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3 Georgia Math Teacher Guide

Grade 3 Teacher Guide

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

ISBN: 979-8-88826-662-5

3 GEORGIA

MATH G3

GEORGIA

Teacher Guide: Grade 3 ISBN: 979-8-88826-662-5 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 Relationships ................................................................................... 20

SCOPE 2

Compare Numbers .............................................................................................. 36

SCOPE 3

Rounding ........................................................................................................... 50

SCOPE 4

Addition and Subtraction Fluency ........................................................................ 66

SCOPE 5

Addition and Subtraction Models ......................................................................... 84

SCOPE 6

Arithmetic Patterns .......................................................................................... 100

SCOPE 7

Multiplication Models ....................................................................................... 114

SCOPE 8

Division Models ................................................................................................ 140

SCOPE 9

Multiplication and Division Strategies ................................................................ 162

TABLE OF CONTENTS

Table of Contents

SCOPE 10 Multiply Multiples of 10 .................................................................................... 184 SCOPE 11 Multiplication and Division Problem Solving ...................................................... 200 SCOPE 12 Area in Square Units ......................................................................................... 220 SCOPE 13 Apply the Area Formula..................................................................................... 234 SCOPE 14 Perimeter ......................................................................................................... 256 SCOPE 15 Lines and Angles .............................................................................................. 278 SCOPE 16 Two- and Three-Dimensional Figures ................................................................ 294 SCOPE 17 Represent and Compare Fractions ..................................................................... 316 SCOPE 18 Equivalent Fractions ......................................................................................... 342 SCOPE 19 Time ................................................................................................................ 366 SCOPE 20 Measurement ................................................................................................... 382 SCOPE 21 Represent and Interpret Data............................................................................. 406 © 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 • Materials and preparation needed to complete the activity • Procedure and facilitation points that identify how to use the activity • A printable Student Handout

Use the Interactive Notebook to allow students to take notes, express ideas, and/ or process the information presented in class. • Provides students with the opportunity to solidify their learning Ideas for using this element: • 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 Standard-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 Relationships Scope Introduction SCOPE SUMMARY Students demonstrate understanding of place value up to 10,000. They exhibit this by using concrete manipulatives, pictorial models, and numbers (including standard numbers, words, and expanded form).

Student Expectations

VERTICAL ALIGNMENT

3.NR.1.1 Read and write multi-digit whole numbers up to 10,000 using base-ten numerals and expanded form.

Background Knowledge

Future Expectations

In second grade, students extend their understanding of base-ten numbers through the hundreds place as they become proﬁcient using the structure of the base-ten number 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.

Students will continue to build on this concept as they extend their understanding of place value. In fourth grade, students are expected to demonstrate comprehension of place value by reading and writing numbers to the hundred thousands place by using standard, expanded, and word forms. Fourth graders also work on 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 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.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

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

compose numbers up to 10,000.

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

Read and Write Numbers In this exploration, students will read and write numbers from 0 to 10,000 using standard, word, and expanded forms. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

ﬁll in a deposit slip representing their money amounts in standard form, expanded form, and word form.

Compose and Decompose Whole Numbers In this exploration, students will compose and decompose four-digit numbers in multiple ways. Students will: •

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

use place value disks, drawings, expressions, and equations to represent numbers of signatures for a petition.

PLACE VALUE RELATIONSHIPS

Home

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

PLACE VALUE RELATIONSHIPS

Place Value Relationships 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 identify numbers up to 1,000 written in standard, word, and expanded forms. This activity is intended to assess mastery of the following standard(s): 2.NR.1.1 Explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Reusable •

Print a Student Handout for each student. Prepare a set of base ten blocks for each group of students.

PLACE VALUE RELATIONSHIPS

Home

1 Set of base ten blocks (per group)

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

Divide students into groups of 3. Distribute a Student Handout to each student and a set of base ten blocks to each group. Read the teacher statement at the top of the Student Handout to the class. Have students read the ﬁve student statements and decide which student or students they agree with. Have students record their answers and explain their thinking. Have students, with partners, groups, or the whole class, facilitate a discussion about each student statement and why they agree or disagree with the statement. 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. a.

Student 1 is not correct. The 9 in 907 is in the hundreds place not the tens place.

Student 2 is correct. There are 9 hundreds, zero tens, and 7 ones in the number 907.

Student 3 is not correct since the 9 has a place value of 900 in expanded form.

Student 4 is correct. This is the way you would write the number 907 in words.

FACILITATION TIP If you prefer, project the ﬁve statements on the Student Handout one at a time and provide students think time in small groups. Decide ahead of time if your students need to know how many statements are correct/ incorrect. FACILITATION TIP Students may need more space to effectively communicate their mathematical thinking. Allow students to explain their thinking on the back of the handout or even on a large sheet of chart paper. FACILITATION TIP Start by taking a quick class poll, having students use a thumbs-up or thumbs-down signal to show whether they agree with each statement. Then, call on individual students to justify their reasoning.

e. Student 5 is not correct since the 9 has a place value of 900 in expanded form. (9 + 7 is not being “added”). 6.

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

PLACE VALUE RELATIONSHIPS

Place Value Relationships Hook – Used Car Shopping ACTIVITY PREPARATION Students compose numbers up to 10,000.

Materials

Preparation

Printed •

• •

1 Play Money (per group)

Reusable • • •

1 Phenomena Video (per class) 1 Resealable bag (per group) 1 Projector or document camera (per class)

•

Plan to show the Phenomena Video. For Part II, print and cut out a set of Play Money for each group of students. Each set of Play Money should total $9,873. Print Play Money on card stock and laminate for durability, if desired. Mix each set of money (so that students will need to sort the bills), and place each set into a resealable bag. Prepare to project Play Money.

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

FACILITATION TIP

Consider displaying a baggie ﬁlled with play money to increase student engagement. 4.

DOK-1 How would we go about making sure you have the correct amount of money? We would count it.

FACILITATION TIP

DOK-1 How many 100s are in 1,000? 10

Provide concrete models such as place value blocks to help students visualize that place value digits are related by powers of 10.

DOK-1 How many 10s are 100? 10

DOK-1 How many 1s are in 10? 10

e. DOK-3 How does understanding place value help us sort and count money? We can sort the bills by place value, and we can eﬃciently count the bills by composing bundles of 10 within bill type. We can ﬁnd the value of each bill type and then add those totals together.

FACILITATION TIP Follow up the discussion with some realworld examples of when students will need to be able to count money. Consider sharing some stories from your life when knowing how to count money was critical.

5. 6.

Explain that students will learn strategies for reading, writing, composing, and decomposing numbers up to 10,000 in this scope. Move on to complete the Explore activities.

Part II: Post-Explore 1. FACILITATION TIP Discuss different strategies students could use to count their money. If students are struggling, suggest they sort their bills by place value and compose bundles of 10 for each bill type. 24

After students have completed all the Explore activities in this topic, show the Phenomena Video again and repeat the situation. Discuss the following questions with the class: a.

DOK-1 How would we go about making sure you have the correct amount of money? We would count it.

Engage

Explore

DOK-1 How many 10s are 100? 10

DOK-1 How many 1s are in 10? 10

Explain

Elaborate

Evaluate

Write the budget value, $9,873, on the board for the class to reference. Call on several volunteers to read aloud this value using word form. Then, read aloud the total amount in unison as a whole class. Place students into groups, and distribute a money baggie to each group. a.

Acceleration

STEMscopes Tip

Intervention

Optionally, you may take a few random bills from each bag to shortchange them; students would then need to add or subtract to determine how much money they are missing.

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.

PLACE VALUE RELATIONSHIPS

Home

FACILITATION TIP Instruct students to use their understanding of place value to count their money. If their amount is not correct, they will need to count the money Guide students to understand that they back to you, to prove that they are shortchanged. can count the money in the same way they write an amount in expanded form. They Discuss the following questions with the class: can start by counting the thousands, then a. DOK-2 How did you count your money? We sorted the bills by place add the hundreds, then the tens, and then value. the ones. b.

DOK-3 How did place value help you count the money? We made stacks of ones, tens, hundreds, and thousands, and then added them all together to get the total amount.

DOK-3 What is $9,873 when it is decomposed using expanded form? As students assist with the answer, record expanded form on the board. 9,000 + 800 + 70 + 3 = $9,873

FACILITATION TIP Ask students what other expressions they could use to decompose 9,873 besides expanded form. For example, the expressions 9,000 + 873, 9 thousands + 873 ones, or 98 hundreds + 73 ones all represent 9,873.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 1 – Read and Write Numbers ACTIVITY PREPARATION Students read and write numbers from 0 to 10,000 using standard, word, and expanded forms.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials Printed • • • • • •

1 Student Journal (per student) 1 Bank Deposit Slip Work Mat (per group) 1 Place Value Chart (per group) 1 Set of Number Cards (per group) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

Preparation • • •

• •

•

Reusable • • • •

3 Sheet protectors (per group) 1 Gallon-size resealable bag (per group) 1 Dry-erase marker (per group) 1 Set of place value disks (per group)

•

• •

Consumable •

1 Roll of tape (per class) • •

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Bank Deposit Slip Work Mat, on card stock for durability, for each group of students. Place each work mat inside of a sheet protector to create an erasable surface. Print the Place Value Chart for each group of students. Place each page of the Place Value Chart inside of a sheet protector. Tape the two pages of the Place Value Chart together with the thousands/hundreds page on the left and the tens/ones page on the right. Print a set of Scenario Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them inside of a gallon-size resealable bag for each group. Print a set of Number Cards, on card stock for durability, for each group of students. Cut the cards apart along the dashed lines, and place each set inside the same resealable bag as the Scenario Cards. Gather a set of place value disks for each group of students. Each set needs to include 9 thousands, 9 hundreds, 9 tens, and 9 ones. Set up group workstations around the room. Students will not be rotating through stations, as each workstation will be the same. Each workstation will have a bag of Scenario Cards and Number Cards, a Bank Deposit Slip Work Mat, a Place Value Chart, place value disks, and a dry-erase marker. For students who need more support in recalling information, please see our Place Value Chart 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. 3. 26

Read the following scenario to the class: You work for a clothing business that pays you every week. However, you like to hold on to your money for two months until taking it to the bank to deposit it into your account. When you arrive at the bank, you must ﬁll out a bank deposit slip representing the amount of money you earned over the last two months. Give a Student Journal to each student. Place each group of students at a workstation around the room. © Accelerate Learning Inc. - All Rights Reserved

9. 10.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Challenge students to examine the Place Value Chart and Bank Deposit Slip Work Mat. Ask the following questions: a.

DOK-3 What do you notice about your Place Value Chart? Answers may vary. I notice that there are four boxes for four different places. I notice that there is a place called the thousands. I notice that there is a comma between the thousands place and the hundreds place.

DOK-3 What do you notice about your Bank Deposit Slip Work Mat? I notice the words standard form, word form, and expanded form.

Explain to the class that they will be working with their groups to count out their place value disks and place them on their Place Value Charts to represent the money they will be depositing into their accounts. They will then be representing their money amounts in standard form, expanded form, and word form using their Number Cards to help them represent the word form and expanded form. Explain to students that they will be exploring a new place value today, and that place is called the “thousands.” There is a comma between the thousands place and the hundreds place because commas help make large numbers easier to read. Quickly review place value vocabulary by discussing the following questions: a.

DOK-1 How would you describe the standard form of a number? Standard form is a way to represent a number by simply writing the digits of a number.

DOK-1 How would you describe the word form of a number? Word form is writing and representing a number in the form of how you would say it in words.

DOK-1 How would you describe the expanded form of a number? Expanded form is where you take a number and decompose it into the value of each digit and then represent the number as a sum of each value.

Instruct students to begin working with their groups to read each Scenario Card and represent the amount earned with their place value disks on their Place Value Charts. They will then use the Number Cards and dry-erase markers on their Bank Deposit Slip Work Mats to represent the standard, word, and expanded forms of the amount earned. When students in the group agree that the model and each form are represented correctly, they can then record their individual 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 form of the number is represented on the Scenario Card? Answers will vary depending on the card.

DOK-3 How can we represent that form using the place value disks? Answers may vary depending on the form of the number on the card. I will represent each digit by counting out the value of that digit with its matching place value disk value. For example, if there is a 6 in the thousands place, then I will place 6 place value disks that are valued at 1,000 in the thousands place on my Place Value Chart.

DOK-3 Examine your completed Place Value Chart. How can we use the value of each place to help us write our expanded form? We can match the value of each place with the correct Number Card and write an addition equation with those cards on the Bank Deposit Slip Work Mat by writing an addition sign between the number cards in order to represent expanded form.

FACILITATION TIP

PLACE VALUE RELATIONSHIPS

Home

As you discuss different ways to represent amounts, consider creating an anchor chart that students can reference as they work through the activity.

FACILITATION TIP These activities are designed to help reinforce students’ understanding of place value. Ensure that students work through each of these steps in order before completing their Student Journal. FACILITATION TIP Be prepared to provide any necessary reading support for the Scenario Cards. You could read them aloud to the whole class before students begin, provide each student with individual copies so they can read along with their small group and write notes on them, or pre-select skilled student readers for each group.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 1 – Read and Write Numbers d.

DOK-3 How can we use the model on the Place Value Chart to help us write our standard form? We can add the values from each place on the mat and write the sum of that value as digits in order to represent our standard form.

e. DOK-3 How can we use the model on the Place Value Chart to help us write our word form? We can match our word Number Cards to how you would say each number on the Place Value Chart and make sure to include the thousand and hundred word cards when necessary. f. 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.

11.

12.

DOK-4 Do you think the thousand Number Card goes after the number in the thousands place or would it go at the end of all the numbers? I think the thousand Number Card goes after the number in the thousands place because it is telling us how many thousands are in our number. Just like the word hundreds after its number tells us how many hundreds are in the number.

Students will continue working until they’ve finished representing each number in each Scenario Card in word, standard, and expanded forms on their Student Journals. Once students have finished all of their work, instruct them to answer 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.

Math Chat •

•

DOK-3 After working with the place value disks, what do you notice about the values of each place? I notice that each place is 10 times bigger than the place to the right. I notice that the place on the right is one-tenth the value of the place on the left. DOK-3 How can we use the given form of each number to help us write the other forms? For example, if we were given the standard form, how can we use the standard form to write the word form and the expanded form? I can use the standard form to write the word form by writing how I would say each number as a word and making sure to write “thousand” after the thousands place. I can use the standard form to write the expanded form by decomposing the standard form into a sum of each digit’s values.

Post-Explore FACILITATION TIP

On this Exit Ticket, consider providing a word bank to support student spelling in the word form.

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

PLACE VALUE RELATIONSHIPS

Home

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PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 2 – Compose and Decompose Whole Numbers ACTIVITY PREPARATION Students compose and decompose four-digit numbers in multiple ways. They use place value disks, drawings, expressions, and equations to represent numbers.

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

• •

Reusable • •

7 Resealable bags (per class) 1 Set of place value disks (per group)

•

Plan to divide students into groups of 2 or 3 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Place Value Chart for each group. Print a set of Scenario Cards for each group. Cut the cards apart, and place them in a resealable bag. Gather a set of place value disks for each group. For students who need more support in recalling information, please see our Place Value Chart 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 1.

FACILITATION TIP

2. 3.

Use manipulatives such as place value blocks to help students visualize the regrouping process. FACILITATION TIP If time is limited, consider using the questions on page 8 of the Student Journal as a guide for your Math Chat rather than requiring students to generate detailed written explanations. 30

Read the following scenario to the class: On a recent ﬁeld trip to the zoo, your class noticed the zoo needed some updating. Some of the animals needed new cages, and some of the cages were empty. You want to convince your city to update the zoo with newer animal enclosures and add more animals. Your class decides to collect signatures from the people living in your city to show support for updating the zoo. You place signature sheets in seven different businesses in your city. Your job is to represent the total number of signatures collected at each business. Distribute place value disks and Scenario Cards to each group. Invite students to examine the Scenario Cards and turn and talk to their groups about what they notice: a. DOK-3 What do you notice? Answers will vary. I notice that some cards have more than 10 of a place value. For example, the Grocery Store card says “12 ones” and the Clothes Shop card says “41 tens.”

DOK-1 What is another way we could describe “12 ones”? We can regroup 12 ones into 1 ten and 2 ones.

DOK-1 What is another way to write the expression 10 + 2? 10 + 2 is the same as 12. It’s also equivalent to 5 + 5 + 2.

Engage

Explore

Explain

Elaborate

Evaluate

Explain to students that they will be working with their groups to create models and write expressions in different ways to represent each number of signatures from the different locations. Tell students to challenge themselves to create two more expressions to represent each number. These can vary within the group, but group members should check each other for accuracy. Give a Place Value Chart to each group. Instruct students to lay the pages of their Place Value Charts side by side with the thousands period sheet to the left of the ones period sheet. Students use their Place Value Charts to build their numbers prior to drawing it on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 If you have a group of 10 in one place value, what do you need to do? We need to regroup the 10 to create one of the next-highest place value.

DOK-1 What is the value of 13 hundreds? 1,300

DOK-2 What would the expression look like after you regrouped? We would take 10 of those hundreds and make 1 thousand. We would have 3 hundreds left over. We could write the expression 1,000 + 300.

DOK-2 How can you decompose 7,413 in different ways? We could choose any place value and decompose it into smaller units. We know that 13 is the same as 10 + 3, so we could write the expression 7,000 + 400 + 10 + 3 or 7,000 + 400 + 13.

Intervention

Acceleration

FACILITATION TIP Watch for confusion about how to write expressions when there are no digits in a place value expression. FACILITATION TIP Encourage students to use a variety of expressions other than expanded, word, and standard forms to reinforce their understanding of place value. For example, students could write an expression using a combination of words and numbers, or they could group place values together (e.g., instead of 7 thousands, 4 hundreds, use 74 hundreds).

PLACE VALUE RELATIONSHIPS

Home

FACILITATION TIP Ensure students are building numbers using the Place Value Chart ﬁrst. Using a place value chart helps students see that a digit represented by a 0 still holds a spot for that digit.

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

Math Chat DOK-1 Why did some place values need to be regrouped? In some place values, we had 10 or more circles. If you have a group of 10, you have to regroup them to become one unit of the next-highest place value. • DOK-2 If you look at the standard form of a number, how can you know the value of a speciﬁc digit within that number? If you know the place value of the digit, you can ﬁgure out the value. For example, if you have a 3 in the hundreds place, then you have three groups of 100, which equals 300. • DOK-2 Describe the process of decomposing a number. We are used to decomposing by place value, but we know that we can regroup the digits in any place value to make lots of new expressions. For example, 923 could be written as 900 + 20 + 3, 900 + 23, 900 + 13 + 10, 800 + 123, and so on. •

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. 4.

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. Notes

PLACE VALUE RELATIONSHIPS

Place Value Relationships 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

Read and Write 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

Compose and Decompose 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

Downtown Dogs

Erin Condren

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 Eights Have It!

Place Value Relationships within 10,000 – Models and Expanded Form

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

PLACE VALUE RELATIONSHIPS

Home

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

Super Spinner

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

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 RELATIONSHIPS

Place Value Relationships

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 numbers up to 10,000 using base-ten numerals and expanded form.

What prompts will be used?

What does mastery look like?

PLACE VALUE RELATIONSHIPS

Home

I can write numbers up to 10,000 using base-ten numerals and expanded form.

I can compose and decompose four-digit numbers in various ways using thousands, hundreds, tens, and ones using objects.

I can compose and decompose four-digit numbers in various ways using thousands, hundreds, tens, and ones using drawings.

I can compose and decompose four-digit numbers in various ways using thousands, hundreds, tens, and ones using expressions or equations.

SCOPE 1

Compare Numbers Scope Introduction SCOPE SUMMARY Students use and build on their prior knowledge of representing, plotting, and comparing numbers up to 10,000. The concept is similar to what students learn in kindergarten, ﬁrst grade, and second grade; they simply must extend the concept to numbers up to 10,000. Students must ﬁrst look at place value. Next, they must look at the value of the numbers within the place value. Student Expectations

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.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Between ﬁrst and second grade, 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, and second graders make comparisons up to 1,000.

In fourth grade, students will use their base of understanding of how to plot and compare numbers to 10,000 to extend that concept to include numbers up to the hundred thousands place. Students will also order numbers within this range from greatest to least and from least to greatest. Additionally, fourth graders will compare and order decimals by using number lines and place values to the hundredths place.

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

represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality.

•

use >, =, and < symbols to record the results of comparisons.

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 whole numbers up to 10,000, using the symbols >, <, and =.

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

Explore 1

EXPLORE ACTIVITIES Compare Numbers

COMPARE NUMBERS

Home

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

use place value and number lines to compare the number of tickets that were sold for each ride during a county fair.

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

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

COMPARE NUMBERS

Compare 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 three student statements about comparing numbers and choose the statement they agree with. This activity is intended to assess mastery of the following standard(s):

COMPARE NUMBERS

Home

2.NR.1.3 Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbols to record the results of comparisons.

Materials

Preparation

Printed • •

•

1 Student Handout (per student or class) 1 Open Number Line (per pair)

•

Print a Student Handout for each student, or prepare to project the Student Handout for the class. Print the Open Number Line for each student or pair.

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

Distribute a Student Handout to each student, or project the Student Handout for the class. Also distribute an Open Number Line to each pair of students. Instruct students to read the three students’ statements that describe their thinking about how the numbers are compared. Invite students to work with partners to use the open number line to help determine which of the students’ statements is correct. Have students hold up the number of ﬁngers that matches the statement they agree with. Facilitate a class discussion about the student statement they chose. 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. If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Allow students a few moments to read and make sense of the statements individually. Then, have them stand and confer with a partner. After students make their decision, they can return to their seats to indicate that they are ready to share with the whole class. FACILITATION TIP Invite students to share how they used the open number line under a document camera. If students are not sure how to use the number line, model the process using 3 other numbers, and then challenge students to do the same for the example presented.

COMPARE NUMBERS

Compare Numbers Hook – Video Game Showdown ACTIVITY PREPARATION Students compare whole numbers up to 10,000, using the symbols >, <, and =.

Materials

Preparation

Printed •

• • •

1 Symbols (per class)

Reusable • • •

1 Phenomena Video (per class) 2 Dice (per class) 1 Projector or document camera (per class)

Plan to show the Phenomena Video. Prepare to project Symbols. Part II • Create a three-column space on the board for the whole class to see. The left and right columns are for a four-digit number. The center column is for a comparison symbol. • Gather 2 dice for the class. Have an area near the board for students to roll the dice.

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

2. FACILITATION TIP Invite students to share their experiences with high scores in video games to increase student motivation and engagement.

3. 4.

a. DOK-2 Which number is bigger: 4 or 8? How do you know? The number 8 is bigger, because 8 ones is more than 4 ones.

FACILITATION TIP Students have prior experience comparing numbers up to 1,000. Discuss multiple examples up to 1,000, especially numbers that have greater values in lower place values and lesser values in higher place values. 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.

5. 6.

DOK-2 Which number is bigger: 14 or 41? How do you know? The number 41 is bigger, because 41 is composed of 4 tens, but 14 is only composed of 1 ten.

DOK-2 There are more ones in 14 than in 41, so why isn’t 14 greater than 41? A ten is bigger than a one, so the tens give it a greater total value.

DOK-2 Which place value do we look at ﬁrst when we’re trying to decide which number is greater? We look at the place value farthest to the left— in this example, the tens place.

Explain that students will learn strategies for comparing numbers up to 10,000 in this scope. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After completing all the Explore activities for this topic, show the Phenomena Video again and repeat the situation. Discuss the following questions with the class: a. DOK-2 Which number is bigger: 4 or 8? How do you know? The number 8 is bigger, because 8 ones is more than 4 ones. b.

4. 5.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 There are more ones in 14 than in 41, so why isn’t 14 greater than 41? A ten is bigger than a one, so the tens give it a greater total value.

DOK-2 Which place value do we look at ﬁrst when we’re trying to decide which number is greater? We look at the place value farthest to the left— in this example, the tens place.

Create an open number line and a three-column space on the board for the whole class to see. This will be for students to record the comparison expression. The left column is for a student to write the first number in the comparison and the right column is for another student to write the second number. The center column is where the comparison symbol will be written. DOK-1 What symbols can we use to compare numbers? Record these symbols on the board. Greater than >, less than <, and equal to = Call two students up to the three-column space on the board. Instruct the students to each roll a die; this will represent their scores on a video game they are playing against each other. The first digit they roll will be the value of the ones place. Have them write this digit on the right side of their column’s workspace. Have them roll again. The second digit they roll will be the value of the tens place. Have them write this to the left of the first digit. Continue rolling until the students each have a four-digit number written in their columns on the board. DOK-2 Ask the students to plot both numbers on the number line and to determine which number is greater. Have them use place value to support their reasoning. DOK-2 Call on another student to write a comparison symbol in the center column between the 2 numbers formed. Read aloud this comparison and ask the class if they agree with the symbol chosen. Do not erase the numbers or comparison symbols. Select different students to repeat steps 4-6 several times. Discuss the following questions with the class:

Intervention

Acceleration

COMPARE NUMBERS

Home

FACILITATION TIP Take time to carefully review the meaning and how to say each of these symbols. Have students say complete inequalities aloud to strengthen comprehension. For example, they should say, “two hundred seven is less than four hundred ninety two”. This focused practice will support comparing decimals, fractions and integers in later lessons.

FACILITATION TIP

Have students insert a 0 between digits rather than rolling the dice, or have them a. DOK-2 When comparing 2 four-digit numbers, which place value position record the same digit in the thousands do you look at ﬁrst? You look at the thousands place. place for more challenging comparisons.

DOK-2 If those digits are equal, which place value should you look at next? You look at the hundreds place, then the tens, and lastly the ones.

DOK-2 Which direction should your comparison symbol point? The symbol shows the direction of one number compared to the other on a number line. When a number is to the right of another number it has a greater value, and when it is to the left it has a lesser value.

DOK-2 If the numbers are the same, which symbol should you use? You use the equal sign (=).

e. DOK-3 Do numbers with more digits always have greater values than numbers with fewer digits? Explain your reasoning. Yes, the more digits a whole number has, the greater place value it has.

COMPARE NUMBERS

Compare 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.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • •

• • • •

1 Student Journal (per student) 1 Ticket Sales Chart (per group) 1 Place Value Mat (per group) 1 Exit Ticket (per student)

Reusable • • • •

•

1 Set of place value disks (per group) 2 Clear sheet protectors (per group) 1 Dry-erase marker (per group) 1 Sheet of extra paper (per group)

•

Plan to divide the class into groups of 4 to complete this activity. Print a Student Journal and Exit Ticket for each student. Print a Ticket Sales Chart for each group, and place it in a clear sheet protector. Print a Place Value Mat for each group, and place it 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 tissues, paper towels, cloth, etc. For students who need more support in recalling information, please see our Place Value Chart, Open Number Line, 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. (Place Value Disks and Number Lines)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Consider showing a picture or a short video of a midway to increase student engagement.

FACILITATION TIP

After partners discuss what they notice about the numbers, have a few students share their discoveries with the class.

FACILITATION TIP Being conﬁdent locating numbers in between on the number line is an important skill for comparing integers, decimals, and fractions. Take time to support students as they count the tick marks and try to locate the unmarked numbers. 42

5. 6.

Ask students if they have ever been to a county fair. Allow them to share their experiences. Explain that most county fairs have an area called the midway where all the rides are located. People buy tickets to ride the rides. Read the following scenario to the class: The week-long county fair has begun! You can’t wait to get to the midway and ride the rides! Before you go, you decide to compare ride ticket sales from last year’s fair to see which rides were the most popular. Give a Student Journal to each student. Give each group a Ticket Sales Chart and a set of place value disks. Allow students time to turn and talk with their neighbors about what they notice about the ticket sales numbers. Instruct students to use place value and number lines to compare the number of tickets that were sold for each ride during last year’s county fair. Instruct students to use the Place Value Mats and place value disks to model the place values, use the dry-erase markers to write the digit representing each place value on the mats, and then record their models or digits on their Student Journals. Be sure to check that students are correctly using the place value disks to build the numbers. Challenge students to think about which place value would make the most sense to compare. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Students place the numbers on the number line and write comparison statements 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 place value did you look at to compare those two numbers? Answers will vary. We looked at the hundreds place because the digits in the thousands place were the same.

DOK-1 How do you know what symbol to use? The symbol with the open end is greater, so we put the greater number beside it. The symbol with the point is smaller, so we put the smaller number beside it.

DOK-1 Why couldn’t you start by using the ones place to compare numbers? The ones place is the least place value. When we compare numbers, we have to start with the digit in the highest place value. If they are the same, we look at the digits in the next highest place value until we ﬁnd two digits that are different.

