TIP Remind students that data is constantly being collected and analyzed. Website traﬃc, purchasing habits, spread of diseases, video gaming, test scores, and prices are all being recorded and used by large organizations to make decisions. It is important that students learn how to analyze data for themselves to be able to make good decisions as they get older. 426

Explain that today, students will be working as data consultants. Each station shows the data given by one of their clients. They will need to analyze each set of data and answer the questions on their Student Journals to generate a report for their client. Divide the class into groups, and assign each group a station at which to begin. Walk to one of the Station Cards, and explain that each group will start in a different place. Students will work together to answer the questions to generate a report about that data on their Student Journals. Have students rotate to the next Station Card on your signal. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-2 What connections did you make during this activity? I was adding and subtracting fractions to analyze the data. I was looking at different measurements, and I remembered the times when I’ve measured things and recorded the measurements. • DOK-3 What parts of this activity did you find challenging, and what did you do to overcome it? We thought it was really difficult to add together all the data and find the total. We chose to add all the wholes first, combine fractions we knew could make one whole, and then add the rest of the fractions. • DOK-3 Why is it important to be able to analyze data this way? If you can’t analyze it and make sense of it, then there is no point in having the data. Data can be helpful, but it’s only helpful if you can analyze it and understand it. •

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Post-Explore 1. 2. 3. 4.

FACILITATION TIP This Exit Ticket might work as a good pre-assessment tool before this Explore activity.

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REPRESENT MEASUREMENT WITH LINE PLOTS

Represent Measurement with Line Plots Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Create Line Plots to Display Data Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Problem Solve Using Line Plots Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Georgia Food Tour

Florence Knoll Bassett

A quick story to engage student interest along with four problems over previously learned skills

STEM careers come to life with these career exploration videos and student guides designed to take the learning further

Math Story

Fluency Builder

The Multicultural Pickle

Problem Solving with Line Plots

Reading passage that supports literacy and expands the students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Origami Master

Match Frequency Tables to Line Plots

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

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Students who are still acquiring the concept and need remediation

REPRESENT MEASUREMENT WITH LINE PLOTS

Represent Measurement with Line Plots

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

430

 Interactive Practice

 Problem-Based Task  Math Today  Create Your Own

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can create a statistical investigative question that can be answered by gathering data.

What prompts will be used?

What does mastery look like?

REPRESENT MEASUREMENT WITH LINE PLOTS

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I can graphically represent and describe the distribution of the numerical data through line plots.

I can graphically represent and describe the distribution of the categorical data through bar graphs.

I can describe and interpret the shape of the distribution.

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