DOK-1 What if all the digits are the same? The two numbers are equal.

e. DOK-2 Describe a process you could use to compare numbers using place value. We could look at the highest place value ﬁrst. If the digits are different, we can tell which number is greater based on that digit. f.

10.

Intervention

Acceleration

FACILITATION TIP Guide students who are having diﬃculty placing the numbers on the number lines correctly because of the scales of 50 and 100. Have students ﬁrst determine which two number line numbers the number they want to plot falls between, and then determine which of the two number line numbers it is closest to.

COMPARE NUMBERS

Home

FACILITATION TIP If students are confusing the symbols for greater than and less than, consider using a trick to help them remember the proper placement. For example, compare the symbol to an alligator mouth. Explain that an alligator always wants to eat the greatest amount of food, so its mouth is always open toward the greatest number.

DOK-2 Describe a process you could use to compare numbers using the number line. We could place both numbers on the number line. If a number is farthest to the right, it is greater than the other number. If the number is farthest to the left, it is less than the other number.

As students show readiness, challenge them to complete the remaining comparisons by writing the digits on their Place Value Mats and comparing the numbers without building them. The goal is for students to be able to compare two numbers without the use of place value disks. However, allow students to use the disks 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-1 How did you know which number was greater or less using place value? We looked at the digits in the largest place value. If they were the same, we had to move on to look at the digits in the next-highest place value. The greatest digit in the highest place value told us which number was greater. The smallest digit in the highest place value told us which number was less. DOK-1 How did you know which number was greater or less using a number line? We placed the numbers on the number line and could see which number was farthest to the right. That meant the number was greater. DOK-1 What tools can you use to help you compare numbers? We could build numbers using place value disks to compare them. We could record the numbers in a place value chart and compare the numbers one place value at a time. We could place the numbers on a number line and see which number is greater and which number is less. DOK-1 Choose a few comparison statements, and have students model how to read the statements, including the symbols. Answers will vary. 9,746 > 9,100 Nine thousand seven hundred forty-six is greater than nine thousand one hundred. 2,455 < 4,133 Two thousand four hundred ﬁfty-ﬁve is less than four thousand one hundred thirty-three. DOK-2 Describe the next steps for comparing numbers if the digits in the highest place value are the same. We would look at the digits in the next highest place value. The larger digit would tell us which number was greater. If the digits were the same in the next highest place value, we would move one place value smaller.

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.

COMPARE NUMBERS

Compare Numbers Explore 1 – Compare Numbers Post-Explore 1. 2. 3. 4.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE NUMBERS

Home

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COMPARE NUMBERS

Compare 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

Interactive Notebook

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

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

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

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

Finding Jax

Wladimir Köppen

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

Walking for a Badge

Compare Numbers within 10,000

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 NUMBERS

Home

Problem-Based Task Taking the Scenic Route Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

COMPARE NUMBERS

Compare Numbers 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

What prompts will be used?

COMPARE NUMBERS

Home

What does mastery look like?

I can use place value reasoning to compare multi-digit numbers up to 10,000.

I can use symbols to represent the comparison of multi-digit numbers.

SCOPE 1

Rounding Scope Introduction SCOPE SUMMARY Students use place value to round numbers up to 1,000 to the nearest 10 or 100. They approximate the value of a number by representing values on a number line and then using relative language to describe the position of the number between two intervals to round to the closest interval. Students learn that rounding is valuable when estimating and for predicting and justifying the reasonableness of solutions while solving problems. Student Expectations

3.NR.1.3 Use place value understanding to round whole numbers up to 1000 to the nearest 10 or 100.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students extend their understanding of base-ten numbers up to 1,000. Second-grade students become proﬁcient using the structure of the base-ten number system by repeated bundling in groups of 10 or 100, with each unit being ten times as much as the unit to the right.

By fourth grade, students have had a lot of experience with place value, base-ten numbers, and number lines. Fourth-grade students use this experience to generalize the process of rounding numbers to the 1,000s, 10,000s, and 100,000s. This leads to being able to round much larger numbers and round to digits other than the leading digit. For example, to round 15,397 to the nearest ten, the tens place changes from 90 to 100, and this affects the resulting digits in the ones, tens, and hundreds place.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

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.

round to the nearest ten to see if the family has enough money to buy the furniture and accessories they like for their study.

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

ROUNDING

Home

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

Explore 2

Explore 1

EXPLORE ACTIVITIES

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

Round to Justify Reasonableness In this exploration, students will mentally round solutions to addition and subtraction problems using reasoning. Students will: •

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

mentally estimating the cost of supplies to get an idea of how much we will spend on a camping trip.

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

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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 use models to represent the number of hundreds, tens, and ones in a three-digit number. This activity is intended to assess mastery of the following standard(s): 2.NR.1.1 Explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

Materials

Preparation

Printed •

•

Print a Student Handout for each student.

1 Student Handout (per student)

Reusable •

1 Set of base ten blocks (per group)

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

Place students in groups of three or four. Distribute a Student Handout to each student and a set of base ten blocks to each group. Students will use the base ten blocks to model each problem on their Student Handouts. Facilitate a class discussion about the bundles of ones, tens, and hundreds, including the special cases of 100 (10 tens or 1 hundred), 200 (2 hundreds), 300 (3 hundreds), and so on to 900 (9 hundreds). 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. a.

If I bundle together 10 tens, I get 1 hundred. That means 100 = 10 tens.

If I bundle together 7 hundreds, I get 700.

When I add together 10 tens three times I get 3 hundreds, or 300.

I know order doesn’t matter in addition, but I have to make sure I put the hundreds all the way to the left, the tens in the middle, and the ones on the right because place value is important.

e. When I bundle together 10 tens, it changes the place value to the left: the hundreds place. 5.

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

FACILITATION TIP Before distributing the Student Handout, consider a quick review of modeling with base 10 blocks with the whole group. Then, have students work on the Student Handout problems so you can see where any misconceptions come up.

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.

ROUNDING

Rounding Hook – Rounding at the Furniture Store ACTIVITY PREPARATION Students round to the nearest ten to see if the family has enough money to buy the furniture and accessories they like for their study.

Materials

Preparation

Printed •

• •

1 Furniture Specials (per class)

Plan to show the Phenomena Video. Prepare to project Furniture Specials.

Reusable • •

1 Phenomena Video (per class) 1 Projector or document camera (per class)

Consumable •

1 Piece of lined notebook paper (per student)

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.

Part I: Pre-Explore 1.

DOK-1 How can you know if your family has enough money without adding up the cost of each item? You can estimate.

DOK-2 What steps would you take to estimate the cost of the furniture? Round to the nearest ten, and then add up the costs in your head or on paper.

DOK-1 What are the rules for rounding a number to the nearest ten? Look at the digit in the ones place.

FACILITATION TIP When rounding down, students might lower the place value digit being rounded to the previous ten. Use a number line to show students that the place value digit being rounded stays the same. FACILITATION TIP

Remind students that 5 can be rounded up or down, depending on the place value being rounded. For example, if rounding to the tens place, 125 rounds to 130; if rounding to the hundreds place, 125 rounds to 100.

ii. If the digit in the ones place is 5, 6, 7, 8, or 9, round up and add one to the digit in the tens place. 67 has a 7 in the ones place, so it is rounded up to 70, adding 1 to the tens place. The ones digit becomes a zero.

FACILITATION TIP One catchy phrase that might help some students remember this rule is “Four or less, let it rest. Five or more, raise the score!” 54

Move on to complete the Explore activities.

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 situation. Discuss the following questions with the class: a. DOK-1 How can you know if your family has enough money without adding up the cost of each item? You can estimate. b.

DOK-2 What steps would you take to estimate the cost of the furniture? Round to the nearest ten, and then add up the costs in your head or on paper.

DOK-1 What are the rules for rounding a number to the nearest ten? Look at the digit in the ones place.

ROUNDING

Home

FACILITATION TIP Ask students: “What are we trying to ﬁgure out?” “How will rounding help us solve this problem?”

i. If the digit is 0, 1, 2, 3, or 4, round down and keep the current digit in the tens place. Example: 84 has a 4 in the ones place, so it is rounded down to 80, keeping the 8 in the tens place. The ones digit becomes a zero. ii. If the digit in the ones place is 5, 6, 7, 8, or 9, round up and add one to the digit in the tens place. 67 has a 7 in the ones place, so it is rounded up to 70, adding 1 to the tens place. The ones digit becomes a zero. 3. 4.

5. 6. 7.

Give students pieces of paper. Tell them they can use these if they can’t keep track of prices in their heads but that they are not required to use them. Tell students to look at Furniture Specials and determine whether the family can afford to purchase the furniture and accessories. Remind them they cannot add up the exact prices; instead they need to round to the nearest ten. Give students about 5 minutes to round the individual prices and estimate the final cost. Take a vote using a show of hands at the end of the five minutes to find out who thinks the family can afford their list of purchases for their study. Discuss the following questions with the class: a. DOK-1 Did everyone agree on whether the family could afford the furniture and accessories for their study? Answers will vary. b.

DOK-1 How many students could do the problem in their heads? How many students felt better writing down the rounded numbers on the notebook paper and adding them up? Answers will vary.

DOK-1 Based on rounding and estimating, what was the ﬁnal cost of the furniture and accessories for the study? i. Desk and chair…….$152 → $150 ii. Sofa…….$399 → $400 iii. Lamp…….$48 → $50 iv.

Rug…….$81 → $80

Bookshelf…….$65 → $70

vi.

Total of rounded furniture and accessory costs……$750

vii. 150 + 400 + 50 + 80 + 70 = 750

FACILITATION TIP Challenge students to round and estimate in their heads ﬁrst and then to write down and add the rounded numbers to see if the two estimates are the same. FACILITATION TIP Students may want to round the desk to the hundreds place. Discuss why rounding to the nearest ten will give them a more accurate estimate of the amount of money the family will need.

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.

d. DOK-2 How does rounding help with estimating? It is easier to work with rounded numbers because they are easier to add. e.

DOK-3 Why should you round to the nearest ten instead of the nearest hundred for the prices in Furniture Specials? Because the prices of the furniture and accessories are in the tens and hundreds, so rounding to the nearest ten is a more accurate estimate of the total.

ROUNDING

Rounding Explore 1 – Round Using a Number Line ACTIVITY PREPARATION Students place a number on a number line between intervals of 10 or 100. Students 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.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

Materials Printed • • • • •

Reusable

1 Student Journal (per student) 1 Set of Bus Stop Signs (per class) 1 Set of Bus Route Names (per class) 1 Discourse Sheet (per group) 1 Exit Ticket (per student)

• • •

4 Resealable snack-size plastic bags (per group) 4 Cups of dry beans (lima, pinto, etc.) (per group) 1 Clear sheet protector (per group, optional)

Consumable • • • •

1 Roll of painter’s tape (per class) 1 Permanent marker (per class) 1 Pad of sticky notes (per class) 1 Roll of transparent tape (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 one Discourse Sheet per group. Laminate or put it in a sheet protector for reuse. Place 1 cup of beans in each plastic bag, and close the bag. Secure the closure with tape to ensure the bag does not open. Label each group’s bags with a letter (“A”, “B”, “C”, “D”) using the permanent marker. Find an area with enough room to tape down six lengths of painter’s tape. Each tape strip should be approximately 10 feet long. Place tape strips far enough apart that groups can easily work at the number line. Print and cut out the Bus Stop Signs. Mark intervals on each tape strip at each foot by taping down the Bus Stop Signs. Number lines should show the following increments: • • • • • •

Multiples of 10 (10, 20, 30, 40, 50) Multiples of 100 (100, 200, 300, 400, 500) Multiples of 10 with numbers in the hundreds (510, 520, 530, 540, 550, 560) Multiples of 100 (500, 600, 700, 800, 900, 1,000) Multiples of 10 with numbers in the hundreds (800, 810, 820, 830, 840, 850) Multiples of 10 with numbers in the hundreds (460, 470, 480, 490, 500, 510)

See the example below:

• • • 56

Print one set of Bus Route Names on card stock and cut them out. Place the Bus Route Names cards near each number line so students can identify the route name. For students who need more support in recalling information, please see our Base Tens, Open Number Line, 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. (Number Lines) © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ROUNDING

Home

PROCEDURE AND FACILITATION POINTS Part I: The Closest Stop 1.

Invite students to gather around the Number Line 1 Tens Trail Route. Allow students time to notice and wonder around the number line, and then discuss the following questions: a. DOK-1 What do you observe about the tape on the ground? The tape on the ground is numbered and is in a straight line. b.

DOK-1 What would you call a line that has evenly spaced intervals or lines on it? You would call it a number line.

DOK-2 Can you identify a pattern with these numbers? It is going up by 10s. The pattern is adding 10. Tell students the numbers on the number line are called “multiples.” For example, the numbers on this number line are multiples of 10.

FACILITATION TIP Discuss with students how a number line is helpful when rounding numbers. Students can visualize the locations of numbers, visualize the distances between numbers, and make connections to place value.

d. DOK-1 What number comes in the middle of 0 and 10? 5 e. DOK-1 What number comes in the middle of 10 and 20? 15 We call these “midpoints.” That is the number that is exactly between the two points or numbers. Ask students to help you mark the midpoints on this number line using sticky notes. f. DOK-2 Where do you see straight lines like this around town? (Accept numerous correct answers.) Streets are like straight lines. 2.

3. 4.

Imagine the number line is a road. Tell students that when they toss the beanbag, it represents their location on that road in the city. Demonstrate how to toss the beanbag between the numbers on the number line. Give a Student Journal to each student. Explain to students that they will take turns within their groups tossing the beanbag and determining which bus stop is the closest. They will record their information on their Student Journals. Discuss the following questions:

FACILITATION TIP Remind students that the goal is to toss the beanbag at different points on the number line.

a. DOK-1 Which bus stop would you want to go to? I would want to go to the one that was closest to me. b.

DOK-1 Does it mean that you will always go forward? No, sometimes the closest one is behind you.

DOK-2 How do you determine the number that shows the location of the beanbag your teammate tossed? If it is closer to the multiple that is greater than the midpoint, then we know the number will end in a 6, 7, 8, or 9. If it is smaller than the midpoint, then it ends in 1, 2, 3, or 4.

d. 6.

7. 8.

DOK-2 What if it lands on the midpoint? Then, go up because if you are at the midpoint, you always go up.

Encourage students to use the language that helps them understand the relative distance, such as closer, nearer, almost, and farther. Have students refer to the Discourse Sheet for sentence stems as they discuss their work with number lines. Have students rotate to the other ﬁve number lines. Students will continue to toss the beanbag at each one. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

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.

DOK-1 Where did your beanbag land on the number line? My beanbag is in the middle of the number line.

ROUNDING

Rounding Explore 1 – Round Using a Number Line

FACILITATION TIP Lead students to notice that when they are rounding down, the digit in the tens place is not lowered to the previous ten before it (for example, 24 is rounded to 20, not 10).

DOK-1 Which two multiples is your beanbag between? My beanbag is between 20 and 30.

DOK-1 Can you tell me if your beanbag is closer to 20 or 30? My beanbag is closer to 20.

DOK-2 What could your number actually be? 21, 22, 23, or 24

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

Math Chat FACILITATION TIP Students may not agree about the actual location of the beanbag. Encourage them to discuss their reasoning.

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.

DOK-1 What number is directly in the middle of two multiples on your number line? Answers will vary depending on the number line being referred to but may include that the number 150 is between 100 and 200. • DOK-2 How does knowing the middle number help you? It can help you ﬁgure out which multiple you are closest to. • DOK-1 How did you determine what multiple a number was closest to on a number line? First, we determined the two multiples it was between. Having the midpoint helped us determine if it was closest to one or the other. For example, if I was rounding 178 to the hundreds place and there was a 1 in the hundreds place, I knew it was between 100 and 200. The number has 7 tens, and the midpoint is 5 tens, so it has more tens than the midpoint. This means the number is closer to 200 than 100. • DOK-2 If your number line were counting by tens, what number would it round to? The number would be between 170 and 180, and it would be closer to 180 because there are 8 ones, which is greater than the ones in the midpoint 175. •

Explain the following to the class: Finding the closest multiple of 10 or 100 is called “rounding.” Rounding numbers is useful when you need to estimate or ﬁnd an answer that is close to the actual answer. Estimating makes the numbers easier to add, subtract, multiply, or divide, especially when doing math in your head. An estimated answer is not the exact amount, but it is a strategic number that is close. Part II: The Closest Stop, Continued 1.

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.

3. 4. 5.

Explain to students that they will rotate through the number lines again, but this time a member of each group will choose where to place his or her beanbag on one of the tick marks (bus stop). Give a Discourse Sheet to each group to help guide discussion. (Students will be discussing rounding using the Discourse Sheet during this part of the Explore activity instead of working in their Student Journals.) Once students place their beanbags at a bus stop, that number indicates the bus stop that is closest to their previous location. Challenge students to determine what that previous location (number on the number line) could have been. Invite students to discuss what exact number could be rounded to that multiple. a.

6. 7.

For example, if the beanbag is placed on 300, the range of potential exact numbers that could round to 300 is 295–304 if rounding to the tens. If rounding to the hundreds, an exact range of answers is between 250 and 349.

Challenge students to continue the discussion by placing the beanbag at a different location or “bus stop” on the number line. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-3 Is everybody coming up with the same number? Why? Why not? No, because there are several numbers that can round to any multiple. Some are less than the multiple; others are greater.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

•

Acceleration

DOK-2 Did you use the midpoint to help determine your number(s)? How? Yes, the midpoint helped us determine the range of numbers. If we wanted to ﬁnd a number that was less than the multiple and rounded up to it, we would use the midpoint and the numbers leading up to the multiple. For the numbers that are greater than the multiple but rounded down to it, any number below the midpoint would be considered.

Give each group about 5–7 minutes at each number line, and then rotate to a new number line. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

Intervention

ROUNDING

Home

DOK-3 Did everyone come up with the same number? Why or why not? No, they did not because there are various numbers that are close to (the multiple). DOK-2 If we were looking at numbers less than (multiple), what are the two multiples of 10 and 100 we would look at in order to round to (multiple)? Answers may vary depending on the number. For example: 280, 290, and 200, 300 DOK-2 If we were looking at numbers greater than (multiple), what are the two multiples of 10 and 100 we would look at in order to round to (multiple)? Answers may vary depending on the number. For example: 300 and 310 DOK-2 If you listed all the numbers that will round to (multiple) by using the tens place, where would you start? Ask students to turn and talk with their groups. Discuss out loud once students have had the opportunity to talk within their groups. Answers may vary depending on the number. For example, we would need to look at all the numbers before 300 and all the numbers after 300 using our multiples of 290 and 310. DOK-2 How would you decide which numbers will round and which numbers will not? Answers may vary depending on the number. For example, we would need to look at the value of the number in the tens place and decide if it is closest to the multiple of 300. DOK-2 As a group, list all the numbers that will round to (multiple). Ask students to share once they have had the opportunity to discuss and make a list.

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.

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 On this Exit Ticket, challenge some students to also round to the nearest 10.

ROUNDING

Rounding Explore 2 – Round to Justify Reasonableness ACTIVITY PREPARATION Students mentally round solutions to addition and subtraction problems using reasoning.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• • • •

1 Student Journal (per student) 1 Set of Camping Supplies Cards (per class) 1 Exit Ticket (per student)

•

Consumable • • •

6 Sheets of chart paper (per class) 1 Roll of transparent tape (per class) 1 Set of markers (per class)

•

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. Print the Camping Supplies Cards on card stock, and tape them around the room. Prepare chart paper by drawing a T-chart. Label the left column Estimation and the right column Actual Total. For students who need more support in recalling information, please see our Base Tens, Open Number Line, 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. (Number Lines)

PROCEDURE AND FACILITATION FACILITATION TIP Be aware that estimating and creating answers that are “about how much” is very uncomfortable for some students. Reassure them that estimating skillfully is a powerful life tool. It’s a very helpful thinking skill; having an exact answer is not always necessary or needed. FACILITATION TIP

a. DOK-2 What did you do to add the numbers mentally? Students could ﬁnd several different ways to mentally calculate the total. Allow multiple students to share different ideas. Here’s an example: I know $41 is close to $40, and $16 is close to $20. From there, it’s easy to add $40 and $20 to equal $60.

Draw students’ attention to the wording “about how much.” Point out that when this wording appears in problems, the solutions should be estimates, not actual amounts.

i. Explain to students that it is helpful to estimate the solution to a problem to help you know what number the actual answer is close to. In this case, if you have a limit to how much you can spend, it could help you stay within that limit.

FACILITATION TIP Encourage students to think of other realworld situations where estimating would be useful. Be prepared with some of your own life experiences with rounding. FACILITATION TIP Monitor students to make sure they are estimating the total ﬁrst, ﬁnding the actual total second, and then comparing the two totals. If their actual answer is not reasonable, students should look for errors in either their estimation or the actual amount and resolve the problem. 60

Read the following scenario to the class: Today, we are going on a camping trip and need to buy supplies. We will be mentally estimating the cost of supplies along the way to get an idea of how much we will spend. Begin with an example. Tell students that gas for the car ride will cost $41, and the campsite entrance fee is $16. Ask students to mentally calculate about how much it will cost to get to their campsite. Discuss the following questions:

3. 4.

Explain to students that they will travel through stations with their groups. At each station, students will record their estimations 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 could you round this cost to? How do you know? Answers will vary but may include the following: In this case, I would round $23 to $20 and $28 to $30. I know that 23 is closer to 20 than 30, and 28 is closer to 30 than 20. If I add both costs together, the total rounded cost is $50. © Accelerate Learning Inc. - All Rights Reserved

5. 6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

After students have gone through all stations, post a sheet of chart paper under each problem on the wall. Tell students that they will rotate through the stations once more, showing their thinking and strategies for estimation and actual total calculations. After groups have rotated through the stations and written on the chart paper, encourage students to do a gallery walk. They are looking for strategies different from their own and determining if they agree or disagree. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

ROUNDING

Home

FACILITATION TIP Allow students to write or draw to show their thinking and strategies.

STEMscopes Tip

Math Chat DOK-1 What does it mean to estimate an answer? An estimate is a strategic number that is close to the exact answer. Rounded numbers are easier and faster to add or subtract. • DOK-3 Which strategies help you get the closest to the actual answer? The less you change the numbers, the closer you can get to the actual answer. Your estimate is more accurate if you use numbers that are really close to the original. • DOK-3 Why is estimation helpful? Sometimes you only need to know the estimate. You don’t always need to know an actual amount. Estimating ﬁrst can help you know what the exact answer will be close to. In this case, it can help us know about how much money we need to pay for our camping gear. •

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.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Take time to clarify your criteria for success on this Exit Ticket. How students show their thinking may vary, and some will be tempted to merely write the solution.

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 to Justify Reasonableness 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

The Ice Cream Tradition

Tailor

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

Matt’s Plant: Why Isn’t It Growing?

Round Numbers within 1,000 – Tens Place and Hundreds Place

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 Back to School Sale! 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 my understanding of place value to round numbers to the nearest 10 or 100.

I can explain the process for rounding numbers.

I can use rounding to determine whether an answer is reasonable.

SCOPE 1

Addition and Subtraction Fluency Scope Introduction SCOPE SUMMARY Students become accurate and eﬃcient in adding and subtracting within 1,000. They apply strategies based on place value, properties of operations, and the relationship between addition and subtraction.

VERTICAL ALIGNMENT

Student Expectations

3.PAR.2.1 Fluently add and subtract within 1000 to solve problems.

Background Knowledge

Future Expectations

Second-grade students learn to add and subtract numbers up to 100 using a variety of strategies. They expand their knowledge of base-ten numbers by forming units of 100 from bundling groups of 10.

In fourth grade, students will extend their work with the base-ten system to become ﬂuent and eﬃcient with computation. Fourth-grade students will begin to incorporate the standard algorithm as a representation for the processes of addition and subtraction. They will also use their understanding of place value and properties of operations to represent multiplication and division of multi-digit numbers.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

use models and other methods to add and subtract various methods.

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: •

add within 1,000 through by using addition strategies of traditional algorithms.

•

add within 1,000 through by using addition strategies of partial products.

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

Add Using Base-Ten Strategies In groups, students learn how to solve 3-digit addition problems by solving a scenario. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

use base ten blocks and partial sums to solve and model each part of the addition problem.

•

work together to solve scenario problems.

•

determine who bought the most baseball and football cards from the ﬂea market.

Add Using Number Line Strategies In groups, students will solve different scenarios within Mission Challenge stations. Students will: •

add using number lines.

•

choose strategies for solving mission problems.

Once students have solved the scenario, they discuss learning with the class and ﬁnish with an Exit Ticket.

Subtract Using Base-Ten Strategies In groups, students will solve a scenario involving a carnival director who needs help determining how much of each kind of food was left at the end of the ﬁrst day of a carnival. To help students solve the scenario, they will: •

solve 3-digit subtraction problems.

•

model the problem using base ten blocks.

•

write the problem in expanded form before solving.

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.

Upon completion of the Explore activities, they will discuss their learning and complete with an Exit Ticket for assessment.

ADDITION AND SUBTRACTION FLUENCY

Home

Subtract Using Number Line Strategies Students will solve a scenario in which they help determine the distance traveled by hikers between the start and the ends of the day. To help solve the scenario, students will: •

ﬁnd the difference between distances using a number line.

•

ﬁnd the difference between distances using algorithms.

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

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency 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 use models to add and subtract within 100. This activity is intended to assess mastery of the following standard(s): 2.NR.2.4 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Materials

Preparation

Printed •

•

Print the Student Handout for each student.

1 Student Handout (per student)

Reusable •

1 Set of base ten blocks (per student or per group)

ADDITION AND SUBTRACTION FLUENCY

Home

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

Distribute a Student Handout to each student and a set of base ten blocks to each student or group. Students may work individually, with a partner, or in a small group to solve the problem on their Student Handouts. Encourage students to model the problem using base ten blocks. They should sketch their models on their Student Handouts. Facilitate a class discussion about how the students solved the problem. 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. Ask the following questions: a. What mistake did Lin make? Answers may vary. Lin added each place value up but did not regroup. She just wrote all the digits in one place. Her answer was 8 tens and 11 ones. She forgot to change out the extra ones for tens. b. How can Lin ﬁx her mistake? Answers may vary. Since her answer has more than 9 ones, she needed to regroup 10 ones for a ten so that she had 9 tens and 1 one. c.

How many tickets does Lin actually have? The correct number of tickets she has is 91.

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

FACILITATION TIP Consider projecting the scenario and reading it together with students before distributing the base ten blocks. FACILITATION TIP Some students may still need support when using the base ten blocks, which indicates that they could beneﬁt from the Foundation Builder. Other students may be ready to show a more abstract representation of their thinking. If those students no longer need base ten blocks, encourage them to show their thinking using a number sentence or vertical calculation. FACILITATION TIP Invite a student to show the error(s) they think Lin made by acting out the process with base ten blocks. Have the student verbalize Lin’s thought process for each step. Then, have another student use the base ten blocks and verbally describe how to accurately determine the correct answer.

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency Hook – Ferris Wheel Riders ACTIVITY PREPARATION Students use the addition strategies based on place value and the relationship between addition and subtraction to develop ﬂuency with addition within 1,000.

Materials

Preparation

Printed •

• • •

1 Ferris Wheel Riders (per class)

Reusable • •

Plan to show the Phenomena Video. Prepare to project Ferris Wheel Riders. Decide how you will put students into pairs..

1 Phenomena Video (per class) 1 Projector or document camera (per class)

Consumable •

2 Pieces of lined notebook paper (per pair of students)

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

2. FACILITATION TIP

Consider reading the scenario several times or stopping after each question to ask students what operation they need to use to solve the problem.

DOK-2 Are there multiple ways to solve this problem? What are some strategies? Yes: make a concrete model, use a number line, use an algorithm, etc.

DOK-2 What are some skills that could help us effectively solve this problem? Knowing our addition facts ﬂuently

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.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

DOK-2 Are there multiple ways to solve this problem? What are some strategies? Yes, make a concrete model, use a number line, use an algorithm, etc.

3. 4. 5. 6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Review the problem, and pair up students. Give each pair of students notebook paper. Instruct students to solve the problem using a strategy of their choice. Encourage students to use multiple strategies to check their answers. Discuss the following questions with the class:

Intervention

Acceleration

FACILITATION TIP Consider allowing students to work in pairs so they can talk through the problems and discuss what strategies they will use to solve the problems.

a. DOK-3 Which strategy did you choose to use to solve this problem? Why? Answers will vary. I chose to use the partial sums algorithm because I think the numbers are easier to work with. I can do more of it mentally and can work the problems more eﬃciently. b.

FACILITATION TIP DOK-2 Was regrouping necessary with the traditional algorithm? Explain. Yes, it was required because the sum of the addends in the ones Ask students to explain why the order of column was 13, which is two digits. A ten had to be regrouped to the the numbers matter when subtracting. tens column, leaving 3 ones behind in the ones column.

DOK-2 Was regrouping necessary with the partial sums method? Explain. No, all of the partial sums when added together did not require regrouping.

DOK-4 Understanding the relationship between addition and subtraction, what is a situation from which a subtraction problem could be created using the same information from the addition problem you just solved? Answers will vary. A carnival came to town for the weekend and workers set up a Ferris wheel ride. Over the weekend, 683 people rode the Ferris wheel. On Friday 275 people rode the Ferris wheel. The Ferris wheel was closed on Sunday. How many people rode the Ferris wheel on Saturday? 408 (683 – 275 = 408)

ADDITION AND SUBTRACTION FLUENCY

Home

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency Explore 1 – Add Using Base-Ten Strategies ACTIVITY PREPARATION Students solve three-digit addition problems. Students model each part of addition problems using base ten blocks and partial sums to solve.

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 Printed • • • •

1 Student Journal (per student) 1 Place Value Work Mat (per group) 1 Set of Card Purchasing Records (per group) 1 Exit Ticket (per student)

Preparation • •

• •

• • •

Reusable • • • • •

1 Dry-erase marker (per group) 1 Dry-erase eraser (per group) 1 Set of base ten blocks (per group) 2 Sheet protectors (per group) 1 Roll of transparent tape (per class)

Plan to have students work in groups of 4 to complete this activity. Print a Place Value Work Mat for each group, and put each page inside a clear sheet protector or laminate for reuse. Tape the two pages together so the mat for baseball cards is above the mat for football cards. Print and cut out a set of Card Purchasing Records for each group. Prepare a set of base ten blocks for each group. Each set should have at least the following blocks:

• •

9 ﬂats (100) 12 rods (10) 18 units (1)

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

2. 3. FACILITATION TIP Ask students what operation they use to ﬁnd the total number.

4. 5. 6.

1. Read the following scenario to the class: A group of friends goes to a flea market to buy used baseball cards and football cards. When the group arrives home, they want to determine which friend bought the most cards. You need to help them figure out who bought the most cards by adding up the total number of cards for each friend. Divide the class into groups of four. Give each student a Student Journal, and give each group a set of base ten blocks, a set of Card Purchasing Records, a Place Value Work Mat, a dry-erase marker, and a dry-erase eraser. Direct students to look at the first card purchase (Henry). Students should record the equation on the right-hand side of their Student Journals in the place value chart. Have students build the number of baseball cards using the base ten blocks on the work mat. Students should use the dry-erase marker to write the value of the blocks in each column on the Place Value Work Mat. © Accelerate Learning Inc. - All Rights Reserved

7. 8. 9. 10. 11. 12. 13.

Engage

Explore

Explain

Elaborate

Evaluate

Students should then draw their models of the number on their Student Journals. Students should complete the same steps for the number of football cards. Have student groups collaborate to combine values to ﬁnd the total. Encourage students to record what they did and the value of their solution on their Student Journals. Encourage students to draw any regrouping they had to do. Guide students in translating this process into the standard algorithm by adding the numbers together using the equation on the right-hand side of the page. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

• • • • •

DOK-3 What do you notice when you look at the value of a number in each place compared to the digit? The place value on the left is greater than the place value on the right. Each place value is represented by groups of ten from the previous place value. DOK-3 How did you use each part of a number to combine the two amounts? Each digit in a number represents a value depending on its position within the number. By decomposing it and combining the values in each place, we were able to bundle groups of ten and use partial sums to ﬁnd the total more easily. DOK-1 Looking at Henry’s number of cards, what do you notice about the number of tens he has? He has 12 tens. DOK-1 What is another way we can represent it using base ten blocks? Allow students to use base ten blocks to come up with 1 hundred and 2 tens. DOK-1 What pattern do you notice? Every time we have 10 in a place, we regroup our base ten blocks into the next place value. DOK-1 Would this be the same for every place value? (Allow students a moment to use manipulatives if needed to come to the conclusion.) Yes DOK-2 How is this represented in the equation on the right? If we’re demonstrating regrouping in an equation, we add the number of bundles of ten that are left over from the place value on the right.

Intervention

Acceleration

FACILITATION TIP When regrouping is necessary, watch for students who transpose the number they should write down and the number they should carry. Also be aware that students may forget to add in the regrouped number. Model how to use the information from the work mat to write and solve using the standard algorithm. FACILITATION TIP Discuss whether students think the numbers can be added in any order and still get the same sum. Encourage students to change the order of the numbers on one of the cards to see if they arrive at the same solution.

ADDITION AND SUBTRACTION FLUENCY

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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.

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

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency Explore 2 – Add Using Number Line Strategies ACTIVITY PREPARATION Students add using a number line and work through stations to collaborate in ﬁnding the best possible strategies.

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 Set of Mission Possible Cards (per class) 1 Number Line (per group) 1 Exit Ticket (per student)

•

Reusable • • • •

1 Timer (per class) 1 Sheet protector (per group) 1 Dry-erase marker (per group) 1 Roll of tape or stapler if using ﬁle folders (per class)

• • • •

Consumable •

•

5 Large clasp envelopes or ﬁle folders (per class)

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 Mission Possible Cards on card stock, laminate, and cut apart. Print a Number Line for each group as needed. Place the Number Line in a sheet protector, and provide a dry-erase marker for students to use as needed. Put each Mission Possible Card in an envelope or ﬁle folder. If using a ﬁle folder, tape or staple 2 of the sides closed. Label the front of the envelope or folder with the mission name and number. Place the cards around the room in different locations. Prepare to play spy music to set the mood for the scenario. For students who need more support in recalling information, please see our Base Tens 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. (Base Ten Blocks and Number Lines)

PROCEDURE AND FACILITATION 1. FACILITATION TIP

Create engagement with the different Missions in the Explore activity by playing spy music. This can include printing badges for students and spy party decorations in the classroom. 3. 4. 5. 6. 74

Give a Student Journal to each student, and give a Number Line and a dry-erase marker to each group. Play spy music in the background as you read the following scenario to the class: Around the room, you will find five missions you must complete. You will have 5 minutes to solve each mission. On each mission, there is a “mission challenge.” This number challenges your skills to solve the problem in the indicated number of jumps. Remember, agents, the challenge is not an obligation as long as you complete the challenge. Collaborate with your team of agents, but try to complete the final one on your own. Good luck, agents. Invite each group to find a card to start with. Encourage students to use their Number Lines as needed to work out problems. Inform students that they will complete the missions in order from here. For example, a group starting on mission 3 will continue on to 4. Point out to students that each group of agents will start recording at a different place in their Student Journals. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Allow students about 5 minutes at each mission. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 How could you decompose the addend? Break it apart by place value

9. 10.

DOK-1 How could you add now that you see the values of the digits? I could jump by place values to get to the sum faster.

DOK-1 If a number is still too large after decomposing by place value, could you decompose it again to get to friendlier numbers? Yes

Facilitate group rotation as they continue on through the rest of the missions. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How did you decide how many jumps to use on the number line? I decomposed the number by place value and usually combined each place value in a jump. • DOK-2 Notice our number lines always started with the ﬁrst number in our equation. Does it have to be done that way? No, it does not. Because it is adding, you can switch the numbers and still get the same answer. • DOK-2 How would you lead someone else through using this strategy to add? First, decompose the addend by place value. Then, start at your number on a number line and jump by place values while adding on each time to quickly ﬁnd the sum. •

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 After each mission, have students selfcheck their work with the list at the top of the Student Journal.

FACILITATION TIP In the Math Chat, have students compare the Line strategy and the Base Ten strategy for addition.

ADDITION AND SUBTRACTION FLUENCY

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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.

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency Explore 3 – Subtract Using Ten-Base Strategies ACTIVITY PREPARATION Students solve three-digit subtraction problems. Students model using base ten blocks and then write the problem in expanded form before solving.

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 Work Mat (per group) 1 Set of Carnival Food Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • • • • •

•

1 Dry-erase marker (per group) 1 Dry-erase eraser (per group) 1 Set of base ten blocks (per group) 2 Clear sheet protectors (per group) 1 Roll of transparent tape (per class)

•

Plan to have students work in groups of 4 or 5 to complete this activity. Print a Place Value Work Mat for each group, and put each page inside a clear sheet protector for reuse. Tape the two together so the Number Made row is on top. Print and cut apart the Carnival Food Cards for each group. Gather enough base ten blocks for each group to have at least eight ﬂats, twelve rods, and twelve ones. 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 FACILITATION TIP

Ask students what operation they will use to solve the problem. FACILITATION TIP Allow students a few moments to discover the materials and discuss how they can be connected to the scenario. FACILITATION TIP Discuss whether students think the numbers can be subtracted in any order. If students think the order of the numbers does not matter, model a simpler problem (for example, 8 – 5), and have students ﬁnd the solution. Then, switch the numbers around, and point out that it is not possible to take a larger amount from a smaller amount.

2. 3.

4. 5. 6.

7. 8.

9. 76

Read the following scenario to the class: A carnival has just opened! On the first day of the carnival, the carnival director wants to know how much food is left over. Help the director by figuring out how much of each kind of food is left at the end of the first day. Divide the class into five groups. Give each student a Student Journal. Give each group a set of base ten blocks, a set of Carnival Food Cards, a Place Value Work Mat, a dry-erase marker, and a dry-erase eraser. Direct students to look at the first food card (corn dogs). Students should record the equation on the right-hand side of their Student Journals in the place value chart. Have students build the number of corn dogs that were made using the base ten blocks on the top row of the Place Value Work Mat. Students should use the dryerase marker to write the value of the blocks in each column on the work mat. Students should then draw their model of the number on their Student Journals. Students will model the number of corn dogs that were bought by removing those corn dogs from the original amount and moving the blocks down to the Number Bought row. Students should record what they did and the value of their solution on their Student Journals. © Accelerate Learning Inc. - All Rights Reserved

10. 11. 12. 13.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Encourage students to draw how pieces were taken away from the total as well as any regrouping they had to do. Guide students in translating this process into the standard algorithm by subtracting the numbers using the equation on the right-hand side of the page. Students should move on to the next two Carnival Food Cards and repeat the same steps. 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 how many need to be subtracted from this place value? There are more (ones or tens) that need to be subtracted than what I have.

14.

15.

DOK-1 Hmmm . . . do all of these blocks represent the same thing? Yes, they all represent corn dogs.

DOK-2 Why are they in different places? Even though they are all corn dogs, they are bundled or grouped differently into 10 or 100 and put into a different place.

DOK-2 Well, can you regroup any of the bundles into the (ones or tens) place so you have enough to subtract from since they represent the same item? Yes, I could probably take one group of (tens or hundreds) and break it apart to regroup it into the place where I need them (ones or tens). Once I do that, I can have enough to subtract from.

When students get to the funnel cakes card, encourage them to subtract the numbers without building the model. Students can just do the expanded form and the algorithm, or they can jump to just using the algorithm if they are ready. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

STEMscopes Tip

ADDITION AND SUBTRACTION FLUENCY

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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.

Math Chat DOK-2 What observations did you make about some of these problems? Some didn’t have enough ones or tens to subtract from, so we had to regroup some of the groups or bundles from the place value to the left. We broke it apart and regrouped it to give us enough to subtract in that place value. • DOK-2 What did you notice about the equation on the right? The equation represented what we were modeling with our base ten blocks. The digits on the right showed how many of each block we had in each column and what we did with them as we were subtracting. •

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

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency Explore 4 – Subtract Using Number Line Strategies ACTIVITY PREPARATION Students ﬁnd the difference between distances using a number line. Students relate these models to algorithms.

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 Printed • • •

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

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 a set of Hiking Mount Robson Task Cards for each group, laminate (optional), and cut apart. For students who need more support in recalling information, please see our Base Ten 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 (Base Ten Blocks and Number Lines).

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Teacher can model how to use a number line on the board with students guiding the process. FACILITATION TIP Provide base ten blocks for struggling students to visualize how to decompose the numbers.

2. 3. 4. 5. 6. 7.

Distribute a set of Hiking Mount Robson Task Cards, and read the following scenario to the class: DeAnthony and Niyah are doing a 3-day hike on Mount Robson. Each group needs to determine how many meters of elevation they cover during different parts of their 3-day hike to the top. You are determining the distance they travel between the start and end of the day. Divide the class into groups of up to four students. Give each student a Student Journal. Encourage groups to collaborate to ﬁnd the difference using a number line. As students work together, monitor groups and listen for understanding. For struggling students, guide them to decompose numbers for easier use on the number line. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 How can you ﬁnd the distance between the numbers? By seeing how many jumps it will take b.

DOK-3 What would be the most eﬃcient way to ﬁnd the difference? Ones? Tens? Hundreds? How do you know? Answers will vary depending on the number but may include the following: Probably not by ones because it would take too many jumps. If we decompose it by place value, we can group the tens or hundreds together and make it easier to subtract.

FACILITATION TIP

Discuss how a ruler, thermometers, and meter sticks have different intervals like the number lines.

DOK-2 What do you do if you can’t jump by tens anymore, but you’re still not at your number? I would jump by ones.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Have students complete all 5 Hiking Mount Robson Task Cards. 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 which place value to jump first? I decomposed the number being subtracted by hundreds, tens, and ones. I began with hundreds because those were the largest numbers. When there were no hundreds left, I subtracted by tens and, finally, ones. DOK-1 What did you do when you finished all of the jumps on the number line? I used addition to check my answer. DOK-2 Explain how adding works when finding the difference of the numbers. Because subtracting is just finding the distance between two sets of numbers on a number line, you can also add up the parts to find the distance to the next point. DOK-2 Number lines can also be used to find a sum. What is the difference between the two strategies? When adding, only one point is known, and you have the “difference” between the points. The other end point needs to be found. When subtracting, both points are known on the number line; the difference needs to be found. DOK-1 In a subtraction equation or expression, what does the subtraction sign mean? It represents the need to find the distance between the two numbers.

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.

ADDITION AND SUBTRACTION FLUENCY

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Post-Explore 1. 2. 3. 4.

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency 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

Add Using Base-Ten Strategies 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 Using Number Line Strategies 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 Using Base-Ten Strategies

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

Subtract Using Number Line Strategies

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

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

Family BINGO Night

Police Patrol Oﬃcer

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 Wonders of the Chesapeake Bay

Addition and Subtraction within 1,000

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

Problem-Based Task

Interactive Practice

Campground Chaos!

Prairie Dog Village

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

ADDITION AND SUBTRACTION FLUENCY

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

Students who are still acquiring the concept and need remediation

ADDITION AND SUBTRACTION FLUENCY

Addition and Subtraction Fluency

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 my understanding of place value to apply an algorithm for adding and subtracting numbers within 1,000.

What prompts will be used?

What does mastery look like?

ADDITION AND SUBTRACTION FLUENCY

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I can use what I know about properties of operations to add and subtract numbers within 1,000.

I can use what I know about the relationship between addition and subtraction to add and subtract numbers within 1,000.

SCOPE 1

Addition and Subtraction Models Scope Introduction SCOPE SUMMARY Students demonstrate their understanding of one-step and two-step addition and subtraction problems by employing appropriate pictorial models, number lines, diagrams, and equations with a letter standing for the unknown. The use of models helps promote understanding of concepts and aids in decision-making regarding which strategies to use to solve problems. Student Expectations

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.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students ﬂuently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationships between addition and subtraction to solve problems that require determining the unknown whole number in an addition or subtraction equation.

Fourth-grade students will 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 used include an open number line, partial sums and differences algorithms, and the traditional standard algorithm.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

solve problems involving the addition and subtraction of twodigit numbers using part-whole strategies.

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

model addition and subtraction within 10,000.

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

Model Problems with Diagrams In this exploration, students will use base ten blocks, diagrams, and equations to represent one- and two-step problems involving addition and subtraction of whole numbers. Students will: •

use paper strips to create diagrams that model the problem.

•

build models to represent the part-and-whole relationships.

Explore 2

Explore 1

EXPLORE ACTIVITIES Model Problems with Number Lines In this exploration, students will use number lines and equations to represent one- and two-step addition and subtraction problems. Students will: •

create number lines to represent facts about the Franklin Library.

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 an Exit Ticket for assessment.

ADDITION AND SUBTRACTION MODELS

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ADDITION AND SUBTRACTION MODELS

Addition and Subtraction Models 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 represent and solve addition and subtraction word problems in which unknowns may be any one of the terms in the problem. This activity is intended to assess mastery of the following standard(s): 2.NR.2.3 Solve problems involving the addition and subtraction of two-digit numbers using part-whole strategies.

Preparation

Materials

• •

Printed •

1 Addition and Subtraction Models (per class)

•

Print Addition and Subtraction Models for the class. Prepare to project the question page of Addition and Subtraction Models. Post each student statement around the room.

ADDITION AND SUBTRACTION MODELS

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Procedure and Facilitation Points 1. 2.

3. 4. 5.

Project the question page. Read the following scenario to the class: Tariq and Roberto put all of their baseball cards together. Tariq knew 32 of the cards were his, but Roberto wasn’t sure how many cards he put in the pile. They counted all of the cards and found they had a total of 56 cards. How can Roberto ﬁgure out how many baseball cards are his? Instruct students to read each student statement. After students have read each statement, they should stand next to the statement they agree with most. Facilitate a class discussion about their 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. Discuss each statement and the results. a.

Student 1 is correct. To ﬁnd Roberto’s number of cards, we can subtract Tariq’s cards from the total number of cards.

Student 2 is not correct. They have a total of 56 cards. Total means all of the cards together. If 32 of the cards are Tariq’s, Roberto couldn’t have all of the cards.

Student 3 is correct. When I start with 32 and count up until I get to 56, I get 24.

Student 4 is not correct. He is adding the total number of cards plus Tariq’s cards, but Tariq’s cards are already included in the total number of baseball cards. Roberto couldn’t have more cards than the total number of cards.

FACILITATION TIP Consider projecting the scenario and reading it together with students before distributing the base ten blocks. FACILITATION TIP Consider projecting the scenario and reading it together with students before distributing the base ten blocks. FACILITATION TIP Determine ahead of time if you want to let students know that more than one student is correct (Students 1 and 3).

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

ADDITION AND SUBTRACTION MODELS

Addition and Subtraction Models Hook – Cargo Ship ACTIVITY PREPARATION Students model addition and subtraction within 10,000.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Plan to show the Phenomena Video. Print the Student Handout for each student.

Reusable • •

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

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

FACILITATION TIP Project the scenario for students to read along with you. Read through it more than once and encourage students to note down the important details. Help them locate and underline the math phrases/words (how many, can hold, in all, need to ﬁt). FACILITATION TIP Student experience with writing complete equations may still be limited. Adjust your instruction as needed to clarify the essential components of an equation.

5. 6. 7.

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. 8. 88

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? Where can you see math in this scenario? Allow students to share all ideas. Read the following scenario: You own a shipping company. You need to ﬁt 5,000 cargo containers on your cargo ship. Your ship can hold 1,408 containers in the front section of the ship and 1,735 containers in the back section of the ship. How many cargo containers do you need to load in the middle section of the ship in order to have 5,000 containers in all? Have students draw a picture of the scenario on their Student Handout. Tell them they do not have to draw every single shipping container, but they should draw a rectangle to represent the shipping containers with a number that shows the quantity. You can draw an example for them on the board. Next, instruct students to write at least one equation to represent the scenario in their Student Handout. After students complete the Explore activities on this topic, they will revisit this problem and update their Student Handout. Discuss the following questions with the class: a.

DOK-1 What information is given in this problem? We know two amounts and a total amount.

DOK-2 What information are we missing that we need to ﬁnd? We need to know the number of cargo containers that need to go in the middle of the ship.

DOK-1 What does your picture look like? Where did you put the unknown in your picture? I drew boxes on the back, middle, and front of the boat. The box in the back has the number 1,735 in it, the box in the front has the number 1,408 in it, and the box in the middle has a question mark for the unknown. I wrote the number 5,000 inside the boat because that’s how many cargo containers we need in all.

DOK-2 What operations could we use to solve this problem? We could use addition and subtraction.

Move on to complete the Explore activities.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4.

5. 6.

DOK-2 What information are we missing that we need to ﬁnd? We need to know the number of cargo containers that need to go in the middle of the ship.

DOK-2 What operations could we use to solve this problem? We could use addition and subtraction.

Have students look at their Student Handout and look at the picture they drew. Is it correct? Do they need to revise it? Students should have at least one equation written down. If they only have one, have them write a second equation that can be used to represent the problem. Some students may be able to think of more than two equations that could be used. They can write down as many equations as they can think of to help them solve the problem. Finally, in the blank space at the bottom of their Student Handout, have them use one of the equations to solve the problem. Discuss the following questions with the class:

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 MODELS

Home

a. DOK-2 What equation did you use to solve the problem? I used 5,000 – 1,735 – 1,408 = c b.

DOK-2 Are there other equations that would work? Yes, 1,735 + c + 1,408 = 5,000

DOK-3 Is it important to write down the equation when you are solving a problem? It is important to help you make sure you have included all the information from the problem and to help you see what steps you need to take to ﬁnd the answer.

FACILITATION TIP As a follow up to this yes or no question, remind students that an equation is a way to take a math word story and translate it into math symbols and numbers. Being ﬂuent in both “languages” (symbols and words) is a powerful tool. Turning math stories into equations will continue to be a challenge in the grades ahead.

ADDITION AND SUBTRACTION MODELS

Addition and Subtraction Models Explore 1 – Model Problems with Diagrams ACTIVITY PREPARATION Students use base ten blocks, diagrams, and equations to represent one- and two-step problems involving addition and subtraction of whole numbers.

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 Domino World Record Cards (per group) 1 Exit Ticket (per student)

Reusable • • • •

1 Set of base ten blocks (per group or pair) 1 Plastic resealable bag (per group) 1 Set of markers (per group) 1 Glue stick (per group)

Preparation • • • • • • • •

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Gather one set of base ten blocks for each group. Print on card stock and cut one set of Domino World Record Cards for each group. Laminate for durability (optional). Place one set of Domino World Record Cards in a resealable bag for each group. Cut sheets of colored copy paper lengthwise into 2 in. strips. 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).

Consumable • •

30 Sheets of colored copy paper (per group) 1 Sheet of chart paper (per group)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Clarify your expectations for what a competed Student Journal should look like. Complete one of the countries together (USA has subtraction) as a class, model for students and have a student bring up a successful sample to share. 90

2. 3.

Read the following scenario to the class: Everyone enjoys a good domino show! Believe it or not, there are several world records for various ways to use dominoes thanks to increasingly complex designs and extraordinary effects. Let’s explore the number of objects used in some of these thrilling and nail-biting domino world records. Distribute a set of 20 paper strips, a set of Domino World Record Cards, and a set of base ten blocks to each group. Students will begin working with Domino World Record Cards 1–3. a.

5. 6. 7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

For each card, students will use the paper strips to create diagrams that model the problem. Students should reﬂect on what they have learned about part-andwhole relationships to build the models. Remind students that one paper strip will represent the whole and another paper strip will need to be folded and cut apart to represent the parts. Students should write the numeric values on the parts and the whole of their diagrams. Students will then draw their models and answer the questions on their Student Journals. Students may use the base ten blocks as needed to compute and solve the problems. Once students have completed Domino World Record Cards 1–3, pause their work to discuss. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 What helped you build your diagram? When I read the problem, I looked for the whole or total and the parts that make up the total to build the diagram. b.

11.

Acceleration

FACILITATION TIP These diagrams can be excellent thinking tools as students progress into decimals, percents and fractions later. Although the model may be complicated at ﬁrst, reassure students that it will be helpful for many of them. FACILITATION TIP Having students write clear solution statements may take time and require some extra adult or peer support for struggling students. Encourage students to read their statements out loud and have other students listen carefully to support success. FACILITATION TIP Struggling readers may need the Domino World Record Cards read aloud to them.

As students move on to the next half of the Domino World Record Cards, support their model-building of the two-step problems. a.

10.

DOK-2 How did the diagram help you solve the problem? I could use the diagram to determine whether to add or subtract to ﬁnd the solution. If I was looking for a part, I had to subtract the other parts from the total. If I was looking for the total, I had to combine (or add) the parts to ﬁnd the total.

Intervention

ADDITION AND SUBTRACTION MODELS

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Let them know they can break apart a strip however they need to in order to show multiple parts. Students can also create more than one diagram for a problem if they’d like. It is important to emphasize that there is more than one way to build a diagram for these problems. The goal is to accurately show what is happening in the problem.

Students should draw their models 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.

Math Chat DOK-1 What was different about the last few problems? We had to do more than one step in order to ﬁnd the solution. • DOK-2 Explain how you found the number of laptops used to make the record in China. I knew the total number of laptops collected. I also knew I needed to take away 62 and 200 from that total because these were not used or did not fall down like dominoes. I added 62 and 200 to ﬁnd the total number of laptops they did not use and then took that number away from the total. •

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 multiple groups to share how they solved the same problem. Emphasize that there are different paths you can take to make it to the same answer. •

DOK-1 Did everyone’s diagrams look the same? Explain why. No, our diagram for Germany looked a lot different from another group’s diagram. However, we both got the same answer. There is more than one way to represent a problem, as long as you’re showing what is happening in the situation.

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.

ADDITION AND SUBTRACTION MODELS

Addition and Subtraction Models Explore 2 – Model Problems with Number Lines ACTIVITY PREPARATION Students use number lines and equations to represent one- and two-step addition and subtraction problems.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • •

1 Student Journal (per student) 1 Set of Number Line Jump Arrows (per group) 1 Set of Library Scenario Cards (per group) 1 Exit Ticket (per student)

Reusable • • • •

1 Ruler (per group) 1 Set of markers (per group) 1 Glue stick (per group) 1 Large resealable plastic bag (per group)

• • • •

•

Consumable •

• • •

4 Sheets of 12” × 18” construction paper (per group)

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print on card stock and cut one set of Library Scenario Cards for each group. Laminate for durability (optional). Print on card stock and cut one set of Number Line Jump Arrows for each group. Laminate for durability (optional). Place one set of Library Scenario Cards and one set of Number Line Jump Arrows in a resealable bag for each group. Cut the large construction paper sheets in half lengthwise so each group has eight half-sheets. For students who need more support in recalling information, please see our Base Tens 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 FACILITATION TIP Take some time to preview some of the unique vocabulary included in the Library Scenario Cards with students. FACILITATION TIP Although some students may be hesitant to use the Number Line as a tool, encourage them to take the time to show their thinking on the number line. Being ﬂuent with number lines will support their success on later math standards.

2. 3. 4. 5.

a. DOK-1 What is the problem asking for? The number of nonﬁction books in the library

FACILITATION TIP When you complete the ﬁrst Library Scenario Card together, model for students what their Student Journal should look like. Use a student work sample or demonstrate how they are to complete the written solution statements. 92

Read the following scenario to the class: Start spreading the news! The librarian at Franklin Library thinks her library is an amazing place to be! Help the librarian ﬁgure out different facts about Franklin Library and the events that are hosted there! Give a Student Journal to each student. Read the directions together. Place students in groups. Give a set of Number Line Jump Arrows to each group. Read the ﬁrst Library Scenario Card together as a class. Discuss the following questions:

DOK-1 What information do you have? The first floor has 798 nonfiction books, and the second floor has 4,632 nonfiction books.

DOK-2 How can we organize this information? We could create a number line with the jump arrows and construction paper.

Allow groups time to organize the problem on their Student Journals and explore the materials by building their number lines for the ﬁrst library scenario.

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

Invite students to draw their groups’ number lines on their Student Journals. Discuss the following questions: a. DOK-3 How could we represent what we did with an equation using a letter for the unknown? We need to add 798 and 4,632 to find the number of nonfiction books in the library. We can use the letter n to stand for the total number of nonfiction books. Note that students may need guidance on how to translate these steps into an equation and determine letters to use to represent the unknown.

Intervention

Allow students to solve the problem using any strategy they choose (if they haven’t solved it already). Discuss the following questions:

FACILITATION TIP The questions on the Student Journal provide good space for students to note the critical information. However, some students may prefer to to underline or highlight directly onto the Library Scenario Cards.

a. DOK-3 How did your group choose to solve the problem? We ﬁrst estimated that the answer should be close to 5,400 because 800 + 4,600 = 5,400. We then decomposed the number by place value to add the ones, tens, hundreds, and thousands. After regrouping some place values, we got 5,430, which we know is reasonable because it is close to our estimate. b.

10.

11.

12.

DOK-3 What challenges do you think you will run into as you complete the rest of the library scenarios? Problems with several steps will be a challenge. I think when a problem has more than one step, it will require extra jumps on the number line. If we stop after every step to label our jumps on our number line, we will stay organized.

Tell students they will likely struggle, since several of the problems require two steps. Let your students know there is more than one right way to model a problem. Give students ﬂexibility in how they create their number lines as long as their number lines accurately represent what is happening in the problems. Students should now read each of the remaining Library Scenario Cards and organize the information given on their Student Journals. a.

Students will use the ruler to draw a number line toward the bottom of one strip of construction paper.

Students should look at one piece of information from the problem at a time and model that piece of information by placing one of the arrows on the number line and labeling it. Students should also label where the jump lands each time.

Students will repeat this process for each piece of information until they arrive at the ﬁnal value on the number line. For each new piece of information, students should start where the last jump landed.

ADDITION AND SUBTRACTION MODELS

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FACILITATION TIP Because students may be struggling with the two-step problems, you might allow each student to have their own copy of those scenario cards. They need to be able to read them independently several times, carefully locate the math vocabulary, and determine the correct operations. FACILITATION TIP To save time, consider providing this number line already drawn for students.

Students will draw the number lines on their Student Journals and record equations that represent the problems and have letters for the unknowns. They should write their answers as statements and, on their last 3 problems, explain their reasoning. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

ADDITION AND SUBTRACTION MODELS

Addition and Subtraction Models Explore 2 – Add Using Number Line Strategies Math Chat •

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.

•

• •

•

DOK-1 Where did you have to start your number line each time? I had to look at the first piece of information and figure out the size of the jump I needed on the number line. I started at 0 and jumped to the number that represented that information. DOK-1 What direction did you need to jump if the information said you were combining things? I had to jump to the right. If I’m adding more, the number will increase, and numbers increase to the right on a number line. DOK-1 What operation does this represent? This represents addition. DOK-1 What direction did you need to jump if the information said something was missing or damaged? I had to jump to the left. If I’m taking some away, the number will decrease, and numbers decrease to the left on a number line. DOK-1 What operation does this represent? This represents subtraction. DOK-1 How did you know where your jumps were landing on the number line? I had to add or subtract the amount we were jumping from the place where I started in order to find my new spot on the number line. DOK-1 How did you know what your final solution was? Once I represented each piece of information, I knew the place I last landed on the number line was my solution.

Post-Explore FACILITATION TIP On this Exit Ticket, provide support for struggling readers by reading the problem with them. Underline the critical numbers and math words. Some students may need help transferring the multi-digit numbers neatly and carefully into the spaces to do their work.

1. 2. 3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ADDITION AND SUBTRACTION MODELS

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ADDITION AND SUBTRACTION MODELS

Addition and Subtraction Models 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 Problems with Diagrams 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 Problems with Number Lines 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

A Week on the Beach

Jeffery Thomas

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 Clubhouse

Addition and Subtraction within 1,000 – Models and Equations

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 MODELS

Home

Problem-Based Task Always in Stock 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 MODELS

Addition and Subtraction Models

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 apply part-whole strategies to add and subtract multi-digit whole numbers to solve mathematical problems.

What prompts will be used?

What does mastery look like?

ADDITION AND SUBTRACTION MODELS

Home

I can apply my knowledge of properties of operations to add and subtract multi-digit whole numbers to solve mathematical problems.

I can use my understanding of place value to apply an algorithm to add and subtract multi-digit whole numbers to solve mathematical problems.

I can represent one-step addition and subtraction problems, using equations with a letter standing for the unknown quantity.

I can represent two-step addition and subtraction problems, using equations with a letter standing for the unknown quantity.

SCOPE 1

Arithmetic Patterns Scope Introduction SCOPE SUMMARY Students explore how a numeric pattern can be created, extended, and described while representing multiplication expressions. They identify patterns involving multiplication and explain them using a hundreds chart and multiplication tables. Students examine patterns of products and explain the results as odd, even, and ending digits within the product. They examine patterns within products along the rows and columns of a hundreds chart and multiplication tables. Student Expectations

3.PAR.3.1 Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

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 fourth grade, students generate and analyze a number or shape pattern that follows a given rule. Students also represent problems using an inputoutput 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.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

represent even and odd numbers by forming two groups of equal size or with one left over.

•

separate a handful of counters into two groups to determine whether the number of counters is even or odd.

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: •

ﬁnd arithmetic patterns.

•

justify the arithmetic patterns using a calculator and repeated addition.

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.

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. Notes _____________________________________________________________________________________________________________ _____________________________________________________________________________________________________________

100

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Patterns on a Hundred Chart In this exploration, students will use a hundred chart to describe, extend, and create numeric patterns related to multiplication. Students will: • •

Explore 2

Explore 1

EXPLORE ACTIVITIES

to ﬁnd patterns and determine a product for each problem. represent problems on the Hundred Chart.

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

Patterns on a Multiplication Chart In this exploration, students will describe and create numeric patterns to problems involving multiplication using a multiplication table. Students will: •

ﬁnd the total amount of items by using patterns.

•

compare similarities and differences between their strategies and the strategies of others.

ARITHMETIC PATTERNS

Home

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

101

ARITHMETIC PATTERNS

Arithmetic Patterns Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

102

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students will determine whether a sum is odd or even. This activity is intended to assess mastery of the following standard(s): 2.PAR.4.1 Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtraction.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Reusable •

ARITHMETIC PATTERNS

Home

Print the Student Handout for each student. Divide counters so that each table has enough for every student to grab a handful.

1 Set of counters (per group)

Procedure and Facilitation Points 1. 2. 3. 4. 5. 6.

Distribute a Student Handout to each student, and have each student grab a handful of counters. Group students with partners, in a small group, or as an entire class. Invite students to count the number of counters they grabbed. Challenge students to decide whether the number of counters they have is even or odd. Have students draw pictures of their counters and write how they know whether their numbers are odd or even. Facilitate a class discussion about the different strategies students used to determine whether a number was odd or even. 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. a.

I had 7 counters. I lined up the counters in sets of two. I know that if there is an extra counter, it is an odd number. If all of the counters are matched, it is an even number. I had an extra counter, so 7 is an odd number.

I grabbed 12 counters. I counted by 2s. When you count by 2s you are making sure each counter has a match. If you can count by 2s to your number, it is even. If you can’t, it is odd.

Students that have an even number should be able to tell the teacher an equation with two equal addends that equals their number. For example, if a student grabs 6 counters, they should know that 3 + 3 = 6.

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

FACILITATION TIP Some students may notice that even numbers end with the digit 0, 2, 4, 5, or 8 and that odd numbers end with the digit 1, 3, 5, 7, or 9. If students make this observation, have them prove it with at least a couple visual models and explain their thinking to the class. Challenge early ﬁnishers to consider whether there is a relationship between the even doubles and odd doubles and the types of numbers that they form. (Doubles formed by either even numbers or odd numbers result in an even sum.) FACILITATION TIP Take digital pictures of the arrangements students form with counters and/or collect completed pictorial models. Label each arrangement by the number it forms. Set up a T-chart with columns Even and Odd, and display examples for student reference throughout this scope.

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ARITHMETIC PATTERNS

Arithmetic Patterns Hook – High Score Detective ACTIVITY PREPARATION Students recognize number patterns using a multiplication table as a tool to help identify patterns.

Materials

Preparation

Printed •

• • • •

1 Student Handout (per pair of students)

Reusable • • •

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1 Calculator (per pair of students)

•

Plan to show the Phenomena Video. Prepare to project the ﬁrst page of the Student Handout. Print a Student Handout for each pair. Have calculators and scrap paper available for the class to share. Decide how you will pair students for the Hook.

Consumable •

Scrap paper (as needed)

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

FACILITATION TIP

Provide students with a sheet of paper or dry-erase board to jot down notes from the scenario for review later.

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? Where can you see math in this scenario? Allow students to share all ideas. Show students the first page of the Student Handout, and read the following scenario: You and your friend are playing video games about a detective who solves mysteries by finding clues. There are two versions of the game: Version A: Every clue you find is worth 5 or 10 points, depending on how fast you solve it. When you solve the mystery, you earn 10 bonus points. Version B: Every clue you find is worth 2 or 10 points, depending on how fast you solve it. When you solve the mystery, you earn 10 bonus points. During your friend’s turn, you go to the kitchen to get a snack. When you return, the video game is off but your friend says, “I got the new high score! 482!” It is your turn to be a real-life detective. Which version of the game did your friend play? How do you know?

Ask students to predict which version of the game the friend played. Have them signal with a show of hands. a.

FACILITATION TIP

As students are discussing, listen for misconceptions and misunderstandings that can be addressed in the lessons.

Ask students what mathematical tools they could use to justify their reasoning. Discuss, accept, and record all ideas. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

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DOK-3 “Who thinks the friend played Version A? Who thinks the friend played Version B?”

After students have completed the Explore activities for this topic, show the Phenomena Video again and repeat the situation. Review the problem and pair up students. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Give each pair of students copies of the Student Handout. Have calculators, scrap paper, and any other tools that students may have suggested for use available for them to access, and instruct students that they need to use these tools to solve the mystery. Allow students about 10 minutes to solve the problem and to answer the questions on the second page of the Student Handout. They should make use of the tools while recording answers. a.

If students are struggling with how to use the multiplication chart, give them a hint and ask them what they notice about the rows and columns involving the multiples of 5s and 10s.

If students are not sure how to make use of the calculator, demonstrate how to generate multiples. For example, “Press 5 + 5 =. Then, press = again. Each time you press =, the next multiple of 5 will be shown.”

Take another class poll to determine which version of the game they think the friend played. Did everyone in the class agree? Discuss the following questions with the class: a. DOK-2 Name some possible scores that could result from Version A. Any scores ending in a 0 or 5.

FACILITATION TIP As a quick engagement activity, have students compete counting by 3s, 5s, or 9s. Have students start at any number.

DOK-2 Name scores that could result from Version B. Any even scores.

STEMscopes Tip

DOK-2 Name some scores that could result from either Version A or Version B. Any number that ends in 0 is even, so it is a multiple of 2. Numbers ending in 0 are also multiples of both 5 and 10. Therefore, any number ending with a 0 in the ones place could result from both versions of the game.

DOK-2 How was the calculator used to help determine arithmetic patterns? When I added up potential scores on the calculator and wrote them down, I could start to notice a pattern in the scores. A calculator can generate the multiples of numbers of a number by adding a number to itself and then entering the equal sign repeatedly. The more hypothetical scores I wrote down, the more obvious the patterns were, and the more it was reinforced. For the Version A, I noticed that all the scores ended with a 5 or a 0. For Version B, I noticed that all the scores were even and ended with a 0, 2, 4, 6, or 8.

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.

e. DOK-2 How was the multiplication table used to help determine arithmetic patterns? I could look at the multiplication chart to ﬁnd patterns within multiples of 5, 10, and 2. All multiples of 5 end with a 5 or a 0 in the ones place. All multiples of 10 end with a 0 in the ones place. All the multiples of 2 end with an even number in the ones place. f.

DOK-3 How did noticing the patterns from this investigation help you to solve the mystery? Both tools showed the same patterns. A ﬁnal score of 482 is not possible because in Version A, there is a 2 in the ones place.

DOK-2 Do other numbers in the multiplication chart follow similar patterns? Yes. Answers will vary. For example, multiples of 4 are always even.

ARITHMETIC PATTERNS

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FACILITATION TIP Provide students with a multiplication table to help them ﬁgure out their answers.

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ARITHMETIC PATTERNS

Arithmetic Patterns Explore 1 – Patterns on a Hundred Chart ACTIVITY PREPARATION Students will use a hundred chart to describe, extend, and create numeric patterns related to multiplication.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure.

Materials Printed • • • • •

1 Student Journal (per student) 1 Assembly Line Work Mat (per group) 1 Set of Assembly Line Cards (per group) 1 Hundred Chart (per group) 1 Exit Ticket (per student)

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 a set of Assembly Line Cards, an Assembly Line Work Mat, and a Hundred Chart for each group. These may be printed on card stock for durability if desired. Cut apart each set of Assembly Line Cards, and place them into a bag. Place each Hundred Chart inside a sheet protector to create an erasable surface. These may also be laminated if desired. Place both pages of the Assembly Line Work Mat front-to-back in a sheet protector to create an erasable surface. This document can also be printed double-sided and laminated if desired. For students who need more support in recalling information, please see our 120 Chart and Blank 120 Chart 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. (Hundred Board)

• • • • • •

Reusable • • •

1 Dry-erase marker (per group) 2 Sheet protectors (per group) 1 Quart-size resealable bag (per group)

• •

PROCEDURE AND FACILITATION FACILITATION TIP If students don’t already have a copy of a Hundred Chart printed on card stock that they keep at their desk, print one in color (They will need a different colored multiplication chart on card stock for the next Explore activity).

FACILITATION TIP Product, factor, multiple, quotient, sum and difference should all be reviewed at the same time. Take time to post them prominently on your word wall and check for student understanding. Use the Visual Glossary.

2. 3. 4.

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Read the following scenario to the class: Funzone Warehouse sells an assortment of different toys that can be purchased online. When toys are purchased, the workers at the warehouse must place all of the parts that go with that toy into a box in order to prepare it to be shipped to the customer. To make this process faster, the warehouse uses their assembly lines for their workers to pack the boxes quickly. Each item ordered uses a different length of the assembly line depending on the number of parts needed for each item and how far apart the workers need to be in order to have enough time to place the parts in their shipping boxes. The Funzone Warehouse managers need your help in determining the length of each assembly line. Give each student a Student Journal. Distribute a set of Assembly Line Cards, an Assembly Line Work Mat, a Hundred Chart, and a dry-erase marker to each group. Explain to students that the Hundred Chart represents the assembly line and that they will be working together to read each Assembly Line Card and using their Hundred Chart and Assembly Line Work Mat to ﬁnd patterns and determine a product for each problem. Remind students that a product is an answer to a multiplication problem. Give students time to complete the Assembly Line Card problems and record their ﬁndings on their Student Journals.

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 How many toy parts are needed for this problem? The toy needs 8 parts to go into the shipping box. b.

DOK-1 How far apart is each worker? The workers are spaced 5 feet apart.

DOK-2 How can you represent this problem on the Hundred Chart? I know that the workers are 5 feet apart from each other. My ﬁrst worker will start at 5, so I shade in that box. Then, my next worker is 5 feet away, so I will skip count by 5, which shows me that my next worker is at 10. I will keep skip counting by 5 until I get to all 8 parts.

DOK-2 How can you determine what multiple you are using to multiply? I can determine what multiple I am using to multiply by because it is the number I am skip counting by.

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.

ARITHMETIC PATTERNS

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e. DOK-2 How can you determine the product? The product will be the number of parts multiplied by the number of feet each worker is spaced apart. The product will be the last number shaded once I am ﬁnished skip counting by the number of parts and how far apart each worker is.

7. 8. 9.

DOK-2 What patterns do you notice for the multiples on your assembly line? I notice that the multiples are all even/all odd/switch between even and odd. I notice that the multiples have a repeating pattern in the ones place/tens place.

DOK-3 If the pattern were to extend, what do you notice about the extended pattern? I notice that the extended pattern just continues the pattern from the original multiple.

Encourage students to look for similarities and differences between their strategy and the strategies of others when using a hundred chart. Instruct students to answer the reﬂection questions with their groups after they have completed the problems 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 is a hundred chart helpful when finding the multiples and product to a multiplication problem? A hundred chart is helpful because it can help us skip count from one multiple to another multiple until we find our product. • DOK-2 How can a hundred chart be used to find patterns? A hundred chart can be used to find patterns because it lists out the multiples to a multiplication problem, and we can then use those multiples to see if they are all even or odd or switch between even and odd. We can even find patterns among the ones and tens places. • DOK-2 What did you notice about the multiples when you extended the pattern? I noticed the extended pattern continued the same pattern from the original multiples. •

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.

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 On this Exit Ticket, preview the text with students, allow for questions and support struggling readers.

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Arithmetic Patterns Explore 2 – Patterns on a Multiplication Chart ACTIVITY PREPARATION Students will describe and create numeric patterns to problems involving multiplication using a multiplication table.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure.

Materials Printed • • • •

1 Student Journal (per student) 1 Multiplication Table (per group) 1 Set of Pack the Boxes Cards (per group) 1 Exit Ticket (per student)

Reusable • • • •

1 Dry-erase marker (per group) 1 Highlighter (per student) 1 Sheet protector (per group) 1 Resealable bag (per group)

Preparation • • •

• • • • •

Divide the class into groups of 3 or 4 students to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Multiplication Table, on cardstock for durability, for each group. Place each Multiplication Table into a sheet protector to create an erasable surface, or you can laminate it for long-term use if desired. Print a set of Pack the Boxes Cards for each group, cut them apart, and place them in a resealable bag. Gather enough dry-erase markers for each group to have one. Gather enough highlighters for each student to have one. For students who need more support in recalling information, please see our 120 Chart and Blank 120 Chart 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. (Hundred Board)

PROCEDURE AND FACILITATION

FACILITATION TIP If this is the students’ ﬁrst time exploring a Multiplication Table up close, provide time for them to discover patterns. This table has patterns that will be used in later grades when factoring and multiplying polynomials, performing operations with fractions, and more. If they don’t discover all of the patterns, take time to directly show the patterns in each multiple.

2. 3.

FACILITATION TIP Provide students with their own copy of a multiplication table printed on colored card stock to always keep at their desk and/or to take home. Keep extras available in the classroom.

5. 6.

FACILITATION TIP After locating the factors and multiples on this Multiplication Table, help students label their own multiplication tables with the words factor and multiple. 108

Read the following scenario to the class: Fantastic Food Bank received donations from their local community of items that will help those in need. The donation boxes had the same number of objects in each box. The food bank staff recorded the number of items in a table in which, if you multiplied the number of items in each box by the number of boxes, then you could find the total amount of items in all the boxes. Look at the table the staff made, and see what patterns you notice. Give a Student Journal and a highlighter to each student. Display the Multiplication Table. Highlight the first row and first column of the Multiplication Table. Instruct each student to do the same with the multiplication tables on their Student Journals. Explain that the highlighted row and column are the factors being multiplied. The numbers to the right of the highlighted column and below the highlighted row are the products of those numbers being multiplied. Divide students into groups. Distribute a set of Pack the Boxes Cards, a Multiplication Table, and a dry-erase marker to each group. Instruct students to read about each donation received (on the Pack the Boxes Cards) and work in their groups to investigate the multiplication table and the patterns they notice. Students will record their observations on their Student Journals. Encourage students to use their dry-erase markers to shade the pattern being used on their Multiplication Tables and circle the product.

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 How can you use a multiplication table to ﬁnd the number of items in each box? I can look at the column that is labeled Number of items in each box and ﬁnd the factor that is being used in my problem. Since this problem has 9 cans of beans in each box, then I will go down the column of the number of items in each box until I reach the number 9. b.

DOK-1 How can you use your Multiplication Table to determine how many items will be in the number of boxes listed in the word problem? If I am packaging 9 boxes with 7 items in each box, then I will shade the 7 items in each box row until I get to the 9 Number of boxes column. If I am packaging 9 boxes with 7 items in each box, then I can skip count by 7 until I get to 9 boxes.

DOK-1 What multiplication expression is represented by your highlighted table? Answers will vary based on the problem.

DOK-1 What is the product for the total number of items needed in all the boxes? Answers will vary based on the problem.

FACILITATION TIP Preview some of the unique vocabulary included on the Pack the Boxes Cards. Some students might beneﬁt from a pictorial representation of the cards that shows the items in boxes and the number of boxes.

ARITHMETIC PATTERNS

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FACILITATION TIP Reassure students that another way to double check these problems is to draw a visual representation. Although using the multiplication table is an excellent tool, encourage the use of any method.

e. DOK-2 What patterns do you notice about the highlighted numbers? I notice that all the multiples were even or were odd and even. 9. 10. 11.

Encourage students to look for similarities and differences between their strategies and the strategies of others. Instruct students to answer the reﬂection questions with their groups after they have completed the problems 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 pattern do you notice when you multiply an even number by an even number? When you multiply an even number by an even number, the product is even. • DOK-2 What pattern do you notice when you multiply an odd number by an even number? When you multiply an odd number by an even number, the product is even. • DOK-2 What pattern do you notice when you multiply an odd number by an odd number? When you multiply an odd number by an odd number, the product is odd. •

FACILITATION TIP A follow-up question might be to compare what happens when you add or subtract evens and odds.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP On this Exit Ticket, allow (or encourage) students to use a pictorial model as well.

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ARITHMETIC PATTERNS

Arithmetic 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

Patterns on a Hundred Chart 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

Patterns on a Multiplication Chart 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

Art Class Mosaic

Elizebeth Smith Friedman

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

The Buddy System

Arithmetic Patterns

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

PhET Interactive Simulation

How Many Moves?

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

ARITHMETIC PATTERNS

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ARITHMETIC PATTERNS

Arithmetic 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

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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?

ARITHMETIC PATTERNS

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What does mastery look like?

I can identify arithmetic patterns within a hundreds chart or multiplication table.

I can explain arithmetic patterns using what I know about the properties of operations.

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SCOPE 1

Multiplication Models Scope Introduction SCOPE SUMMARY

Student Expectations

3.PAR.3.2 Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division. 3.PAR.3.4 Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent.

Students explore multiplication of two whole numbers, and they understand and interpret the product of whole numbers when given an equal number of groups with an equal number of objects in each group. A variety of strategies, such as equal groups, arrays, area models, diagrams, number lines, and equations, are used to determine the product. Students also explore various scenarios in which different expressions can be used to represent the same multiplication problem. They work with the meaning of the equal sign and equal representations to create equalities to show how two separate expressions, including multiplication, addition, and subtraction, can be equivalent.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Kindergarten and ﬁrst grade form the foundation for our base-ten number system through representing objects in sets, composing and decomposing numbers, building place value relationships, and developing addition and subtraction strategies and skills. Second grade advances this progression as students work with equal groups, arrange objects in rectangular arrays, and write equations to express the total as a sum of addends. This establishes the foundation needed for third grade to fully develop the relationship between addition and multiplication; comprehend patterns; provide strategies by using equal groups, arrays, area models, and equations; ensure the ability to represent multiplication in multiple ways; and understand how multiplication is related to division.

In fourth grade, students extend their knowledge of multiplication by solving problems involving multiplication of a number with up to four digits by a one-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.

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

use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

•

write an equation to express the total as a sum of equal addends.

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: •

determine how many party favors they have, using multiplication models (equal groups).

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. 114

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Equal Groups and Repeated Addition In this exploration, students will determine the total number of objects in a scenario by using equal groups. Students will: •

read a scenario and make a model of the problem with plates and counters.

•

write a descriptive sentence, and practice writing multiplication sentences.

Explore 2

Explore 1

EXPLORE ACTIVITIES

•

Explore 4

Explore 3

In this exploration, students will interpret products of whole numbers using diagrams to solve problems in scenarios. Students will: determine a strategy for ﬁnding the total number of windows in 9 houses without having to count them individually.

As students solve the scenario, they discuss their learning with the class and conclude with an Exit Ticket for assessment.

Explore 5

In this exploration, students will determine the total number of objects in a scenario by using arrays and area models as multiplication strategies. Students will: •

arrange grocery items according to the rules stated on Task Cards.

•

design game boards for USA Games, Inc.

After students have solved the scenario, the teacher guides students in color coding, sharing, and discussing ﬁndings; then, the activity ends with a discussion of their learning and an Exit Ticket.

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 their learning. Diagrams

Arrays and Area Models

MULTIPLICATION MODELS

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Number Lines and Skip Counting In this exploration, students will determine the total number of objects they have packed for their camping trip. Students will: •

represent multiplication problems using number lines and multiples.

•

skip count by twos.

After students have solved the scenario, they share and discuss their ﬁndings; then, their learning is assessed via an Exit Ticket.

Equalities In this exploration, students will use the meaning of the equal sign to represent expressions involving addition, subtraction, and multiplication to ﬁnd equivalent representations of various scenarios. Students will: •

read each problem to analyze the Receipt Cards to ﬁnd the ones that match.

•

build a model that matches each receipt.

After solving the scenario, students discuss their learning with the class, complete an Exit Ticket for assessment; then, revisit the Hook to solve.

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MULTIPLICATION MODELS

Multiplication Models 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 use addition to ﬁnd the total number of objects arranged in an array and write an equation to express the total as a sum of equal addends. Students are expected to model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined. This activity is intended to assess mastery of the following standard(s): 2.NR.3.2 Use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Materials

Preparation

Printed •

MULTIPLICATION MODELS

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•

1 Student Handout (per student, per group, or per class)

Print a Student Handout for each student or group, or prepare to project the Student Handout for the class.

Slideshow

Procedure and Facilitation Points 1. 2. 3.

Distribute the Student Handout, or project it for the class. Have students read the four students’ responses. With partners, groups, or the whole class, facilitate a discussion about which number sentence is correct. 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. a.

Riya is not correct. There are more than two groups of four.

Gabriel is not correct. There are three groups, but each one has four, not three.

Noa is not correct. There are only four groups of three, not ﬁve groups of three.

Isaac is correct. There are three equal groups of four cookies.

FACILITATION TIP Allow students time to read and make sense of the statements individually before placing them in pairs. This gives students a chance to think things through and experience productive struggle before expressing their ideas and opinions with others. FACILITATION TIP Ask students to stand up if they agree with each student’s statement. Then, invite students to justify their reasoning in relation to the array.

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

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MULTIPLICATION MODELS

Multiplication Models Hook – Party Favors ACTIVITY PREPARATION Students determine how many party favors they have, using multiplication models (equal groups).

Materials

Preparation

Printed •

• •

1 Party Favors (per class)

Reusable • • •

•

1 Phenomena Video (per class) 1 Projector or document camera (per class) 21 Sandwich bags (per class)

Plan to show the Phenomena Video. Print one Party Favors. Cut out each item. Put similar items together in the same bag. Write how many items are in each bag, like you would ﬁnd on party favor packages you buy in a store. • • • •

•

Three fidget spinners in each of eight bags Six yo-yos in each of four bags Eight finger lights in each of four bags Five pairs of sunglasses in each of five bags

Prepare to project Party Favors.

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

2. FACILITATION TIP Provide students with a dry-erase board or sticky notes so they can draw the scenario while they listen. Help students notice that these numbers are written as words; this style may be new for some students. Carefully reading math stories includes looking for both number form and word form for values. 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.

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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? Where can you see math in this scenario? Allow students to share all ideas. Read the following scenario to the class: You are planning a birthday party, and you picked out a bunch of party favors to give to friends. You have eight bags with three fidget spinners each. You have four bags with six yo-yos each. You have four bags with eight finger lights each. You have five bags with five pairs of sunglasses each. How many of each type of favor do you have? Discuss the following questions with the class: a. DOK-2 What information would we need to know to determine how many party favors we have? We would need to see how many party favors are in each bag and how many bags of each party favor we have.

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 situation. Discuss the following questions with the class: a. DOK-2 What information would we need to know to determine how many party favors we have? We would need to see how many party favors are in each bag and how many bags of each party favor we have.

3. 4.

Review the problem and split students into four groups. Give each group all the bags with similar party favors (8 bags of ﬁdget spinners, 4 bags of yo-yos, 4 bags of ﬁnger lights, and 5 bags of sunglasses). © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions with the class: a. DOK-1 How did you ﬁnd how many party favors your group had? We counted that we had 4 bags of yo-yos. We also saw that each of the bags had 6 yo-yos in it. So, we knew we had 4 groups of 6; 6 + 6 + 6 + 6 = 24. We also knew that 4 × 6 = 24. So, we had 24 yo-yos in all. b.

DOK-2 Did anyone else ﬁnd the number of party favors they had in another way? We saw that we had 5 bags of sunglasses and 5 sunglasses in each bag. So, we counted by multiples by counting like this: 5, 10, 15, 20, 25. We knew that 5 × 5 = 25. Have each group explain to the class how many favors they had and discuss how they found their total.

d. DOK-3 Can you think of a real-world situation or context where you would need to ﬁnd the total number by using equal groups? If I want to know how many markers are in our class, I could count how many boxes we have and how many markers are in each box. If I wanted to know how many baseball cards I bought, I could count how many packs I bought and how many cards are in each pack.

FACILITATION TIP If students added, guide them to ﬁnd an easier way to count, such as skip counting. Skip counting is a scaffold that can be used prior to writing a multiplication equation. FACILITATION TIP Consider displaying a visual of each bag and having students provide the total number. Then, write the equation under the visuals.

MULTIPLICATION MODELS

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FACILITATION TIP Challenge each group to brainstorm as many real-world situations for ﬁnding the total number for equal groups as they can.

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MULTIPLICATION MODELS

Multiplication Models Explore 1 – Equal Groups and Repeated Addition ACTIVITY PREPARATION Students determine the total number of objects in a scenario by using equal groups.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • • •

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

Reusable • • • • •

• •

2–3 Sets of two-color counters (per class) 1 Dry-erase marker (per student) 1 Dry-erase eraser (per student) 1 Dry-erase board (per student) 1 Projector (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. Print, cut apart, and laminate (optional) a set of Scenario Cards for the class. Set up 6 stations around the classroom. Place 9 paper plates and 50 counters at each station. Gather a dry-erase marker, eraser, and board for each student. For students who need more support in recalling information, please see our Base Tens 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. (Two-Color Counters)

Consumable •

9 Small paper plates (per station)

PROCEDURE AND FACILITATION 1. FACILITATION TIP

Time students as they count individually. Next, time students as they skip count. Finally, challenge students to use multiplication. Ask students which method was the fastest.

3. 4.

Begin by projecting counters in a few groups with an equal number of counters in each group (for example, four groups of three counters). DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means. Answers will vary. We see four groups. Each group has three counters. All groups are equal. If we add all the counters together, we can get 12 counters. Distribute dry-erase markers, boards, and erasers to students. Ask students to write a sentence on the dry-erase board that describes what they see and share their sentences. Emphasize how each time a group is added, the total increases by the same number. a. DOK-1 What mathematical operation does your sentence represent? Multiplication or addition b.

FACILITATION TIP Direct students’ attention to the fact that the number in each group and the number of groups is translated into an equation such as 3 × 4. 120

Follow the students’ lead, and write a multiplication symbol down. Pose the question, “What does this symbol represent?” It represents “times,” “multiplied by,” “multiplication,” “repeated addition,” and “equal groups of.”

DOK-2 Have students look back at the model. Ask students, “How could you describe the model using the phrase groups of of?” ?” Have students share their ideas. You should emphasize the student response that means “three groups of four.” Show how “three groups of four” can be written as 3 × 4. © Accelerate Learning Inc. - All Rights Reserved

8. 9.

10.

Engage

Explore

Explain

Elaborate

Evaluate

Repeat this three more times with different equal groups (2 × 3, 8 × 9, 6 × 6). For each new group of counters, ask students to write the following on their desks using the dry-erase marker: a.

Sketch the model of equal groups on the screen.

Write a repeated addition sentence (for example, 3 + 3).

Write it in word form, using “groups of” (for example, two groups of three).

Translate that into a multiplication sentence (for example, 2 × 3).

Distribute paper plates and counters to each group and a Student Journal to each student. Explain to students that at each station, they should read a scenario, make a model of the problem with plates and counters, write a descriptive sentence, and practice writing multiplication sentences. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 How many equal groups are there? How many are in each group? Answers will vary depending on the scenario. b.

11.

DOK-1 How can you say it using “groups of”? Answers will vary depending on the scenario.

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

Math Chat DOK-1 What is multiplication? Multiplication is when there are equal groups being joined together to make a greater number. • DOK-2 Why use multiplication? The reason why we use multiplication is because it is a lot faster than adding the numbers one by one or counting individually. • DOK-2 What are some ways we can model and solve a multiplication sentence? We can use equal groups. • DOK-2 How are the models and multiplication sentences related? The models directly represent the numbers being multiplied. If there are 2 groups with 5 counters in each group, the number 5 is being multiplied by 2. This translates into multiplication because the × sign represents “groups of.” This means that every time an amount appears, that represents 1 group. So if the number 5 appears 2 times, this means there are 2 groups of 5, which is written “2 × 5 = 10” as a multiplication sentence.

Intervention

Acceleration

FACILITATION TIP Post the steps on the board for students to follow for each example. The process will help students understand what the multiplication sentence represents.

MULTIPLICATION MODELS

Home

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.

•

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 Emphasize that words like “of” and “by” in between two numbers in a scenario often means multiply. Show some real-world examples: holiday treat bags with equal amounts, packaging of products, seats at the cafeteria tables.

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MULTIPLICATION MODELS

Multiplication Models Explore 2 – Arrays and Area Models ACTIVITY PREPARATION Students determine the total number of objects in a scenario by using arrays and area models as multiplication strategies.

Standards for Mathematical Practice • • •

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 Grocery Item Cards (per class) 1 Set of Game Board Requests (per group) 1 Exit Ticket (per student)

Reusable • • • • •

50 Colored tiles (per group) 1 Die (per group) 1 Resealable bag (per group) 4 Trays or plastic bins (per class) 1 Projector (per class, optional)

Preparation • • •

• • •

•

Plan to divide the class into groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Grocery Item Cards (preferably in color) on card stock. Cut and sort the Grocery Item Cards, and place them on trays or in plastic bins. Create 4 stations around the room with a tray or bin at each station. Each station should have all of the cards with the same grocery item (for example, all of the cupcakes at one station, all of the eggs at the next station, etc.). Print out a set of Game Board Requests for each group. Gather 50 colored tiles, and place them in a resealable bag for each group. For students who need more support in recalling information, please see our Multiplication Array 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. (Colored Tiles)

PROCEDURE AND FACILITATION Part I: Grocery Store Stocking (Arrays) 1.

FACILITATION TIP Some students may need help aligning their arrays as they draw them. Consider distributing boldly printed small grid paper for them to place under their Student Journal to show through.

FACILITATION TIP

Have students circle the criteria for each grocery item on their Student Journals. Students can then draw a model and translate it into an equation. FACILITATION TIP Monitor students as they make their models to ensure that the groups are equal. Students may label the model’s rows and columns with numbers. 122

3. 4.

Read the following scenario to the class: Close your eyes and imagine shopping in a grocery store. Think about how different items are displayed. Grocery stores place their inventory in rows on shelves based on how much space they have and how many items they have. Today, you will act as shelf-stocking experts as we go from station to station completing each stocking challenge. Tell students that there are grocery items around the room that need to be arranged according to the rules stated on their Student Journals. Give a Student Journal to each student. Explain that students will have a few minutes at each station to arrange the Grocery Item Cards based on the criteria listed on their Student Journals. Students should record how they arranged the Grocery Item Cards and answer the questions on their Student Journals for each station. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 What is the number of rows and columns you need to try to make, according to the challenge? Answers will vary depending on the item. b.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 How could you ﬁnd the total number of items? I could skip count by the number of items in each row. I could use multiplication because I have __ rows with ___ in each row. DOK-1 What do you call a model of equal rows of items? It is called an array.

Part II: USA Games, Inc. (Area Models) 1.

2. 3. 4.

Explain to students that they are now designing game boards for USA Games, Inc. Each game board request gives speciﬁc instructions on what the company wants students to build. Distribute colored tiles and Game Board Requests to each group. Students should build each game board requested and record their work on their Student Journals. Discuss the following questions: a. DOK-1 Do these models remind you of anything? Yes! These look like arrays, but they are squares pushed together.

DOK-2 Where do you see equal groups in the models we just built? Each row has the same number of items.

DOK-1 How could you ﬁnd the total number of items? I could skip count by the number of items in each row. I could use multiplication, because I have __ rows with ___ in each row.

DOK-1 What do we call a model of equal rows of squares that cover a space? It is called an area model.

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

Intervention

Acceleration

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.

MULTIPLICATION MODELS

Home

FACILITATION TIP Project different images of game boards, and ask students about the number in the length and the width.

FACILITATION TIP Use Picture Vocabulary to reveal the terms area model, array, factors, and product.

Math Chat DOK-2 How did you translate the array or area model into a multiplication equation? The number of rows in the model gave me my ﬁrst factor because each row is one group. The number of items in each row gave me my other factor because there is the same number of items in each row. The total number of items was the product. • DOK-2 How are the arrays, area models, and repeated-addition models similar? In repeated addition, area models, and arrays, one factor is being added over and over. Each row has the same number of items, and in repeated addition, each addend increases the sum by an equal amount each time. • DOK-2 How are arrays and area models similar to other multiplication models? Arrays are very similar to equal groups. Each row can represent a group with the same number of items in each one. In an equal-groups model, you don’t line them up, but each group contains an equal number of objects. •

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 If time allows, consider showing students an array model with square tiles. Also, many students may use plastic interlocking bricks that are made of arrays. FACILITATION TIP This Exit Ticket can be used both as a preand post-assessment.

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Multiplication Models Explore 3 – Diagrams ACTIVITY PREPARATION Students interpret products of whole numbers using diagrams to solve problems in scenarios.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • • •

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

Reusable • • • •

• •

1 Dry-erase board (per pair) 1 Dry-erase marker (per pair) 1 Dry-erase eraser (per pair) 1 Set of linking cubes (per pair)

•

Consumable •

1 Resealable bag or envelope (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 set of Scenario Cards for each pair of students. Cut apart the Scenario Cards, and place them in a resealable bag or envelope for each pair of students. Prepare dry-erase materials and linking cubes for each pair. For students who need more support in recalling information, please see our Multiplication Array and Grid Paper 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. (Linking Cubes)

PROCEDURE AND FACILITATION Part I: Linking Cubes 1.

FACILITATION TIP In Part 1, linking cubes are used to create a model to skip count like a tape diagram. In Part 2, students will create a tape diagram for different scenarios.

2. 3.

4. 5.

124

Read the following scenario to the class: On your way to school this morning, you counted 9 houses on your neighborhood street. You noticed that every single house has exactly 6 windows. You started to think you could probably make some money washing windows in your neighborhood. You wished you could ﬁgure out a way to see how many windows there are in all without having to count them individually. Challenge students to turn and talk to a partner to describe different ways they can represent the total number of windows that could be washed. DOK-2 Invite students to share. Student answers may vary. We can multiply the number of windows per house by the number of houses using arrays, area models, equal groups, in words using “groups of,” multiplication sentences, and real-world word problems. Distribute dry-erase boards, markers, and erasers and linking cubes to each pair. Challenge students to discuss with their partners a strategy for ﬁnding the total number of windows in 9 houses without having to count them individually. a.

DOK-1 What do you need to ﬁnd? We need to ﬁnd the total number of windows.

DOK-2 If each linking cube represents 1 house, what else would we need to do to represent the problem? We still need to represent the 6 windows; we could write 6 on each cube to make 9 groups of 6. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

DOK-1 How did you calculate the total number of windows? Each of the houses has 6 windows, so we wrote a 6 on each cube. We skip counted by 6 because we now had 9 groups of 6.

Challenge pairs to draw their models and discuss observations. a.

7. 8.

Engage

DOK-2 What observations can you make about your drawing? This drawing uses a rectangle to show the parts of a total amount. It shows “groups of” in a rectangle. The groups or parts of the rectangle that are the same size represent the same value. It helps us write an equation.

Explain that the rectangular models drawn are called “diagrams.” DOK-1 How does a diagram represent an equation? 6

Part II: Diagrams

3. 4.

DOK-2 How does knowing the “groups of” help you draw your diagram? The number of groups is the number of sections in the diagram. The number in the sections represents the size of the group.

DOK-2 Why should parts of the diagram be the same size? If they represent the same value, they should be the same size.

DOK-1 How would you write the multiplication equation? Answers will vary. It will be the number of sections in the diagram times the number in each section of the rectangle.

DOK-1 What are the factors in the diagram? The factors are the number inside the rectangle and the number of sections in the rectangle.

e. DOK-1 How does the diagram help you ﬁnd the product? You can simply add all the factors in the diagram. You can skip count by the number in the rectangle until you get a product. You can multiply the factor in the diagram by the number of times you see it. You can write the multiplication fact and answer it if you know it.

FACILITATION TIP Reassure and encourage students about the importance of ﬂuency with these models. In later grades, the diagrams will be needed for more complex problems and will help them visualize and think through diﬃcult math scenarios. Model for students how to translate the linking cubes into a multiplication equation. Be sure to have students read the equation out loud.

Give a Student Journal to each student and a set of Scenario Cards to each pair. Explain to students that they should collaborate with their partners to use diagrams to solve 8 scenarios. Students should record their models and solutions on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

Acceleration

FACILITATION TIP

We see 6 nine times. We see 9 groups of 6. We can write 9 × 6 = 54. 1. 2.

Intervention

MULTIPLICATION MODELS

Home

FACILITATION TIP Have one student read the card to the group, another student write the important information from the card, and another student create the tape diagram. The group can work together to complete the equation and sentence.

FACILITATION TIP Reveal the term product, which means “the solution to a multiplication problem.”

If students have completed the Scenario Cards before classmates are done, challenge them to create their own word problems with their partners and have each other draw a diagram and multiplication sentence to match. After the Explore activity, invite the class to a Math Chat to share their observations and learning. Notes

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MULTIPLICATION MODELS

Multiplication Models Explore 3 – Diagrams Math Chat DOK-3 What situations are you noticing in these problems that tell you the operation is multiplication? We are asked for a total, which can imply multiplication. We are given the parts of the product we have to determine, and the parts represent equal-sized groups and the number of equal-sized groups there are. • DOK-2 How do diagrams compare to other multiplication models? Diagrams may look different from number lines, equal groups, and arrays, but they all represent equal groups being multiplied a certain number of times to result in a product. • DOK-2 Explain how the diagram model represents a multiplication equation. In a diagram, we have a number of equal sections that represent the number of groups in a problem. Within each of the equal sections there is the same number, which represents the second factor being multiplied or the number of objects in each group. •

FACILITATION TIP For this Exit Ticket, clarify your criteria for success and be sure you model it for students. The written responses for the questions require reading and writing skills that may still be emerging in some 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.

126

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MULTIPLICATION MODELS

Home

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MULTIPLICATION MODELS

Multiplication Models Explore 4 – Number Lines and Skip Counting ACTIVITY PREPARATION Students determine the total number of objects they have packed for their camping trip by representing multiplication problems using number lines and multiples.

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 Packing Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • • •

1 Meterstick (per group) 1 Dry-erase marker (per group) 1 Dry-erase board and eraser (per group, optional)

• •

Consumable • • •

•

1 Roll of packing tape (per group) 1 Manila envelope (per group) 1 Glue stick (per class)

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print each group of items from the Packing Cards on different-colored card stock. Cut and put a set of Packing Cards in a manila envelope for each group. Glue a camping backpack picture from the Packing Cards to the front of each envelope. Cover the front of the metersticks with packing tape to create an erasable surface. For students who need more support in recalling information, please see our Base Tens 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 Part I: Counting Equal Groups 1.

FACILITATION TIP

Guide students with questions about the topic to expand upon it. The topic could be shoes or another of your choosing.

5. 6.

128

DOK-1 Begin by asking students to look around the classroom and find equal groups of something. Ask students to share. Answers will vary. We noticed that every student in this class has two shoes on his or her feet. I see that each window has six panes. Each person’s hand has five fingers. Choose one of the students’ ideas to expand upon. The example below focuses on the number of shoes per student. Distribute a dry-erase marker, dry-erase board, dry-erase eraser, and meterstick covered by clear tape to each group. DOK-2 Ask students to draw a model of the number of shoes on four people. Ask students to share how they modeled the problem. We can make equal-groups models. If there were four students with two shoes each, we drew four circles with two dots in each circle. We could also draw an array of four rows with two columns in each row. DOK-1 Ask students to write down a multiplication equation for this problem and explain what the equation means. Share with the class. 4 × 2 = 8. This means there are four students, each with two shoes, meaning there are a total of eight shoes at this table. Divide the class in half, and have each half stand in a line across from each other. Have students figure out how many shoes there are on the other side of the classroom. Listen for the different strategies students used to figure out the total number of shoes. Listen specifically for skip counting. © Accelerate Learning Inc. - All Rights Reserved

9. 10.

11.

Engage

Explore

Explain

Elaborate

Evaluate

3. 4. 5. 6. 7.

Acceleration

DOK-1 Allow a few students to share how they found the total number of shoes. I counted each shoe. I counted by twos because each student has a set of two shoes. Ask the following questions: a.

DOK-1 What numbers would you say when you count by twos? I would say 2, 4, 6, 8, 10, and so on.

DOK-1 How many times did you count a group of two? Explain. I counted them eight times because there are eight students.

DOK-1 How many shoes are there? There are 16 shoes.

Tell the class that when we count by a certain number, it is called skip counting. Put students back in their groups, and have them use their metersticks as number lines and practice skip counting by twos. Students should use the dryerase markers to circle each number they say when they skip count by twos. Explain to students that the numbers circled are called “multiples.” Since they skip counted by two, each number they said was a multiple of two.

FACILITATION TIP Students will create a number line for the multiple. The number line will be used for the skip count and to create the multiplication equation. FACILITATION TIP

Part II: Camping Trip 1. 2.

Intervention

MULTIPLICATION MODELS

Home

Distribute a Student Journal to each student. Tell students that they are preparing for a big camping trip and that each group has begun packing a bag (show the envelopes). Explain that since they are staying for several days, they’ve gone shopping for some essentials, and those items come in packs. Tell students they will use the envelopes with Packing Cards to build a model and answer each problem on their Student Journals. Distribute the camping bag envelopes to each group. Challenge students to use the meterstick as a tool to ﬁnd the total number of different types of items. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How many packs are there? How many are in each pack? Answers will vary depending on the item.

DOK-2 How did you use the number line (meterstick) to model the packs of items? We skip counted by the number of items in each pack. We could skip count that number each time we had a pack. For example, each pack of Battery Buddies is a group of three batteries, so we jumped three numbers higher each time we counted a pack on the number line and skip counted by threes.

If students ﬁnish early, challenge students to skip count by different intervals.

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.

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

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MULTIPLICATION MODELS

Multiplication Models Explore 4 – Number Lines and Skip Counting Math Chat DOK-2 How can we show multiplication on a number line? The factors of a multiplication sentence tell us how many times we’re jumping (the ﬁrst factor tells us how many times a number is being repeated) and what number we’re jumping or skip counting by (the second factor). Each jump on the number line is like an equal group. • DOK-2 What is the relationship between equal jumps on a number line and skip counting? Every time you jump on a number line, you land on a multiple of the factor. You land on the numbers you would say if you were skip counting. • DOK-2 How are multiples of a number and repeated addition similar? Multiples are the numbers we land on when we go higher on a number line every time we jump by the same factor. In the same way, repeated addition adds the same number every time. •

FACILITATION TIP Take time to review all of the vocabulary related these patterns: factor, multiple, product, array, multiplication equation, and equal groups of. FACILITATION TIP On this Exit Ticket, clarify if students need to write a complete sentence on the last question.

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

130

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MULTIPLICATION MODELS

Home

__________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

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Multiplication Models Explore 5 – Equalities ACTIVITY PREPARATION Students use the meaning of the equal sign to represent expressions involving addition, subtraction, and multiplication to ﬁnd equivalent representations of various scenarios.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials Printed • • •

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

Reusable • • • • • • • •

1 Quart-size resealable bag (per group) 2–3 Sets of 50 two-color counters (per class) 2–3 Sets of 50 colored tiles (per class) 2–3 Sets of 10 linking cubes (per class) 2–3 Metersticks (per class) 1 Dry-erase marker (per group) 2 Chenille stems (per group) 1 Projector (per class, optional)

Consumable • •

4 Index cards (per class) 1 Roll of packing tape (per group)

Preparation • • •

• • • • • •

•

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. Print a set of Receipt Cards, on card stock for durability, for each group. Cut the cards apart on the dashed lines, and place them inside a quart-size resealable bag for each group. Gather a dry-erase marker and 2 chenille stems for each group, and place them inside the quart-size bag with the Receipt Cards. Use 4 index cards to label the multiplication model stations where students can represent their multiplication problems and tape them around the room. Station 1: Gather 2–3 sets of 50 two-color counters. Place these sets at the Equal Groups and Repeated Addition station. Station 2: Gather 2–3 sets of 50 colored tiles. Place these sets at the Arrays and Area Models station. Station 3: Gather 2–3 sets of 10 linking cubes. Place these sets at the Diagrams station. Station 4: Gather 2–3 metersticks and a roll of packing tape. Cover the front of the metersticks with packing tape to create an erasable surface. You can use the metersticks from Explore 4. Place these metersticks at the Number Lines and Skip Counting station. For students who need more support in recalling information, please see our Base Tens, Sharing Mats, Multiplication Array, Grid Paper, 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 in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Two-Color Counters, Color Tiles, Linking Cubes, and Number Lines)

PROCEDURE AND FACILITATION FACILITATION TIP Emphasize to students that doublechecking receipts is a commonly used life skill and is used by many workers. Engage students with some meaningful real-world stories.

132

2. 3.

Read the following scenario to the class: Springtime is almost here, which means it’s the best time to start a garden. You decide you would like to build some garden boxes in your backyard but you will need to buy some supplies. You notice that Garden World is offering coupons on some of the items you’d like to purchase. It’s important when purchasing your items to double-check your receipts and make sure the cashier scanned all of your items correctly and included the coupons. This way you can pay the correct amount of money. Give a Student Journal to each student. Divide students into groups, and give each group a bag containing Receipt Cards, a dry-erase marker, and 2 chenille stems. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

Explain to students that they will read each problem on their Student Journals as a group and analyze the Receipt Cards to find the ones that match the problem. Instruct the students to read the first problem and quickly analyze their Receipt Cards to find the two receipts that match the problem. Ask the following questions about what they notice about the problem and their Receipt Cards: a.

DOK-1 What do you notice about the information given in each problem? I notice that each problem explains how many garden items they bought, the cost of each item, and any coupon or discount they received for their purchase. This will help them determine the cost.

DOK-2 Do you think each problem can be solved in one step or two steps? Explain. I think we might need two steps because we ﬁrst need to determine the original cost and then subtract the coupon or discount.

DOK-1 How are the Receipt Cards similar to the information given in each problem? I notice that the Receipt Cards include the number of items bought and the cost of each item. Some Receipt Cards have the coupons listed as well.

DOK-1 What do you notice about the expression on the Receipt Cards? I notice that an expression can contain multiple numbers and one or more operations.

Explain to students that today they will work as a group to build a model that matches each receipt. Students need to prove that the two receipts they chose match the word problem and are equal expressions. a.

Encourage students to work together using any model station around the room that they think will help them represent the scenario and prove that the two expressions are equal in value.

Groups will use their chenille stems to represent the parenthesis in the expression so they can group their materials together. For example, at Station 2, students could model the expression (5 × 3) – 3 by using the colored tiles to make an array of 5 rows with 3 in each row and then put the chenille stems around the array like parentheses. Then, students would model taking away 3 to ﬁnd the value of 12.

Explain to students that they should be looking at equalities in order to create expressions and models that are equal. Tell students the equal symbol means “the same as.” They should determine whether the amount on one side of the equal symbol is the same as the amount on the other side of the equal symbol. If it is, the equation is true. If the amounts on either side of the equal symbol are not the same, the equation is false. If the equation is false, they will need to work with their groups to determine another expression that would make the equation true.

Engage

Intervention

Acceleration

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.

MULTIPLICATION MODELS

Home

FACILITATION TIP If “expression” is a new term for students, take time to use the Visual Glossary to demonstrate. Review equation and clarify the similarities and differences. In later grades, students will often be asked to write an expression or an equation.

FACILITATION TIP “Equalities” may be new term for students; take time to use the Visual Glossary to demonstrate. Review equalities vs inequalities and clarify the similarities and differences. In later grades, students will often be asked to write and read inequalities and create equalities.

Once the groups agree on their models and can determine that the value of each model is the same, they will record their work and ﬁndings on the correct table on their Student Journals.

Quickly discuss the following questions before students get started: a.

DOK-1 What strategies have we learned in order to solve multiplication problems? We can solve multiplication problems using number lines, diagrams, equal groups, and arrays/area models. DOK-3 How can the materials at each model station card around the room help your group create a model? Answers may vary. We can use the two-color counters and colored tiles to make equal groups or arrays. We can use the dry-erase markers and linking cubes to create diagrams. We can use the metersticks to create number lines.

FACILITATION TIP List these strategies for students to refer to as they collaborate.

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Multiplication Models Explore 5 – Equalities

FACILITATION TIP Remind students that they are learning to translate words into symbols. It is like using a new language. They may see the word “is” in a math scenario, and it can often be interpreted as “equals.”

DOK-1 What do you notice about the space between the two expressions on your Student Journal? I notice that there is an equal sign between the two expressions.

DOK-2 Why do you think that symbol is important? (This question is referring to the equal sign from the previous question.) The equal sign is important because it is stating that the two expressions are equal to each other in value.

Allow students enough time to complete their work for each problem and to record and explain their ﬁndings on their Student Journals. Students answer reﬂection questions after they have completed all of the work for their Receipt Cards. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What model do you think we can use in order to solve this problem? Answers will vary based on student preference. I think we should use the (equal group, array/area model, number line, diagram) strategy because _______ .

DOK-1 How many groups are being represented? What is the value of each group? Answers will vary based on the scenario. I noticed that there are 5 groups because I bought 5 bags of potting soil. I noticed that the value of each group is 3 because each bag cost $3.

DOK-2 How can you represent the value of the coupon? I know that a coupon takes away money, so I can subtract the value or multiple values of the coupon or take away a group from my model.

DOK-2 How can you represent the problem with an expression in a single step? The problem tells me how many items I had to pay for, so I can take that amount and multiply it by the value of each item to ﬁnd the amount of money I spent.

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.

e. DOK-2 How can you represent the problem with an expression that contains two steps? I can group my ﬁrst step involving multiplication with parentheses, and then, since I had a coupon, my second step is represented by subtracting the discount. I can check my Receipt Cards to ﬁnd an expression that matches my model. f.

10.

DOK-1 What does it mean if my values are the same? What does it mean if my values are different? If my values are the same, then I know that my equation is true. If my values are different, then I know that my equation is false and I need to ﬁnd another expression that represents the scenario and makes my equation true.

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

Math Chat DOK-2 Why is it important to determine the value of each expression in an equality? It is important to determine the value of each expression so you can determine if the equation is equal or unequal or true or false. • DOK-1 What can we determine if the expressions have different values? What can we determine if they have the same value? If the expressions have different values, then the equation or equality is false. If the expressions have the same value, then the equation or equality is true. • DOK-2 Why do both sides of an equality need to represent the same amount? An equation or equality needs to be balanced. The equal symbol means “the same as,” so the amount on the left needs to be the same as the amount on the right. •

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Post-Explore 1. 2. 3. 4.

FACILITATION TIP On this Exit Ticket, provide reading support for struggling students.

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

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Multiplication Models 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

Equal Groups and Repeated 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

Arrays and 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

Diagrams

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

Number Lines and Skip Counting

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

Show What You Know, Part 5 Equalities 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

Grocery Store Helpers

James Gosling

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

A Snowy Day

Multiplication within 100 – Models and Equations

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

The Math Project: Multiplication Poster

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

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Students who are still acquiring the concept and need remediation

MULTIPLICATION MODELS

Multiplication Models

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?

MULTIPLICATION MODELS

Home

I can solve multiplication problems and interpret products of single-digit numbers using a variety of strategies.

I can determine whether expressions are equivalent.

I can use the words product and factor to describe multiplication.

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SCOPE 1

Division Models Scope Introduction SCOPE SUMMARY

Student Expectations

3.PAR.3.2 Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.

Division problems may be presented in a variety of ways, including equal groups, arrays, diagrams, and repeated subtraction. Students need to interpret the quotient as an amount that can be partitioned into equal shares to ﬁnd the number of groups or that can be shared equally to ﬁnd the number of objects in each group. Students’ understanding of equal groups of objects in multiplication is a direct correlation to division. Ultimately, division is an unknown factor problem within a given context. Students learn different strategies and models to gain a conceptual understanding of division, providing an opportunity for them to be able to describe a context in which a number of objects in each group or a number of groups can be expressed. They build on their knowledge of multiplication by exploring the relationship between multiplication and division through related models and equations with a letter standing for the unknown in real-life scenarios.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students work with equal groups and arrange objects in rectangular arrays, and they write repeated addition equations to express the total as a sum of addends. In the prior scope, third graders continue working with equal groups to represent multiplication models by using the array and area models to build the relationship between addition and multiplication, forming a conceptual understanding. Students also explore other various multiplication models, such as diagrams and number lines. These offer students choices as to which multiplication model may work best for them. Experience with all these models prepares students to make connections between multiplication and division and how these types of models can be used for either operation.

In fourth grade, students will extend 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 will focus on illustrating and clearly explaining their calculations using equations and visual models, such as equal groups, arrays, area models, and partial quotients.

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

use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

•

write an equation to express the total as a sum of equal addends.

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 models to solve division problems.

•

determine how many cookies each friend will take home to share with their families.

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. 140

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Equal Groups and Shares In this exploration, students will explore division of objects through equal groups and sharing at a variety of stations. Students will: • •

Explore 2

Explore 1

EXPLORE ACTIVITIES

draw a picture of models created for each scenario about division. write an equation.

Explore 4

Explore 3

In this exploration, students will interpret solutions to partitive and quotative division problems using diagrams, repeated subtraction, and division. Students will:

Arrays In this exploration, students will interpret solutions to partitive and quotative division problems using array patterns. Students will: •

solve division problems using arrays.

•

write a division equation.

After students have solved the scenario, they will discuss their learning and complete an Exit Ticket.

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

Relate Multiplication and Division Equations In this exploration, students will explore the relationship between multiplication and division through models of real-life scenarios. Students will:

create a model to solve division problems using manipulatives.

•

create models that represent division problems related to a birthday party.

Once students have solved the scenario, they discuss their learning with the class and ﬁnish with an Exit Ticket.

•

use multiplication and division to solve problems.

•

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

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DIVISION MODELS

Division Models 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 set up an array and write a corresponding addition sentence with a given number of objects. This activity is intended to assess mastery of the following standard(s):

DIVISION MODELS

Home

2.NR.3.2 Use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Materials

Preparation

Printed •

•

1 Student Handout (per student, per group, or per class)

Print a Student Handout for each student or group, or prepare to project the Student Handout for the class.

Procedure and Facilitation Points 1.

Distribute a Student Handout to students, or read the scenario from the projected Student Handout.

Students create a number sentence to show the total number of cupcakes and balloons. Facilitate a discussion about the number sentence and equal groups. 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.

When I arranged the 12 cupcakes into 4 equal rows, I could put 3 cupcakes in each row. This is how I did it: I put 1 cupcake in each row, and I crossed off the 4 cupcakes as I drew them. Then, I added another cupcake to each row and crossed off the cupcakes as I drew them. I did it one more time, and all of the cupcakes were crossed off, so there were 3 cupcakes in each row.

I can see that 3 + 3 + 3 + 3 = 12 when I look at my array.

c. When I arranged 20 balloons into 5 equal columns, there were 4 balloons in each column. This is how I did it: I put 5 balloons across the top of my drawing and wrote a 5 out to the side. Then, I put 5 balloons under each of the ﬁrst 5. I wrote a 5 out to the side of that row. I know 5 + 5 = 10, so I kept going. I drew 5 more balloons, one in each column, and wrote a 5 beside the row. 5 + 5 + 5 = 15, so I kept going. I drew 5 more balloons, one in each column, and wrote a 5 beside the row. 5 + 5 + 5 + 5 = 20, so I knew I was ﬁnished. Kassandra’s mom bought 20 balloons. d. 4.

I wrote 4 + 4 + 4 + 4 + 4 = 20 for my number sentence because I see 5 columns with 4 balloons in each column.

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

FACILITATION TIP Point out that there are 2 possible arrangements for each example. There are two types of division problems: One is partitive division, whereby the quotient represents the number per group. The other is quotative division, whereby the quotient represents the number of groups. For the ﬁrst example, there could be 4 rows with 3 cupcakes in each row, or there could be 3 rows with 4 cupcakes in each row. For the second example, there could be 5 rows with 4 balloons in each row or 4 rows with 5 balloons in each row. FACILITATION TIP Precise language is important when communicating mathematical thinking. Take a moment to review the parts of an array. A row is arranged horizontally (left to right), and a column is arranged vertically (up and down). A row and a column can signify two different things in relation to a contextual problem. They could mean the number of groups or the amount per group. Discuss how the terms row and column relate to these contexts, and be consistent in word choice.

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Division Models Hook – Chocolate Chip Cookies and Friends ACTIVITY PREPARATION Students use models to solve division problems. They will determine how many cookies each friend will take home to share with their families.

Materials

Preparation

Printed •

•

1 Chocolate Chip Cookies and Friends (per group)

Reusable • • •

• •

1 Resealable bag (per group) 1 Phenomena Video (per class) 1 Projector or document camera (per class)

Print and cut out the Chocolate Chip Cookies and Friends pictures for each group. Put the 48 cookies in a bag for each group of students. Plan to show the Phenomena Video. Prepare to project Chocolate Chip Cookies and Friends.

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

FACILITATION TIP

Consider having students help divide a snack, stickers, or pencils equally. Ask, “How can we make sure all students get an equal share?”

a. DOK-1 What would we need to know in order to ﬁnd out how many cookies each friend would get? We would need to know how many cookies there are in 4 dozen. We also need to know how many friends are sharing the cookies.

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.

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DOK-2 How could you solve a problem like this? We could pass out the cookies one at a time to each friend until they are gone and the friends have equal cookies.

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 situation. Discuss the following questions with the class: a. DOK-1 What would we need to know in order to ﬁnd out how many cookies each friend would get? We would need to know how many cookies there are in 4 dozen. We also need to know how many friends are sharing the cookies.

FACILITATION TIP As students are discussing different strategies, write their ideas on the board. After the Explore activities, revisit the list and ask, “What is the easiest and the quickest strategy to divide the cookies equally?”

DOK-2 How could you solve a problem like this? We could pass out the cookies one at a time to each friend until they are gone and the friends have equal cookies.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions with the class: a. DOK-1 How many cookies are there to share equally among the friends? We counted them, and there are 48 cookies to share with our friends. b.

DOK-1 How many cookies would each friend get if you are sharing them with 8 friends equally? We made 8 piles and passed them out until there were no more. There were six cookies in each pile. So, each friend got 6 cookies each because 48 ÷ 8 = 6. We also used the multiplication sentence 8 × 6 = 48 to help ﬁnd the answer.

DOK-1 How many cookies would each friend get if you were sharing them among 6 friends? We knew it would be 8 cookies each. We used what we learned in the last problem to help us. We knew 48 ÷ 8 = 6, so 48 ÷ 6 must equal 8. We knew that because 6 × 8 = 48.

DIVISION MODELS

Home

FACILITATION TIP Challenge students with different numbers of groups, such as 2 friends, 4 friends, and 12 friends.

DOK-2 What did you notice about the amount of cookies each friend got when there were a different number of friends? The more friends there were, the fewer cookies they got.

e. DOK-3 Can you think of another real-world situation or context where you will share things equally? I might need to share pieces of candy equally between myself and my sister. You could also share construction paper equally with the other students at your table. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Division Models Explore 1 – Equal Groups and Shares ACTIVITY PREPARATION Students explore division of objects through equal groups and sharing at a variety of stations.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials Printed • • •

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

Reusable • •

9 Small paper plates (per group) 1 Set of counters, such as linking cubes, pom-poms, beans, or beads (per group)

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 one set of Scenario Cards, and cut them out. The activity is conducted in stations, so one scenario should be at each station. Scenario 1 is done as a whole group at the beginning of the lesson. Prepare small paper plates and counting objects (linking cubes, pom-poms, beans, or beads) for each station. For students who need more support in recalling information, please see our Base Tens 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. (Linking Cubes, Color Tiles, and Two-Color Counters)

PROCEDURE AND FACILITATION

FACILITATION TIP Students can work with manipulatives or the Virtual Manipulative – Color Tiles to model and solve the problem. FACILITATION TIP Model the ﬁrst scenario as students read along and identify the information needed to solve the problem.

1. 2. 3.

Give a Student Journal to each student. Instruct students to use the provided materials to solve different problems by modeling what is happening in the problems. Work through scenario 1 as a whole group. Read the following scenario to the class: Mrs. Lopez is making 40 mini-cupcakes for her after-school club. She has 8 students in her after-school club. How many mini-cupcakes can each student have? Ask students to discuss the following questions with their groups and then share: a. DOK-1 What information do we know? There are 40 cupcakes. There are 8 students in the club. b.

Give students 3–5 minutes to try to solve this problem with their group members. They use the provided materials to model what is happening and show their thinking. Actively monitor groups while they work. a.

DOK-1 What do we need to ﬁnd out? We need to ﬁnd how many cupcakes each student can get.

Note that students may make the mistake of trying to make 8 groups of 40 or vice versa. Students won’t have enough manipulatives to do this. Guide students with misconceptions with the student discussion to lead them back to the right track.

Invite groups to share their solutions. Discuss the following questions: a. DOK-1 What did your plates represent? They represented the number of students. Each student was like a “group.”

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Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What did your counting objects (cubes, pom-poms, beans, or beads) represent? Each piece represented a cupcake.

DOK-1 What did you do with the total number of cupcakes? We shared them. We divided them up. We distributed one cupcake to each plate over and over until the 40 cupcakes were gone.

DOK-1 What is another word we could use to describe how you divided up the cupcakes? We could use the word sharing.

Intervention

Acceleration

DIVISION MODELS

Home

e. DOK-1 How many cupcakes can each student get? How do you know? Each student can get 5 cupcakes because we shared the 40 cupcakes evenly between the 8 students, and there were 5 on each plate at the end. f.

8. 9.

DOK-2 Look at your model again. Does this model make you think of another math operation? Students might say it looks like multiplication. Explain your reasoning. It looks like multiplication because there are groups with the same number of objects in each group. DOK-1 How could we check our division work by using multiplication? We could multiply the number of groups by the number of objects in each group and see if it gives us the total we started with. Have students do this and see if they get an answer of 40.

FACILITATION TIP Consider leading a discussion about how addition and subtraction are opposite math operations. Multiplication and division are also opposite operations.

Have students complete the Station 1 section on their Student Journals. They draw a picture of the model they created with their materials and need to write an equation. Work through how to write an equation as a whole group. Discuss the following questions: a. DOK-1 How many cupcakes did we start with? We started with 40. b.

The total in a division problem is called a “dividend.”

Division problems begin with the total number that is to be shared equally. (Show students how to ﬁll this in on the equation portion of Station 1 on their Student Journals.)

DOK-1 How many groups did we have, and what did each group represent from the scenario? We had eight groups, and they represented the number of students. This number (either the number of groups or how many are in each group) is called the “divisor.” The divisor is the number you are dividing the total by. (Show students how to ﬁll this in on the equation portion of Station 1 on their Student Journals.)

e. DOK-1 How many cupcakes did each student get? Each student got ﬁve cupcakes. This is the number of objects in each group. This number (either how many are in each group or the number of groups) is called the “quotient.” The quotient is the answer to a division problem. (Show students how to ﬁll this in on the equation portion of Station 1 on their Student Journals.) f.

10.

11.

DOK-3 Is there a way we could change the question in this scenario to ﬁnd the number of groups instead of the number of objects in each group? We could change what we are looking for by making the scenario like this: There were 40 cupcakes, and each student in her after-school club got 5 cupcakes. How many students were in Mrs. Lopez’s after-school club? I would put 5 objects on each plate until there were no more objects left. This would tell me how many groups, or students, there were.

FACILITATION TIP Model for students on the board how to ﬁll in the equation portion. Have students say the terms dividend, divisor, and quotient in chorus as the equation is being written.

FACILITATION TIP Model for students how the divisor in the equation can be changed to determine the number of groups. Use manipulatives to assist students.

Students rotate through the remaining ﬁve stations with their groups. They read the new scenario at each station, use the provided materials to make a model, and complete the portion of their Student Journals for that station. Assign each group to a station at which to begin the rotation. Have the class come back together as a whole group to discuss the activity.

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Division Models Explore 1 – Equal Groups and Shares 12.

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

Math Chat • 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.

•

FACILITATION TIP On this Exit Ticket, take time to read the scenario and reassure students that they can use any method to solve. Encourage students to wait to start coloring (it can be hard to erase colors) until after they have a solution in mind. They should use a regular pencil to circle groups, use tally marks, use mental math, or any other method to solve before they ﬁll in the colors.

DOK-2 What did you notice about what was happening in the scenarios? The scenarios were dealing with people who needed to take a large number of items and divide or share them equally with other people or groups. DOK-2 What process did you use to divide the totals into their groups? We gave one to each group at a time until all the pieces were given out. We knew how many to put in each group to equal the total because we know our multiplication facts. DOK-3 How did you know if the scenario was asking for the number of objects in each group rather than the number of groups? If the scenario told me how many groups there were, I looked to see how many objects were in each group. I shared the objects between the groups, or plates, until there were no more left. This told me how many objects were in each group. DOK-2 What did you do if the scenario was asking for the number of groups instead of objects in each group? Explain how you did it. If the scenario was putting objects together in sets, then I determined how many groups were needed. I put the objects in sets on a plate until all the objects were grouped and placed on a separate plate. The number of plates used told me how many groups were needed. DOK-2 Do you think that what you’re doing is related to addition or subtraction? How do you know? I think it is related to subtraction because you start with a total amount, and you’re looking for part of the total. DOK-1 Now that you have had some practice, what is division, in your own words? Student answers may vary but should include something along the lines of the following: to take a total amount and share it equally between a number of 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.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

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Division Models Explore 2 – Arrays ACTIVITY PREPARATION Students interpret solutions to partitive and quotative division problems using array patterns.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials Printed • • •

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

Reusable •

Preparation • • • • •

1 Set of counters (per group) •

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print, cut, and laminate (if desired for long-term use) a set of Array Scenario Cards for each group of students. Prepare a set of counters for each group. For students who need more support in recalling information, please see our Multiplication Array 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 1. 2. FACILITATION TIP

For many students, building the array models for each scenario is a scaffold to create the division equation.

FACILITATION TIP

As groups read the scenarios, provide sticky notes or circle the information required to solve the problem.

FACILITATION TIP Project the sentence stem for students to discuss: “The number __ in problem __ represents _________.”

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6. 7.

Give a Student Journal to each student. Divide the class into groups, and distribute the Array Scenario Cards and counters to each group. Instruct students that today they will collaborate with their groups to solve division problems using arrays. Encourage students to use manipulatives to create the arrays and discuss how the arrays would translate to equations. Challenge students to think about what they are ﬁnding: the number of items in each group or the number of groups. Give students enough time to complete the Array Scenario Cards and record their thinking on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 How does the array or area model help you write a division equation? The total is the dividend. The number of rows or the number in each row is the divisor. The number in each column gives us the quotient. b.

DOK-1 What does the number ____ in problem ____ represent? How do you know? The number of rows because in the problem it states that the items were put in __ number of rows. Because when we grouped the dividend into groups of ___, there were ____ rows made.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

Math Chat DOK-1 How does the array model help you write a division sentence? The total is the dividend. The number of rows or the number in each row is the divisor. The number in each column gives us the quotient. • DOK-2 How does this model connect to multiplication? It shows the factors and the product. The number of rows and the number in each row are the factors. The total is the product. • DOK-2 How can using multiplication help us with division? We can use the multiplication fact with an unknown factor to help us solve the division problem. •

FACILITATION TIP

DIVISION MODELS

Home

Take time during this Math Chat to review dividend, divisor, quotient, factor, multiple, and product. These terms are essential for comprehension later math standards.

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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Division Models Explore 3 – Diagrams and Repeated Subtraction ACTIVITY PREPARATION Students interpret solutions to partitive and quotative division problems using diagrams, repeated subtraction, and division.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • •

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

• •

Reusable • •

24 Snap cubes (per pair) Additional snap cubes (as needed 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 one set of Task Cards per pair, cut the cards, and laminate them, if desired, for long-term use. Prepare sets of 24 snap cubes for each pair of students. Have additional snap cubes available for students to access as needed. For students who need more support in recalling information, please see our Multiplication Array 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. (Linking Cubes)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP As pairs read the cards, they should identify whether they are determining the objects or groups. Provide students with a sentence stem such as the following: “I think we are ﬁnding the number of (groups/items) because the card says ___________________.”). FACILITATION TIP A variety of strategies can be applied. Pairs can share their strategies after they have completed several of the Task Cards. Students may adjust their strategies.

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2. 3. 4.

5. 6.

Read the following scenario to the class: Mrs. Flowers takes great care in preparing specific art lessons for each of the grade levels that comes to her class. The kids always love how fun and different each lesson is. However, there is a lot of prep work that needs to be done before the students come so that she is ready! Can you help? Divide the class into pairs, and distribute the Student Journals, Task Cards, and snap cubes. Ask pairs to look at Task Card A and then read it as a class. DOK-1 Encourage student pairs to discuss what information they know and what information they have to find out in order to help Mrs. Flowers prepare. We know there are a total of 20 crayons, and Mrs. Flowers needs to put 4 in each bag for her students. We need to find how many bags she’ll make. Challenge the students to use the snap cubes to represent the information. DOK-2 Invite students to share their strategies out loud. Strategies may vary. a.

Let each cube represent 4 crayons. Connect unit cubes as you skip count by 4s until they form a train that represents 20 crayons. Since 5 snap cubes are needed, Mrs. Flowers needs 5 crayon bags.

Form one train of 20 cubes. Break off 4 at a time to represent the number of crayons in each bag. Continue this process until all the snap cubes are removed. Since there are 5 sets of 4 crayons, 5 bags are needed. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

As a class, determine what a drawn model would look like and why. See the example below:

8. 9. 10.

Explain that these models are diagrams. Encourage students to record their ﬁndings on their Student Journals. DOK-2 Ask students to explain how the snap cube model is similar to the diagram. Diagrams and explanations will vary. Responses may vary. a.

11.

14.

The entire diagram represents all 20 crayons. Partition the diagram into 20 equal sections. Every 4 sections represent one bag. Put boxes around every 4 sections. There are 5 sections of 4 within the whole diagram, which means there are 5 bags.

Intervention

Acceleration

FACILITATION TIP Illustrate a tape diagram for a multiplication problem, and point out its similarity to a tape diagram for a division problem. 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.

Since each bag contains 4 crayons, subtract 4 from 20, and continue this process 5 times, until all crayons are removed. Divide all 20 crayons by 4 crayons shared per group to determine that 5 bags are needed.

Have students mix up the cards and place them facedown. Explain that students take turns to draw and read each Task Card. Students collaborate to solve the problems and record the solutions on their Student Journals. As students work, ensure they are representing each problem accurately. a.

15.

The entire diagram represents all 20 crayons. Since each cube represents 4 crayons and there are 5 groups, partition the whole diagram into 5 equal sections. Each section represents a bag of crayons. 4 crayons × 5 bags = 20 crayons total, and 20 total crayons ÷ 4 crayons per bag = 5 bags.

DOK-3 Ask students how subtraction and division relate to this task. Responses may vary. a.

12. 13.

Evaluate

DIVISION MODELS

Home

DOK-1 If students have difficulty getting started, ask the following question: Do you know the number of groups or the number of items within a group? This varies from problem to problem. If students have difficulty creating the diagram, remind them that the entire diagram represents all the items, and suggest that they try modeling the problem using snap cubes first.

FACILITATION TIP Model for students how to record solutions on their Student Journal. Take time to demonstrate how to list the steps for repeated subtraction accurately. FACILITATION TIP Some students may beneﬁt from the Supplemental Aids in the Intervention Section or the Virtual Manipulatives in the Explore section.

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

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DIVISION MODELS

Division Models Explore 3 – Diagrams and Repeated Subtraction Math Chat DOK-2 When dividing, how do you know which numbers to use? When you divide, you are equally sharing a whole group of items. Sometimes you know the number of equal groups, while other times you know the number of items within each equal-sized group. You can divide the total number by the number of groups to determine the number of items per group, or you can divide the total number by the number of items per group to determine the number of groups. • DOK-1 How does a diagram represent division? The entire diagram represents the total number of items within groups. The diagram is partitioned into equal-sized groups. Each group has a value that represents the number of items within each group. If the number of groups is known, mark the sections ﬁrst. Then, determine the value of each unit within the total number. If the number of items within each group is known, skip count by that number, keep track of how many times it takes to reach the total number, and then form equal groups. • DOK-3 How can subtraction help with division? You can repeatedly subtract the number of groups or the number of items from the total number (keeping track of how many times it takes) to determine the quotient. •

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.

Post-Explore FACILITATION TIP When you preview this Exit Ticket with students, be aware that it shows repeated subtraction of the number of groups (rather than students per group). Struggling students may need clariﬁcation, and other students may need to be challenged to show how to solve it another way.

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

Notes __________________________________________________________________________________________________________________________________________________

DIVISION MODELS

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Division Models Explore 4 – Relate Multiplication and Division Equations ACTIVITY PREPARATION Students explore the relationship between multiplication and division through models of real-life scenarios.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • • •

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

Reusable •

• • •

•

1 Set of counters, such as tiles, linking cubes, beans, beads, etc. (per pair) 9 Small paper plates (per pair) 1 Dry-erase board (per pair) 1 Dry-erase marker (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 and cut out a set of Task Cards for each pair. Prepare a dry-erase board, dry-erase marker, paper plates, and counters for each pair. For students who need more support in recalling information, please see our Base Tens and Sharing Mats 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. (Linking Cubes, Color Tiles, and Two-Color Counters)

PROCEDURE AND FACILITATION 1.

2. 3. FACILITATION TIP

Monitor pairs and intervene as needed with individual students. Check for and address common misconceptions.

5. 6.

Read the following scenario to the class: It’s party time! You are hosting your ninth birthday party at a trampoline park. You need to determine how many tables to reserve, how many pizzas to order, how many pairs of socks are needed for your guests, and how many balloons you will need to buy to decorate! Read each Task Card to ﬁgure out the quotient, and answer the questions that follow. Give a Student Journal to each student. Provide each pair with a set of counting objects and 9 small paper plates. Give them a moment to discover the materials and how they relate to the scenario you just shared. Instruct students to use counters and plates to create models that represent their division problems and how they relate to what they know about multiplication to help them determine the answers to division problems. Have students use the plates to represent the groups and the counters to represent the number of objects in a group according to the scenario. Have students complete their Student Journals in pairs. a.

FACILITATION TIP Project a division equation on the board with labeled parts for student reference.

Challenge students to use the language that helps them understand the division sentence when completing their Student Journals. Are they using the terms dividend, divisor dividend divisor, and quotient correctly? Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

156

Students may use the provided manipulatives to create their models.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 How can you turn your division equation into a multiplication equation? The product is the dividend in a division equation. The factors are determined by the divisor and dividends.

DOK-1 How do you know? The same equal groups are being made, but the processes are different for multiplication and division.

DOK-1 Where are you going to put the unknown amount in your equation? How should you represent it? The unknown will depend on the missing information. If we are missing information about the equal groups, the missing information will be in the quotient or divisor in a division equation or one of the factors for a multiplication equation. If we are missing a total amount being either distributed or joined, the unknown will be the dividend for division and the product for multiplication.

e. DOK-2 How does using multiplication make division easier? I know my multiplication facts pretty well. I am not as good at my division facts yet. I could think of a missing factor to help me divide. For example, if I was trying to divide 45 ÷ 9, I could think of a multiplication fact to help me. I can think, “9 times what would give me a product of 45? I know 9 × 5 = 45, so 45 ÷ 9 = 5.” 9.

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

Math Chat •

•

DOK-1 What happens when you divide? When you divide, you are equally sharing a total. When you divide, you are decomposing a total into equal groups or finding the number of groups needed. DOK-2 How did you know if you were finding the objects in each group or finding the number of groups needed? If I put counters on each plate one by one until they were all gone, I was finding the number of objects in each group. If I put counters together in sets and then placed them on plates until there were no more sets, then I found the number of groups needed. DOK-1 When we divide, are we looking for a total amount? No, we are not looking for the total amount because the total is given in division. We are looking for the number of groups or the number of objects in each group. DOK-1 How did you determine the number to begin the division equation? In division, we always start with the total because the total will be separated into equal groups. This is called the “dividend.” DOK-1 In addition and subtraction, there are fact families. Is this the same in multiplication and division? Yes, just as addition and subtraction use the same three numbers to make the four facts, so do multiplication and division. DOK-2 How can recalling multiplication facts help with division? Being able to recall multiplication facts will help me relate the division facts. I can think, “How many would I need in each group to make the total?” or “What number times the number of groups will provide the total I began with?” DOK-2 What is the relationship between multiplication and division? Multiplication and division involve equal groups. When multiplying, you find the total number by combining equal groups. When dividing, you find out how many are in each group or the number of groups by separating the total.

Intervention

Acceleration

DIVISION MODELS

Home

FACILITATION TIP To elaborate on how using multiplication makes division easier, give students several examples to work on that begin with multiplication and then flip to division. FACILITATION TIP Make time to ensure that students are fluent with their multiplication facts. Reinforce that knowing their number facts will make math easier, just like knowing their letters makes reading easier. FACILITATION TIP Follow up this guiding question with another real-world example. Understanding “finding the number of objects” vs “finding the number of groups” can take repeated practice. FACILITATION TIP Help students to connect that the starting number in division is the total, just like the starting number in subtraction is the total. In contrast, addition and multiplication have commutative properties. FACILITATION TIP Provide students with multiplication tables that they can use at their desk and at home.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP On this Exit Ticket, clarify what types (multiplication and division only) of equations students must write and reinforce that all three numbers need to be used in each equation. 157

DIVISION MODELS

Division Models 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

Equal Groups and Shares 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

Diagrams and Repeated Subtraction

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

Relate Multiplication and Division Equations

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

158

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

Alexander’s Pet Shop

Mindy Weiss

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

Saving a Rainy Day

Division within 100 – Models and Equations

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

PhET Interactive Simulation

The Carnival Treats

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

DIVISION MODELS

Home

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DIVISION MODELS

Division Models 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?

DIVISION MODELS

Home

What does mastery look like?

I can solve division problems and interpret quotients of single-digit numbers using a variety of strategies.

I can use multiplication to determine a quotient. For example, to ﬁnd 18 ÷ 3, I can think, “What number times 3 is 18?”

I can make appropriate use of terminology (quotient, dividend, divisor, and factor) to describe a division problem.

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SCOPE 1

Multiplication and Division Strategies Scope Introduction SCOPE SUMMARY This scope leans heavily on ensuring students are afforded multiple opportunities to develop strategies they understand to multiply or divide. Place value and properties of operations are vital to support students’ ability to become flexible and fluent in both operations. Students use models, pictures, words, or equations to develop and apply strategies for the purpose of becoming efficient, accurate, and fluent with the commutative, associative, and distributive properties. Student Expectations

3.PAR.3.3 Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Kindergarten and first grade build a foundation in the base-ten number system by moving from counting and cardinality to more representational and abstract notions. Students compose and decompose numbers, build place value relationships, and develop addition and subtraction strategies and skills. Second grade advances this progression as students work with equal groups, arrange objects in rectangular arrays up to five rows and five columns, and write equations to express the total as a sum of addends.

In fourth grade, students extend their knowledge of multiplication by solving problems involving multiplication of a number with up to four digits by a one-digit whole number or multiplication of two two-digit numbers. Fourth graders also 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.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

interpret products of whole numbers based on the number of objects in a group and the number of groups.

•

ﬁnd equations to match scenarios.

•

create and describe a context.

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 the associative property of multiplication.

•

determine whether a multiplication problem can be solved in multiple ways.

•

determine that the order in which numbers are grouped does not affect the product.

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. 162

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

The Commutative Property In this exploration, students will experience the commutative property of multiplication using arrays, area models, number lines, and equal groups. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

use their experience with arrays, area models, number lines, and equal groups as models of multiplication to help solve a variety of scenarios.

In this exploration, students will experience the associative property of multiplication using arrays, area models, and equal groups. Students will: •

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 their learning.

Explore 3

The Associative Property

use their experience with arrays, area models, number lines, and equal groups as models of multiplication to help solve a variety of scenarios.

After students have solved the scenario, the teacher guides students in color coding, sharing, and discussing their ﬁndings; then, the activity ends with a discussion over their learning and an Exit Ticket.

MULTIPLICATION AND DIVISION STRATEGIES

Home

The Distributive Property In this exploration, students will create area models that show the distributive property of multiplication and division and the relationship between multiplication and division. Students will: •

create a model that represents the theater as a large array.

•

determine the total number of seats in the theater using smaller arrays.

As students solve the scenario, they discuss their learning with the class and conclude with an Exit Ticket for assessment; then, revisit the Hook to solve.

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MULTIPLICATION AND DIVISION STRATEGIES

Multiplication and Division Strategies Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

164

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students interpret products of whole numbers based on the number of objects in a group and the number of groups. They also draw models and ﬁnd equations to match scenarios. In addition, they create and describe a context and draw a model to ﬁt a given equation. 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 Multiplication and Division Strategies (per class)

Reusable • 100 Counters (per pair) • 1 Dry-erase board (per pair) • 1 Dry-erase marker (per pair)

• • •

•

Group students in pairs. Prepare to project Multiplication and Division Strategies to the class. Gather counters for each pair of students. These can be any object that can be counted (beans, beads, manipulatives, etc.). Gather a dry-erase board and a dry-erase marker for each pair.

MULTIPLICATION AND DIVISION STRATEGIES

Home

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

5. 6. 7. 8. 9. 10.

11. 12.

Project Multiplication and Division Strategies to the class. Distribute dry-erase boards and dry-erase markers to each pair. Invite students to read the scenario on the ﬁrst slide of Multiplication and Division Strategies as a class. Encourage each pair to use the counters to show the groupings and write a number sentence on their board. Invite pairs to share with the class and explain their reasoning. Project the second slide of Multiplication and Division Strategies to the class. Invite students to read the scenario as a class. Discuss the information they know and what they need to know. Allow pairs to use counters to determine what operation is needed and the solution to the question. Project the last slide of Multiplication and Division Strategies. Challenge students to use the counters and create their own scenarios and models on their dry-erase boards to accompany the equation 4 × 6 = 24. Facilitate a class discussion about their 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. Ask the following questions: a.

What types of models did you use? Answers may vary. Some students will say arrays. Others will say drawings.

How do the models help you? Answers may vary. It shows me how the number of groups is one factor and the number of objects in a group is the other factor. The product of the factors gives me the solution.

Were anyone’s models the same? Answers may vary, but most likely the models were the same on the front of the paper.

Allow a couple of volunteer pairs to share their scenarios and models to match the number sentence 4 × 6 = 24. If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP After students choose answers independently, have them confer with a partner. To encourage mathematical discourse, prompt each student to take a turn explaining their mathematical thinking to their partner. As students communicate their thinking, they internalize their thought process and more deeply understand the concept.

FACILITATION TIP Challenge students to create a similar problem and to represent it using a model of their choice. Have students swap problems with a partner and compare the strategies and models they chose to use.

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MULTIPLICATION AND DIVISION STRATEGIES

Multiplication and Division Strategies Hook – Appetizers and Toothpicks ACTIVITY PREPARATION Students use the associative property of multiplication to demonstrate that a multiplication problem can be solved in more than one way and the order in which numbers are grouped does not affect the product.

Materials

Preparation

Reusable • • • •

Plan to show the Phenomena Video. Decide how you will break the class into small groups of 4.

• •

1 Box of crayons or colored pencils (per group) 1 Bottle of liquid glue (per group) 1 Phenomena Video (per class) 1 Projector or document camera (per class)

Consumable • • •

1 Piece of lined notebook paper (per group) 2 Pieces of half-sheet-sized graph paper (per group) 1 Box of toothpicks (per group)

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

2. 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.

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? Where can you see math in this scenario? Allow students to share all ideas. Read the following scenario to the class: Your parents are throwing a party. They want you and your sister to make layered desserts. There will be 2 trays, each holding 7 desserts. Each dessert needs 5 ingredients to construct the ﬁve layers. Your dad asks you and your sister to construct the desserts in the following way from bottom to top: cookie, marshmallow, chocolate, orange, and a cherry on the top—held together with a toothpick. Your mom asks how many total ingredients you will need to construct the desserts. Your sister says you should multiply the number of trays by the number of desserts per tray and then multiply that product by the number of ingredients per dessert. You argue that you should multiply the number of ingredients per dessert by the number of desserts per tray, and then multiply that product by the number of trays. a.

How many total pieces of ingredients do you need to make the desserts?

Who had the correct strategy?

Make models to discover who is correct.

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Engage

Explore

Explain

Elaborate

Evaluate

Discuss the following questions with the class:

Intervention

Acceleration

FACILITATION TIP

DOK-3 How will making a model of the desserts help us ﬁnd how many ingredient pieces are needed to make the desserts? Making the dessert models will allow us to count the pieces necessary to make the correct number of desserts.

Students should discuss a strategy to solve the problem. Groups can compare their strategies before beginning the Explore activities.

DOK-3 How will making a model of the desserts help us determine who had the correct strategy for ﬁnding the number? Making the dessert models will allow us to try both strategies presented and determine which strategy works by having a concrete model to help us visualize.

FACILITATION TIP Have students use dry-erase boards to take notes. Students can also draw a model of the dessert and the dessert tray.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

3. 4.

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

DOK-3 How will making a model of the desserts help us ﬁnd how many ingredient pieces are needed to make the desserts? Making the desserts will allow us to count the pieces necessary to make the correct number of desserts.

DOK-3 How will making a model of the desserts help us determine who had the correct strategy for ﬁnding the number? Making the desserts will allow us to try both strategies presented and determine which strategy works by having a concrete model to help us visualize.

Review the problem and put students into small groups of 4. Give each group of students two pieces of half-sheet-sized graph paper, a box of toothpicks, a bottle of liquid glue, a box of crayons or colored pencils, and a piece of lined paper. Instruct students that they need to make models of the desserts. Tell them that each half sheet of graph paper represents the two trays that will be holding the desserts. They will color in squares in certain colors to represent each ingredient in the desserts. Write the colors to represent each ingredient on the board. They are as follows: a.

cherry = red

orange = orange

chocolate = brown

marshmallow = pink

e. cookie = yellow 6.

8. 9.

Students should follow the instructions to start at the bottom and color squares in a vertical line in the following order: cookie, marshmallow, chocolate, orange, and cherry. They can then use liquid glue to glue a toothpick on top of the squares colored on their tray (graph paper) to represent one dessert on the tray. Students should make 7 desserts to go on each serving tray (graph paper). Tell them the desserts should be spaced apart on the tray like they would be at the party. Give students about 10 minutes to create the two trays of desserts and determine how many pieces of ingredients were used to create the desserts. Students should try out both strategies. Instruct students that they can work the problems in their heads if they are ﬂuent in their multiplication facts or they can use the pencil and notebook paper to ﬁgure out the solutions. a.

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FACILITATION TIP Model for students how to use the graph paper to make the dessert model.

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.

FACILITATION TIP Guide students in using their models with the two different strategies that illustrate the associative property of multiplication.

Sister’s strategy: number of trays multiplied by the number of desserts per tray and then that product multiplied by the number of pieces of ingredients per dessert

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Multiplication and Division Strategies Hook – Appetizers and Toothpicks b.

10. 11. 12. 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.

Your strategy: number of pieces of ingredients per dessert multiplied by the number of desserts per tray and then that product multiplied by the number of trays

Students should then count the number of pieces of ingredients to check their answers. Hint: students can count by 5s. Instruct each small group to tell the class which strategy was right—theirs or their sister’s. Did everyone in the class agree? Discuss the following questions with the class: a.

DOK-2 What was the solution for your sister’s strategy? 2 × 7 = 14 → 14 × 5 = 70

DOK-2 What was the solution for your strategy? 5 × 7 = 35 → 35 × 2 = 70

DOK-1 What was the solution you found when you used the model and counted the number of pieces of ingredients needed to make the correct number of desserts? 70

DOK-1 Do either of the strategies result in the same solution you got when you counted the number of pieces of ingredients needed to make the desserts? Both of the strategies had the same solution as what we counted using the models.

e. DOK-3 Why did both strategies work and result in the same solution? Because the associative property of multiplication explains that when multiplying more than two numbers, changing how they are grouped and the order in which they are multiplied does not aﬀect the product. So, 2 × 7 = 14 → 14 × 5 = 70 results in the same solution as 5 × 7 = 35 → 35 × 2 = 70. f.

DOK-1 Who was correct, your sister or you? We were both right because the grouping of the numbers and the order of the equation do not matter. The solution/product will be the same.

DOK-2 Is there another way the numbers could be grouped/ordered that would also result in the same solution? Yes, the number of ingredients per dessert can be multiplied by the number of trays, and then the product of that can be multiplied by the number of desserts per tray. So, 5 × 2 = 10 → 10 × 7 = 70.

h. DOK-2 Is any one of the ways grouped in a way that makes it easier to ﬁnd the solution? Yes, the last way is easiest because it is easiest to multiply by 5s and 10s.

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Multiplication and Division Strategies Explore 1 – The Commutative Property ACTIVITY PREPARATION Students experience the commutative property of multiplication using arrays, area models, number lines, and equal groups.

Standards for Mathematical Practice • • • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. 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 Number Line (per group) 1 Exit Ticket (per student)

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. Prepare the following materials for each group:

• • •

• Print a Number Line; place it in a sheet protector to create an erasable surface, or laminate it if desired. • A dry-erase marker • 50 square tiles in a quart-size bag • 50 two-color counters in a quart-size bag

Reusable • • • • •

1 Set of two-color counters (per group) 1 Set of 50 square tiles (per group) 1 Dry-erase marker (per group) 1 Sheet protector (per group) 2 Quart-size resealable bags (per group)

For students who need more support in recalling information, please see our Sharing Mats, Multiplication Array, Grid Paper, 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. (Color Tiles, Two-Color Counters, and Number Lines)

•

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Students will compare two different equations that represent the commutative property of multiplication—for example (4 × 5) and (5 × 4), with both equations equaling 20. FACILITATION TIP Take time to show students how to sketch arrays by drawing a simple rectangle and then dividing it into the appropriate rows and columns. Encourage students to label the sides with the numbers.

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Give a Student Journal to each student. Distribute a Number Line, a dry-erase marker, a bag of square tiles, and a bag of two-color counters to each group. Explain to the class that they will be using their experience with arrays, area models, number lines, and equal groups as models of multiplication to help them solve a variety of scenarios. Explain that for each scenario they read, they will be representing the problem in three different ways: by creating a number line, by building an array or area model, and by making equal groups. Quickly ask the class the following questions before they get started: a.

DOK-1 How do you think you can use the Number Line to help you represent the scenario? I can use the Number Line to practice drawing number line models. When my group agrees on how the number line should look, then I can copy our number line model onto the Student Journal. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 How do you think you can use the square tiles to help you represent the scenario? I can use the square tiles to build arrays or area models.

DOK-1 How do you think you can use the two-color counters to represent the scenario? I can use the two-color counters to create equal groups or arrays.

Challenge students to work cooperatively with their groups to solve each scenario on their Student Journals and answer the reﬂection questions. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What information do you know based on the scenario? I know how many times they hopped and that each hop was a certain distance.

DOK-1 What information are you trying to determine? I am trying to determine how many feet Frog and Toad hopped.

DOK-2 How can you represent this problem using the number line? I can draw 4 hops since Frog jumped 4 times. I will then label each hop with a multiple of 5 since each hop was the distance of 5 feet.

DOK-2 How can you represent this problem with an array? I can use the square tiles to create 4 rows. Each row represents a hop. Each row will have 5 square tiles in it to represent that each hop was 5 feet long. Each square tile represents a foot Frog jumped.

e. DOK-2 How can you represent this problem with equal groups? I can make 4 groups. Each group represents a hop. Each group will have 5 color counters. Each color counter represents a foot Frog jumped.

7. 8.

DOK-2 How can you use your models to write an equation? I see that each model had a way to represent 4 groups of 5, so I will multiply 4 × 5. Each model had a product of 20, so I know the product to my equation is 20.

DOK-3 What do you notice about both models and equations within a scenario? How are they the same? How are they different? The models are a little different for each scenario. I notice that the ﬁrst part of the scenario has 4 groups of 5, and the second part of the scenario has 5 groups of 4. However, they each have the same product.

Intervention

Acceleration

FACILITATION TIP In using manipulatives, students should discover that the factors in multiplication can be swapped without affecting the product.

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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.

Allow the groups enough time to model and solve each scenario and to answer 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-2 What did you notice as you solved each scenario using the different models? I noticed that the models were a little different from each other from the ﬁrst part of the scenario to the second part of the scenario, but we always ended up with the same product. DOK-3 Does it matter which model you use to solve a problem? Explain. No it does not, as long as it is a multiplication strategy. Each model we used to solve a problem gave us the same answer. DOK-2 What did you notice about the equations for each model? The order of the numbers we were multiplying switched depending on the wording of the scenarios. DOK-2 What did you notice about the products for each model? The products were the same. DOK-3 Does the order of the numbers matter when you are multiplying? Explain. No, as long as we are multiplying by the same factors, we can switch the factors around and the product will still be the same.

FACILITATION TIP Review with students that order of numbers does matter in division and subtraction equations. 171

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Multiplication and Division Strategies Explore 1 – The Commutative Property 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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Multiplication and Division Strategies Explore 2 – The Associative Property ACTIVITY PREPARATION Students experience the associative property of multiplication using arrays, area models, and equal groups.

Standards for Mathematical Practice • • • • •

Materials

Preparation

Printed • •

• • •

1 Student Journal (per student) 1 Exit Ticket (per student)

• A dry-erase marker • 100 square tiles placed in a gallon-size resealable bag • 100 two-color counters placed in a gallon-size resealable bag

Reusable • • • •

100 Two-color counters (per group) 100 Square tiles (per group) 1 Dry-erase marker (per group) 2 Gallon-size 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. Prepare the following materials for each group:

•

For students who need more support in recalling information, please see our Sharing Mats, Multiplication Array, 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 Two-Color Counters)

PROCEDURE AND FACILITATION POINTS 1. 2. 3.

FACILITATION TIP Students are creating models that demonstrate the associate property of multiplication. The models should show that changing how the factors are grouped does not change the product.

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Give a Student Journal to each student. Distribute a dry-erase marker, a bag of square tiles, and a bag of two-color counters to each group. Explain to the class that they will be using their experience with arrays, area models, and equal groups as models of multiplication to help them solve a variety of scenarios. Explain that for each scenario they read, they will be using their materials to best model that scenario. They can choose to build an array or area model or make equal groups. Quickly ask the class the following questions before they get started: a.

DOK-1 How do you think you can use the square tiles to help you represent a scenario? I can use the square tiles to build arrays or area models.

FACILITATION TIP

Provide students with two different types of manipulatives to use for the models in each scenario.

DOK-1 How do you think you can use the two-color counters to represent a scenario? I can use the two-color counters to create equal groups or arrays.

DOK-1 How do you think you can use the dry-erase marker to help you represent a scenario? I can use it to draw a circle on my desk to place the equal groups of two-color counters inside. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

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Intervention

Acceleration

DOK-1 What information do you know based on the scenario? I know there are 3 containers of gummy bears, with each container holding 5 bags of gummy bears and 6 gummy bears inside each bag.

DOK-1 What information are you trying to determine? I am trying to determine how many gummy bears Sydney purchased.

DOK-2 How can you represent this scenario with a model? I can use my dry-erase marker to draw 3 big circles on my desk. Each big circle represents a container. Inside each big circle, I can draw 5 smaller circles. Each smaller circle represents a bag of gummy bears. Then, I can place 6 two-color counters in each smaller circle to represent the 6 gummy bears in each bag.

DOK-2 How can you use your models to write an equation? I can multiply all my factors together because I have 3 containers of 5 bags of 6 gummy bears, so 3 × 5 × 6. My model and the equation show me that the product is 90 total gummy bears.

FACILITATION TIP Reassure students that representing scenarios with models is an effective thinking tool. Using the models will make them more capable with mental math. Some students may want to solve without manipulatives. However, they will continue to use these models as their math lessons become more complex.

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e. DOK-3 What do you notice about both models and equations for a pair of scenarios? How are they the same? How are they different? The models are a little different for each scenario. I notice that the ﬁrst scenario has 3 bundles of 5 groups of 6, and the second scenario has 5 bundles of 6 groups of 3. However, they each have the same product. 7. 8.

Allow the groups of students enough time to model and solve each scenario and to answer 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-2 How does your model compare to the models drawn here? My models show the same total but they look different. DOK-1 Did everyone write their equations in the same order? No DOK-1 Did everyone get the same products? Yes DOK-1 If we did not multiply the numbers in the same order, would we still end up with the same product? Yes, we all got the same answers. My models show the same total. DOK-2 Does the order of the numbers we are multiplying matter? No DOK-1 Is there another operation that works similarly, where order does not matter? Yes, addition DOK-2 Are there any operations that require a certain order, where changing the order would change the outcome? Yes, subtraction and division DOK-3 Give an example. 7 – 3 is not the same as 3 – 7, and 21 ÷ 7 is not the same as 7 ÷ 21.

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.

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 and Division Strategies Explore 3 – The Distributive Property ACTIVITY PREPARATION Students create area models that show the distributive property of multiplication and division and the relationship between multiplication and division.

Standards for Mathematical Practice • • • • •

Materials

Preparation

Printed • •

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1 Student Journal (per student) 1 Exit Ticket (per student)

• •

Reusable • • •

•

1 Ruler (per student) 1 Set of 50 color tiles (per group) 1 Quart-size resealable bag (per group)

•

Plan to divide the class into groups of 3 or 4 students to complete this activity. Print a Student Journal and an Exit Ticket for each student. Gather a ruler and a set of 50 color tiles for each group, and place them inside of a quart-size bag. For students who need more support in recalling information, please see our Multiplication Array 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, Two-Color Counters, and Linking Cubes)

PROCEDURE AND FACILITATION POINTS Part I: The Distributive Property of Multiplication FACILITATION TIP

The seating for the smaller array can be conﬁgured in various ways to equal the number of sets in each theater. 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. 176

2. 3. 4.

Read the following scenario to the class: At Illumination Theater, there are various sizes of theaters. The larger theaters hold more guests and are used for more popular movies. The smaller theaters hold less guests and are used for showing less popular movies. Each theater has a top section of seats that are a little bit further from the screen and a lower section with seats closer to the screen. Illumination Theater needs your help to determine how many seats each theater holds and how many seats they should put in the top section and the lower section. Give a Student Journal to each student. Give a bag of color tiles to each group. Explain to students that they will be working cooperatively with their groups to solve each theater scenario. For each scenario, they will ﬁrst create a model that represents the theater as a large array and record this model on their Student Journals. Challenge students to then take that large array and their rulers to split it into a top section of the movie theater and a lower section of the movie theater. They will then record these models as the smaller arrays on their Student Journals. Students will then write an equation, using the space provided on their Student Journals, that represents the smaller arrays and determine how many rows are in each theater. © 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.

DOK-1 What information do you know about this theater? I know this theater has 4 rows of seats, and each row has 6 seats.

DOK-2 How can we represent this as a large model using the color tiles? I can take 6 color tiles and make a row. Each color tile represents a seat. I will do this 4 times until I represent 4 rows of 6 seats.

DOK-2 How can we take this large model of color tiles and create a top section of the movie theater and a lower section of the movie theater? I will use my ruler and split the array until we have 3 rows of 6 seats in the top section and 1 row of 6 seats in the lower section.

DOK-2 What do you notice about the smaller array models that is similar to the large array model? I notice that the number of seats in each row stayed the same and that I still have the same total number of seats.

e. DOK-2 What do you notice about the smaller array models that is different from the large array model? I notice that the rows got split into smaller sections. I still have 4 rows, but it got split into 3 rows and 1 row. f.

DOK-3 Describe how you can use the smaller models to write equations to represent what is happening. I know my original equation was 4 × 6. The number of seats in each row stayed the same, but I then split the 4 rows into 3 rows and 1 row. One array represents 3 × 6, and the other array represents 1 × 6. I could also represent this by doing 3 + 1, which equals the 4 rows. That addition sentence would be multiplied by the 6 seats in each row: 6(3 + 1), which represents 6 × 3 + 6 × 1.

DOK-2 How can we now ﬁnd the product or the total number of seats in the theater? We can add the two products in the equation. I found that 3 × 6 is 18 and 1 × 6 is 6. 18 + 6 equals 24, so I know there are 24 seats in the theater.

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.

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h. DOK-1 What do you notice about the product for both equations? I notice that both of the products are the same. i. DOK-2 Why do you think both products for different equations are the same? They are the same because we still have the same number of rows and the same number of seats in each row. The problems were just represented a little differently based on the array model. 8.

Allow students enough time to complete each problem and to record their responses on their Student Journals.

Part II: The Distributive Property of Division 1.

Read the following scenario to the class: Illumination Theater has decided to expand and are adding two new movie theaters to their theater. The new design tells them how many seats will be in each theater, but they need to decide how many seats are in each row or how many rows of seats the theater will have. The sizes of the top section of the theater and the lower section of the theater also need to be determined. Help the movie theater complete the design of the new theaters so they can be built correctly. Challenge students to read each problem and continue to work with their groups to determine the large array for each new theater. Students will then use that array to create a top section and a lower section of the movie theater. Explain to students that when making a top section and a lower section, it is important that the smaller sections you make must be able to be divided by the divisor. Instruct students to then use the small arrays to write an equation using their models to determine the quotient.

FACILITATION TIP Encourage students to use the vocabulary words rows and columns to help them communicate accurately in their groups.

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Multiplication and Division Strategies Explore 3 – The Distributive Property 5.

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

DOK-1 What information do you know about this theater? I know there are 40 seats in the theater, and there are 8 seats in each row.

DOK-2 How can we represent this as a large model using the color tiles? I can count out 40 color tiles and start by putting 8 tiles in a row. I then make another row of 8 tiles. I will continue this until I have put all 40 tiles into rows with 8 seats.

DOK-2 How can we take this large model of color tiles and create a top section of the movie theater and a lower section of the movie theater? I can use my ruler and split the rows in the array. It looks like I have 5 rows, so I will put 3 rows in the top section and 2 rows in the lower section.

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.

e. DOK-2 What do you notice about the smaller array model that is different from the large array model? I notice that the rows got split into smaller sections. I still have 5 rows, but it got split into 3 rows and 2 rows. f.

DOK-3 Describe how you can use the smaller model to write equations to represent what is happening. I know my original equation was 40 ÷ 8. The number of seats in each row stayed the same, but I then split the 5 rows into 3 rows and 2 rows. One array represents 24 ÷ 8, and the other array represents 16 ÷ 8.

DOK-2 How can we now ﬁnd the quotient or the number of rows in the theater? We can add the two quotients in the equation. I found that 24 ÷ 8 is 3, and 16 ÷ 8 is 2. 3 + 2 equals 5. This helps me determine that the theater has 5 rows of seats.

h. DOK-1 What do you notice about the quotient for both equations? I notice that both of the quotients are the same. i. DOK-2 Why do you think both quotients for different equations are the same? They are the same because we still have the same total number of seats and the same number of seats in each row. The problems are just represented a little differently based on the array model. 6. FACILITATION TIP Students can compare their small arrays for the theater seating with other pairs in the Math Chat.

FACILITATION TIP Reassure students that representing scenarios with models is an effective thinking tool. They will continue to use these models as their math lessons become more complex. 178

Allow the groups of students enough time to model and solve each problem and answer 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-2 What is the relationship between the equation and the array model? Each part of the equation represents a portion of the array model. We show each portion using parentheses and add the portions together to find the total. • DOK-2 How are the larger array and smaller arrays similar? Both arrays have the same total color tiles being used. Both arrays have the same number of rows and same number in each row. • DOK-2 How are the larger array and smaller arrays different? The larger array can help you find the missing product or quotient when having all the tiles together. The smaller array can help you find the missing product or quotient by splitting the larger array into smaller parts. • DOK-2 How is this strategy helpful when solving multiplication and division problems? This strategy is helpful because it can break multiplication or division problems into smaller parts, and the smaller problems may be easier to solve. •

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Post-Explore 1. 2. 3. 4.

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Multiplication and Division 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

The Commutative Property 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

The Associative Property 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

The Distributive Property 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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ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Conﬁdent Camper

Food Service Manager

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 Trip to the Aquarium

Multiplication and Division Problem Solving within 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

PhET Interactive Simulation

Crafty Creations

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

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Students who are still acquiring the concept and need remediation

MULTIPLICATION AND DIVISION STRATEGIES

Multiplication and Division 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

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 Interactive Practice

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

Engage

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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 the commutative property to multiply and divide within 100.

What prompts will be used?

What does mastery look like?

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I can use the associative property to multiply and divide within 100.

I can use the distributive property to multiply and divide within 100.

I can recognize the connection between multiplication and division and use this connection to gain ﬂuency.

I can use patterns and relationships to build ﬂuency with multiplication and division facts.

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SCOPE 1

Multiply Multiples of 10 Scope Introduction SCOPE SUMMARY Students accurately multiply one-digit numbers by multiples of 10 in the range of 10–90 using base ten blocks, arrays, and number lines. They use place value strategies and their knowledge of the properties of operations. Students also explain how multiplying by multiples of ten is related to basic facts.

Student Expectations

3.PAR.3.5 Use place value reasoning and properties of operations to multiply one-digit whole numbers by multiples of 10, in the range 10–90.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Second-grade students add to their understanding by using place value and properties of operations to add and subtract. These concepts can then be connected to the associative property of multiplication.

As students progress into fourth grade, they continue building on their understanding of the base-ten number system by learning that the value of each place is ten times the value of the place to the immediate right. Students will use representations and strategies based on place value and properties of operations to multiply and divide multi-digit numbers.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

apply strategies about properties of operations to multiply and divide various whole numbers.

•

multiply up to three one-digit numbers using associative and commutative properties.

•

describe how multiplying by ten is the same as adding groups of tens.

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 one-digit numbers by multiples of ten using strategies based on place value.

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.

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. 184

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Multiplying by Multiples of 10 Using Base Ten Blocks In groups, students will solve a scenario about the number of items shipped from a warehouse. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

multiply one-digit whole numbers by multiples of 10 using base-ten rods.

The scenario presented and solved involves students pretending they have a bed-and-breakfast they must take food inventory for to ensure there is food in stock Students will: •

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

Multiplying by Multiples of 10 Using Arrays

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Home

multiply one-digit whole numbers by multiples of 10 to determine the total number of objects using arrays as a multiplication strategy.

Once students have solved the scenario, they discuss their learning with the class and ﬁnish with an Exit Ticket.

Multiplying by Multiples of 10 Using Number Lines Students in groups will solve a scenario in which students help a candy factory determine how much candy was made during each shift. Through the scenario, students will: •

model and write multiplication problems involving multiplying single-digit numbers by multiples of 10 using equal jumps on a number line.

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

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Multiply Multiples of 10 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 multiply up to three one-digit numbers using the associative and commutative properties and understand that multiplying by ten is equivalent to adding groups of tens. 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. 3.PAR.3.4 Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent. Materials

Preparation

Printed •

MULTIPLY MULTIPLES OF 10

Home

•

Print a Student Handout for each student.

1 Student Handout (per student)

Reusable •

1 Set of base ten blocks (per group, optional)

Consumable •

1 Sheet of graph paper (per student, optional)

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

Place students in small groups or pairs. Distribute a Student Handout and a sheet of graph paper to each student and a set of base ten blocks to each group or pair. Students may or may not use the base ten blocks to model each problem on their Student Handouts. Students may choose to model some of the problems using a grid they can draw on the graph paper. Facilitate a class discussion about the associative and commutative properties of multiplication and about place value when multiplying by 10. 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. a.

When I multiply 3 numbers together, it doesn’t matter which numbers I multiply ﬁrst. I will still get the same answer.

When I multiply 2 numbers together, the order doesn’t matter.

40 is the same as 4 groups of ten. I add 10 four times to get 40. That means 4 times 10 equals 40.

I can use a grid to model 4 × 6. I drew 4 columns and 6 rows, and then I counted the boxes inside. There were 24.

e. When I had to multiply 6 × 10, I took 6 tens from the base ten blocks and counted by tens 6 times. I got 60. I noticed this is just 6 with a zero at the end, so that means the place value of the 6 moved over from the ones place to the tens place. 6.

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

FACILITATION TIP Emphasize that multiplication is the process of determining the total amount in equal-sized groups. For each question, there is a part-to-part-to-whole relationship. The number of groups and the amount per group make up the parts of the total or whole amount. FACILITATION TIP If students use skip counting as a strategy, have them demonstrate the process. Practice oral skip counting in unison with the class. For these examples, skip count by 6 to determine the total amount of candy bars, by 5 to determine the total amount of marbles, by 8 to determine the total amount of baseball cards, and by 2 to determine the total amount of light bulbs.

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Multiply Multiples of 10 Hook – Let’s Battle ACTIVITY PREPARATION Students multiply a one-digit number by multiples of ten using strategies based on place value.

Materials

Preparation

Printed •

•

1 Let’s Battle (per pair)

Reusable • • •

• • •

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1 Gallon-sized resealable bag (per pair)

Print a Let’s Battle for each pair of students. You can reuse them if you have more than one class. You can cut out the cards or have the partners cut them out. Put the cards and answer key in a resealable bag. Plan to show the Phenomena Video. Prepare to project Let’s Battle. In Part II, students will battle each other with their knowledge of multiplying one-digit numbers by multiples of ten.

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

2. FACILITATION TIP Some students may not have experience with multiplying by 10s yet. Decide beforehand how much instruction and support to provide for this Hook Pre-Explore.

4. 5.

DOK-1 How would we ﬁnd out how many cards were in the varying stacks? We would need to think about how many cards are in each stack. Then, we would have to multiply that amount by the total number of stacks.

DOK-2 If there are 7 stacks with 3 packs in each stack, what would we multiply? If there are 3 packs in each stack, that means there are 30 cards in each stack. If there are 7 stacks, we would multiply 30 × 7.

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.

Part II: Post- Explore 1. 2.

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Move on to complete the Explore activities.

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

3. 4. 5.

6. 7.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

Review the problem and put students in partners. Give them the resealable bag with the cards and answer key. They will be solving to find the total number of cards. Instruct students to put all the cards facedown in a stack between them. They will each pick a card from the top of the stack. Each student will solve the multiplication problem to find the product. Students can use the answer key to check their partners’ answers. The student with the highest product (number of cards) wins that round and keeps both of those cards in a separate pile. Continue playing until all the cards are gone from the stack in the middle. The student with the most cards wins the battle. If they finish playing once, students can shuffle cards and play again. Discuss the following questions with the class: a.

DOK-2 How did you ﬁnd the number of cards for each multiplication sentence? I looked at the digits that were not zero. I found that product. Since one of the digits was a multiple of ten, because it was in the tens place and not the ones, I knew the product would have to be ten times greater.

DOK-2 Explain to the class how you found the total number of cards that were in 6 stacks with 5 packs in each stack. That meant there were 50 cards in each of the 6 stacks. That made the multiplication sentence 50 × 6. I know 5 × 6 = 30. I had to make that ten times greater. I know that 30 × 10 = 300. So, there are 300 cards in those stacks.

DOK-3 Can you think of any other real-world situations or contexts where you would use math like this? If there were stacks of dimes, you could use multiplication sentences similar to these to ﬁnd the amount of cents in the stacks. You could also do the same if there were stacks of 10 dollar bills or to ﬁnd the amount of party favors in bags of 10.

Intervention

Acceleration

FACILITATION TIP Depending on your students, consider having them solve the problems more cooperatively. Students can work together side by side or compare answers after working independently for a set time. Finally, they could check the answer key together and keep track of how many they get correct as a team.

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FACILITATION TIP Compare students’ methods. Discuss the advantages and disadvantages of each method.

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Multiply Multiples of 10 Explore 1 – Multiply Multiples of 10 Using Base Ten Blocks ACTIVITY PREPARATION Students multiply one-digit whole numbers by multiples of 10 using base-ten rods relating to the number of individual items in a packaged shipping order.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 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 Shipment Cards (per class) 1 Exit Ticket (per student)

Reusable •

•

1 Set of base-ten rods (per station)

• • • • • • •

Consumable •

Plan to divide the class into 7 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print one set of Shipment Cards. Place Shipment Cards around the room, along with each corresponding item, to create the 7 stations. Prepare base-ten rods as indicated below:

10 Small paper plates (per station)

• •

Insulated Coffee Cups – 20 base-ten rods Reusable Grocery Bags – 20 base-ten rods Aluminum Cans – 40 base-ten rods Biodegradable Can Rings – 20 base-ten rods Egg Cartons – 30 base-ten rods Glass Sauce Jars – 50 base-ten rods Rubber Shoe Soles – 20 base-ten rods

For students who need more support in recalling information, please see our 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. (Base Ten Blocks)

PROCEDURE AND FACILITATION 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.

3. 4. 190

Read the following scenario to the class: You just got promoted to regional manager of the country’s biggest warehouse that packs and distributes goods to stores all over the country. As regional manager, your most important job is to make sure all of the orders and shipments are correct and that you have enough items to ship. Each of the 7 stations represents a different shipment. Ensure that you keep precise records of the number of items being shipped. Tell students that the items are packaged for retail sale, and they must use their knowledge of multiples of ten to determine how many individual items each shipment contains. DOK-1 Invite students to turn and talk to their neighbors: What are multiples of 10? They are the products of a number times ten; they can be evenly divided by ten. DOK-1 How can we ﬁnd out the total number of items shipped if there are multiple packages? We can multiply or skip count by tens. © Accelerate Learning Inc. - All Rights Reserved

5. 6. 7.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

Encourage them to group the base-ten rods into packages at each station to help them calculate the total number of individual items. Give a Student Journal to each student, and assign each group to a starting station. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How many groups of ____ do you have? What do these represent? Answers will vary. There are _____ groups. These represent the number of items in each package.

DOK-1 How many tens are in each group? What do they represent? Answers will vary. There are _____ tens in each group. These represent the number of packages in each shipment.

DOK-2 If we don’t know how to skip count by ___, how can we count these groups? It’s diﬃcult to count by forties, so we could use the baseten rods to count by tens.

Rotate groups after giving 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-1 How does the number of base-ten rods relate to the total number of items in a package? The number of base-ten rods in each group can be multiplied by the number of packages, and then we can multiply the product by 10 because they are each a group of 10. For example, if we have 3 packages that each take 30 cups, I know I’ll have 3 rods in 3 groups; 3 × 3 is 9. From there, we can multiply that product by 10 since each rod represents 10 units or items. • DOK-2 How do the multiplication equation and the number of base-ten rods relate? The multiplication equation would read as 8 groups of 60 items, which can also be read as 8 groups of 6 tens. • DOK-3 What strategies can be used to count the total number of items in a shipping order? If the multiple of 10 is too diﬃcult to skip count, we can skip count the base-ten rods individually since counting by 10 is easier. We can use our multiplication facts and multiply the number of base-ten rods by the number of groups. Then, we can multiply that product by 10 to get the ﬁnal product. •

Intervention

Acceleration

FACILITATION TIP Have students demonstrate skip counting by tens. To help students visualize groups of ten, display a base-ten rod, and ask how many units are in the rod. To help students visualize that repeated addition can be used to find groups of ten, add base-ten rods each time students say the next multiple of 10. Say, “10 plus 10 equals 20, 20 plus 10 equals 30, etc.” Finally, display a group of base-ten rods and ask, “If there are – base-ten rods, how can we find the total amount of units?” Lead students to an understanding of the connection between repeated addition and multiplication, along with the understanding that multiplication is simply a more efficient strategy than repeated addition or skip counting.

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FACILITATION TIP After students identify the number of groups and how many tens are in each group, encourage them to put it all together into one statement: “– groups with __ in each group equals –.” FACILITATION TIP Remind students they can also use repeated addition to ﬁnd the total.

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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MULTIPLY MULTIPLES OF 10

Multiply Multiples of 10 Explore 2 – Multiply Multiples of 10 Using Arrays ACTIVITY PREPARATION Students multiply one-digit whole numbers by multiples of 10 to determine the total number of objects in a scenario by using arrays as multiplication strategies. Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 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 Grocery Item Cards (per class) 1 Exit Ticket (per student)

Reusable • • •

1 Set of base-ten rods (per group) 1 Plastic bin or container (per group) 1 Plastic resealable bag (per group)

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 one set of Grocery Item Cards (in color, if possible) on card stock. Cut and sort the Grocery Item Cards. Put base-ten rods in plastic bags for each group. Place Grocery Item Cards and base-ten rods in plastic containers in different areas around the room. Place students into ﬁve groups. For students who need more support in recalling information, please see our Base Tens and Multiplication Array 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 Base Ten Blocks)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP

Students used arrays to show repeated addition in second grade. Brieﬂy model and review that arrays are objects or numbers that are arranged into rows and columns.

FACILITATION TIP

On page 4 of the Student Journal, provide support to struggling students as they write complete answers to the reﬂection questions. 192

5. 6.

Read the following scenario to the class: You and a friend are opening a bed-andbreakfast! This is a place that is similar to a hotel but typically much smaller with only a few rooms. You are planning a breakfast feast for your guests and want to make sure they have plenty to eat. In order to ensure that you are all stocked up, you have to take inventory to see how much food you have. Tell students that there are grocery items around the room. Their job is to “take inventory” of each item. Explain that you need a visual model to help you and your friend keep track of all the items you have, and you will show the total number of each item using an array. Encourage students to collaborate and use the manipulatives to arrange the best array for each item and then record the model in their Student Journals. Assign each group a station at which to begin. Give students a few minutes at each station to determine the total number of items in their inventory. Monitor and talk with students as needed to check for understanding by using the following guiding questions: © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 How did you and your partner set up the array in order to take inventory of the items? Answers will vary depending on the item. We saw the number of tens in the number and arranged that many rods as our columns. To determine the rows, we looked at how many boxes or cartons there were.

DOK-1 Where do you observe equal groups in the models we just built? Each row and each column have the same number of items.

DOK-2 How could you ﬁnd the total number of items? I could skip count by the number of items in each row. I could use multiplication because I have __ rows with ___ tens in each row.

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

Math Chat •

•

Intervention

Acceleration

FACILITATION TIP Lead students to an understanding that decomposing the tens in each group into the number of tens multiplied by 10 ultimately results in a simpler multiplication problem.

MULTIPLY MULTIPLES OF 10

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FACILITATION TIP

DOK-2 How did you translate the array into a multiplication equation? The number of rows in the model gave me my ﬁrst factor because each row is one group. The number of items in each row gave me my other factor because there is the same number of items in each row. The total number of items was the product. DOK-2 How did the arrays translate to the equations on the right of the models? The numerical expressions told us how many groups of tens we had. By multiplying the rows and columns ﬁrst and multiplying the whole thing by 10, we were able to get the answer. In the model, each row and column was made up of groups of 10, which is why the expression was multiplied by 10.

Avoid saying “add a zero.” Instead, point out that students are multiplying the number of rows and columns by 10 since the arrays are grouped into bundles of 10.

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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Multiply Multiples of 10 Explore 3 – Multiply Multiples of 10 Using Number Lines ACTIVITY PREPARATION Students model multiplication of a single-digit number by a multiple of 10 using equal jumps on a number line.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 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 Shift Reports (per group) 1 Exit Ticket (per student)

•

Reusable •

1 Dry-erase marker (per group)

•

Consumable •

1 Pack of small sticky notes (per group)

•

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Shift Reports for each group. If desired, laminate them for long-term use. Cut them apart along the dashed lines. Gather the materials. Plan for students to have a ﬂat workspace where they can line up sticky notes and draw on the surface with dry-erase markers. For students who need more support in recalling information, please see our Base Tens 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

1. FACILITATION TIP Discuss that a number line is another way to represent multiplication. Demonstrate the connection between number lines and skip counting.

2. 3.

Read the following scenario to the class: Today, you will be working to help the Sugar and Spice Candy Factory evaluate their manufacturing of different candy types! You will look at the details of each shift in the factory to determine the total length of the candy made during each shift. Pass out dry-erase markers, sticky notes, and shift reports to each group and a Student Journal to each student. Have students complete the following steps: a.

Line up sticky notes side-by-side on the desk to create a number line that models the length of candy made during Shift 1. Each sticky note will represent one piece of candy. Label each piece with its length. (See image at top of this section.)

FACILITATION TIP

Remind students that in one equation they can decompose the amount in each group by the number of tens multiplied by ten.

Complete the number line on the Student Journal. Use the model to determine the total length of the candy made during that shift.

Record two different equations that could be used to represent the model.

FACILITATION TIP Make sure students are placing the sticky notes side by side to show equal intervals.

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d. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Repeat this process for each shift. Sticky notes can be reused and relabeled for the different shifts.

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

Math Chat • •

•

DOK-1 What did you observe about each number line? Each number line had equal jumps. Each time we made equal jumps, it was a multiple of 10. DOK-2 What did you do to find the total length of candy made during each shift? We skip counted by the tens place to find out how many tens we had. Then, we used that amount to write the final total. For example, Shift 1 had three groups of two tens. I skip counted “2, 4, 6” to figure out I had 6 tens, which is 60. DOK-2 What is the relationship between the number lines you made today and the other models you have created? They all represent equal groups. We were always multiplying by a multiple of 10, so we could use similar strategies. I could multiply by a certain number of tens in my head and then convert that number of tens to the standard form to write my final answer.

Post-Explore 1. 2. 3. 4.

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FACILITATION TIP Reassure students that ﬂuency with number lines is a powerful thinking skill. It will support their ability to solve more complex problems as they mature as math students. Students will use these number line skills with fractions, decimals, and percents soon.

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Multiply Multiples of 10 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 Multiples of 10 Using Base Ten Blocks 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 Multiples of 10 Using 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

Multiply Multiples of 10 Using Number 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

Football Friends

Oscar Mayer

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

Positively Perfect Pets

Multiplication with Multiples of 10

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

EXTREME Bowling!

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

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Students who are still acquiring the concept and need remediation

MULTIPLY MULTIPLES OF 10

Multiply Multiples of 10

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?

MULTIPLY MULTIPLES OF 10

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I can use place value reasoning to multiply one-digit whole numbers by multiples of 10.

I can use properties of operations to multiply by multiples of 10.

I can recognize patterns when multiplying numbers by multiples of 10.

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SCOPE 1

Multiplication and Division Problem Solving Scope Introduction SCOPE SUMMARY Multiplication and division are new concepts in third grade. Students solve one-step and two-step problems involving multiplication and division within 100, using multiple strategies and representations to determine the unknown number in a multiplication or division equation. Students write equations, with a letter standing for the unknown quantity, and justify their solutions. Student Expectations

3.PAR.3.6 Solve practical, relevant problems involving multiplication and division within 100 using part-whole strategies, visual representations, and/or concrete models. 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.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Second grade works with equal groups, arranging objects in rectangular arrays up to ﬁve rows and ﬁve columns, and writing equations to express the total as a sum of addends using repeated addition. Third grade fully develops the relationship between addition and multiplication, extending the learning to building the relationship between multiplication and division with application to real-world contexts.

Fourth-grade students will solve multistep problems involving addition, subtraction, multiplication, and division, including interpreting remainders, and they are expected to represent the problem with an equation using a letter for the unknown quantity. They will also multiply or divide to solve real-world problems involving multiplicative comparisons.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

determine if multiplication or division is the way to a solution.

•

justify their answers.

•

explain why they were either right or wrong.

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 division model.

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

Model and Solve One-Step Word Problems

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, groups will determine the amounts of strawberry milk, chicken ﬁngers, hot dogs, and cupcakes needed for each scenario. Through various scenarios, students will:

In this exploration, students will play a game in which the group is rewarded for correct answers by rolling the dice and moving forward. Each group cooperatively solves a division problem by:

•

solve a problem using multiplication.

•

making a model.

•

choose a model.

•

writing an equation.

•

write an equation to solve.

•

solving the problem.

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

Explore 3

Model and Solve Two-Step Word Problems

Once students have solved the scenario, they discuss their learning with the class and conclude with an Exit Ticket.

Model and Solve One- and Two-Step Problems In this exploration, students will work in groups to represent one- and two-step problems using various models. Students will: •

solve multiplication and division using tape diagrams.

•

write equations with a symbol for the unknown.

•

use a variety of problem-solving strategies.

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

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Multiplication and Division Problem Solving 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 interpret products and quotients of whole numbers in real-world contexts. 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 Multiplication and Division Problem Solving (per class)

Prepare to project Multiplication and Division Problem Solving to the class.

Procedure and Facilitation Points 1.

Tell students that two children want to convince them that their way of solving a problem is correct.

Read the scenario from Multiplication and Division Problem Solving to the students. Instruct students to read each student’s statement. After students have read each statement, they should choose the statement they agree with the most. Students who agree with Samuel should place their hand palm up on their desks. Students who agree with Meghan should place their hand palm down on their desks. Students should work with partners or a small group to determine a number sentence to represent the problem. Facilitate a class discussion about their 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. Discuss the statements and results.

3. 4. 5.

6. 7.

Samuel is not correct. We are trying to ﬁnd out how many total candies Tariq gave his friends. We are putting all of the gummy bears he gave his friends together, not separating them.

Meghan is correct. We are trying to ﬁnd the total number of gummy bears, so we are grouping all of the candies Tariq gave his friends together.

The number sentence 5 × 2 = 10 represents this situation because there are 2 gummy bears distributed 5 times.

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FACILITATION TIP Students may beneﬁt from acting out the problem. Give a bag of counters to a student. Select 5 other students to stand up. Have the student with the bag of counters give 2 counters to each student standing. Then, count how many counters were given away. Emphasize the number of groups (5), the number per group (2), and the total amount in all the groups (10). Challenge students to write an equation to represent this scenario and to consider whether there is more than one way to do so. Accept all fact families and operations relating to to 5, 2, and 10. For example, students could write 2 + 2 + 2 + 2 + 2 = 10, 2 × 5 = 10, 5 × 2 = 10, 10 divided by 5 = 2, 10 divided by 2 = 5, or 10 – 2 – 2 – 2 – 2 – 2 = 0.

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

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Multiplication and Division Problem Solving Hook – Candy Corn for Days ACTIVITY PREPARATION Students recognize and represent a two-step word problem involving multiplication and division.

Materials

Preparation

Printed •

•

1 Candy Corn for Days (per class)

• •

Reusable • •

1 Phenomena Video (per class) 1 Projector or document camera (per class)

•

Print one Candy Corn for Days for each class. Cut out the four problems solving for the unknown. Plan to show the Phenomena Video. After completing the corresponding Explore activities, hang the 4 problems in the corners of the room. Prepare to project Candy Corn for Days.

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

2. FACILITATION TIP Allow students to explore the candy corn images or other manipulatives to create 4 separate stacks that are even. FACILITATION TIP

a. DOK-1 What information do we know? We have four packages with 10 pieces of candy corn each. We get to eat ﬁve pieces of candy corn each day.

Have groups use the stacks to model repeated addition and repeated subtraction. FACILITATION TIP The problem can be solved using various strategies. Have groups share their different strategies and models with the class.

5. 6.

Explain that we need to solve problems like this. 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 situation. Discuss the following questions with the class: a. DOK-1 What information do we know? We have four packages with 10 pieces of candy corn each. We get to eat ﬁve pieces of candy corn each day. b.

3. 4.

Hang up the four problems from Candy Corn for Days in the 4 corners of the room. Review the problem, and allow students to solve it. Gather students in a whole group. Ask students to stand in a corner of the room by the problem that will lead them to the solution. There are two ways to solve this problem. As they choose a corner, have them turn and discuss with each other why they chose that problem (corner). Discuss the following questions with the class: a.

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Explain that we need to solve problems like this.

Engage

Explore

Explain

Elaborate

Evaluate

Now, you need a second step to arrive at how many days your candy corn will last if you take 5 pieces each day. i.

Acceleration

DOK-3 Walk and stand by one of the corners that has a way to begin solving the problem. Explain your choice. I chose to stand by the problem 4 × 10 = n. I knew that I needed to know how many total pieces of candy corn I had in order to know how many days it would last. The array showed 4 rows of 10. It matched the bags of candy I got.

ii. DOK-3 Explain the other way to begin the problem. What was your thinking? I chose to stand by the problem 10 ÷ 5 = n. I wanted to know how many days one bag of candy corn would last if I took 5 pieces each day. The array showed 10 in two rows of 5, which means each bag will last 2 days. b.

Intervention

FACILITATION TIP Challenge students with different numbers of groups, such as 2 friends, 4 friends, and 12 friends.

DOK-2 Think about what you already know from your ﬁrst step. Walk and stand by a problem that would be the second step and give you the solution. I chose to go to 40 ÷ n = 5. I knew that I had 40 pieces total, and the model showed the 40 pieces being split into 5 groups. So, that told me that the candy would last 8 days.

ii. DOK-3 Explain your thinking if you are at the other corner of the room. I knew that each bag would last 2 days. I knew that I had 4 bags. So, I knew I could use the other facts to help me know how many days the 4 bags would last. I knew 4 × 2 = 8. The candy will last 8 days.

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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MULTIPLICATION AND DIVISION PROBLEM SOLVING

Multiplication and Division Problem Solving Explore 1 – Model and Solve One-Step Problems ACTIVITY PREPARATION Students represent one-step multiplication and division problems within 100 using equations with a letter for the unknown and solve using manipulatives, pictorial models, diagrams, or arrays.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. 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 Exit Ticket (per student)

Reusable • •

• •

1 Set of counters (per group) 1 Projector (per class, optional)

Consumable • •

•

1 Roll of masking tape (per class) 15 Strawberry milk containers (per class, optional)

Plan to divide the class into groups of 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Tape off three square sections on the ﬂoor. They should be large enough for ﬁve students to stand in each section. Prepare a set of counters for each group. For students who need more support in recalling information, please see our Base Tens, Multiplication Array, 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 Part I: Lunchtime Problems (Multiplication) 1.

FACILITATION TIP In the Intervention section, grid paper and a multiplication array are provided for distribution as needed.

2. 3.

a. DOK-1 What are we trying to ﬁnd out? We are trying to ﬁnd out how many cartons of strawberry milk we need to order.

FACILITATION TIP Students should circle the number of students and the number of rooms as the scenario is being read. Have students underline what they are solving for in each problem.

b. 4. 5. 6.

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Read the following scenario to the class: There have been some problems with lunchtime running smoothly, and we have been asked to help. Ordering the correct amount of milk for the kindergartners has been a problem. Order too much, and it spoils. Order too little, and the kindergartners are sad there isn’t enough for everyone. We don’t want either one of those things to happen! We know that ﬁve kindergarten students in each of the three kindergarten rooms order strawberry milk each day. Help us ﬁgure out how much strawberry milk we need to order. Give a Student Journal to each student. Read Part I together. Discuss the following questions:

DOK-1 What do we know? There are three kindergarten rooms. Five students from each room drink strawberry milk.

Show students the places marked off on the ﬂoor. DOK-1 Ask students to discuss what they think these represent. Three kindergarten classes Invite students to draw and label the boxes on their Student Journals. © Accelerate Learning Inc. - All Rights Reserved

9. 10.

11.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 Challenge the class to discuss with their tables or groups how to use the three boxes and the students in the class to model what is going on in the problem. a.

We can have ﬁve students stand in each of the boxes.

Give each student in the boxes a milk carton or other representation.

This way, each student represents a kid getting strawberry milk.

As students make suggestions (right or wrong), have the class act out and reason through each one. Discuss the following questions: a.

How do you know that?

Where are you getting this information?

How is this represented in our real-life model?

What information are we missing? How can we get it?

FACILITATION TIP As students are trying to create a model, they will need to modify and adjust. Guide students with questions as needed.

After the “real-life model,” distribute counters. FACILITATION TIP Challenge students to collaborate with their groups to draw a different model that represents the problem on their Student Journals and to write an equation with a Besides counting, ask students, “What letter that represents the unknown in the equation for their model (diagram, array, other operations can be used?” number line). Invite students to use counters to help. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 How can this model help us organize the information we have and plan how to ﬁnd a solution? It shows us how the separate pieces need to be joined. b.

DOK-1 Which part represents the whole? All of these counters, pieces, parts, groups, or parts of the number line combined

DOK-1 What are we trying tryi to ﬁnd out? We are trying to ﬁnd the total number of cartons of strawberry milk we need to order.

DOK-2 What equation can we write to represent the model? Explain. Our equation can be 3 × 5 or 5 × 3 because there are 3 groups with 5 strawberry milks in each group.

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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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.

e. DOK-2 What letter can we w use in our equation to represent the unknown value we are trying to ﬁnd out? Explain why this would be a good letter to use. Answers may vary. We can use the letter s for strawberry milk. We can use the letter c for cartons of strawberry milk. f.

12. 13.

DOK-1 Do we know the total number of cartons of strawberry milk we need to order? Answers will vary; some students will say no, while other students will have ﬁgured out the problem. Accept all answers.

Invite the class to share their different models and solutions. Explain that we can now see what we are trying to solve and the different ways to solve this problem. Discuss the following questions: a. DOK-1 How can we ﬁgure out how many cartons of strawberry milk to order each day for kindergarten? We can add 5 + 5 + 5; we can multiply 3 × 5. (Have students write this on their Student Journals under “Ways we can solve this problem.”) b.

FACILITATION TIP In groups, students can take turns reading the problem, drawing the models on the dry-erase boards, and writing the equation.

DOK-1 We have three groups of ﬁve. What is 3 × 5? It is 15. (Have students write this answer as a statement on their Student Journals.)

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Multiplication and Division Problem Solving Explore 1 – Model and Solve One-Step Problems Part II: Chicken Finger Boxes (Division) 1.

2. 3. FACILITATION TIP

Closely monitor groups, checking for understanding with the model, the equation, and the explanation.

Tell students that no one seems to know how many chicken fingers to order for the first-grade students on Wednesday. Read the following scenario to the class: First graders love chicken fingers! The teachers decided that 56 chicken fingers needed to be ordered for Wednesday’s lunch. There are 8 chicken fingers in a box. How many boxes need to be ordered? Distribute counters. Challenge students to determine how they might figure out how many boxes of chicken fingers need to be ordered. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 What are you trying to find out? We are trying to find out how many boxes of chicken fingers need to be ordered.

5. 6.

DOK-1 What do you know? First grade needs 56 chicken ﬁngers. There are 8 chicken ﬁngers in a box.

DOK-2 How could you model that with the counters? We could make stacks of eight counters to show the eight chicken ﬁngers in a box. Then, we could count the number of stacks.

As groups ﬁgure out how to model the problem with the counters, have them draw a picture of their model on their Student Journals. Invite students to discuss in their groups how their model could be represented by an equation. a. DOK-2 What is happening to the numbers? We are taking 56 chicken ﬁngers and breaking them apart into groups of eight. DOK-1 What operation is that? We are dividing.

DOK-2 Is your solution going to be greater or less than the number you began with? The solution is going to be less than the original 56 chicken ﬁngers.

d. DOK-3 How do you know? Since the total is being split into groups with an equal number in each group, the original number is being broken apart.

STEMscopes Tip 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.

e. DOK-2 What letter can we use in our equation to represent the unknown value we are trying to ﬁnd out? Explain why this would be a good letter to use. We can use the letter b for boxes of chicken ﬁngers. 7. 8. 9. 10.

Have students write the possible multiplication and division problems on their Student Journals and then write the solution to the problem. Have students read the second scenario and use the counters to ﬁgure out how to model the problem. Invite students to draw their models, write possible equations using a letter for the unknown, and solve the problem. Monitor and check for understanding and misconceptions.

Part III: Model and Solve 1. 2. 3.

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Tell students they have two more problems to solve to be able to place the lunch order. Challenge students to try different models to solve. Have students read the scenario, draw a model, write the possible equations using a letter for the unknown, and solve the problem. They should write their answer as a statement and then explain their reasoning.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Monitor and check for understanding and misconceptions. Ask guiding questions such as the following: a.

What do you know about the problem?

What are you trying to ﬁnd out?

How can you model this?

Can you model this a different way?

e. What are some equations that represent the problem?

What letter can you use to represent the unknown in the equation?

How can you justify the solution to your problem?

Briefly review strategies for solving multiplication and division problems. a. DOK-3 What strategies can help us find the solution to a multiplication or division equation? We can build an array or an area model. I can use repeated addition to add up each group. I can draw a picture, diagram, or number line. I have my multiplication facts memorized, so I can use what I remember to find a missing factor or the product.

DOK-3 How are models helpful? They help me see what is happening in the problem so I can ﬁgure out what I need to do to solve it. • DOK-2 What did you notice about the models you built? They all involved equal groups. They represented either multiplication or division problems. I was looking for the total, the number of groups, or the number in each group. •

Post-Explore

2. 3.

Focus students’ attention on the process of solving each problem and constructing the models instead of whether the factor is correct.

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

Math Chat

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.

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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FACILITATION TIP Reassure students that models are also thinking tools. Conceptualizing a problem using a physical model will help them be able to eventually just visualize it mentally and solve it more quickly. FACILITATION TIP This Exit Ticket can be used before the Explore activity as a pre-assessment and again as a formative assessment at the end.

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Multiplication and Division Problem Solving Explore 2 – Model and Solve Two-Step Problems ACTIVITY PREPARATION Students represent two-step multiplication and division problems within 100 using equations with a letter for the unknown and solve using manipulatives, pictorial models, or arrays.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. 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 Dream Vacation! Cards (per group) 1 Dream Vacation! Game Board (per class) 1 Dream Vacation! Answer Key (per teacher) 1 Exit Ticket (per student)

1 Resealable plastic bag (per group) 1 Die (per group) 1 Game board piece (per group) 1 Container (per group) 1 Pair of scissors (per group) 1 Projector or document camera (per class) Manipulatives: • • •

• •

Reusable • • • • • •

• • •

•

Base ten blocks Two-color counters Tiles

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 Dream Vacation! Cards for each group, and cut them apart. If desired, laminate them for future use. Place them in the plastic bag. Print the Dream Vacation! Game Board on card stock. If desired, laminate it for future use. Gather different objects for each group to be used as game pieces (for example, erasers, paper clips, counters, plastic counting bears). Prepare manipulatives, and place them in a central location so students may use them as needed to support in solving. Print the Dream Vacation! Answer Key and set it aside. You can use it to check a group’s answers when they ﬁnish a problem. For students who need more support in recalling information, please see our Base Tens, Multiplication Array, and Grid Paper 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. (Two-Color Counters, Base Ten Blocks, and Color Tiles)

PROCEDURE AND FACILITATION FACILITATION TIP To facilitate careful reading of the problems on the Dream Vacation! Cards, consider giving one to each student or pair of students so they can read it individually and perhaps circle and underline critical information. FACILITATION TIP Using letters (variables) to represent values may still be a new skill for many students. Always take time to reinforce the concept of using variables in equations. Encourage students to say the equations and variables out loud to become comfortable with the practice. 210

2. 3. 4. 5.

Read the following scenario to the class: Vacation is getting closer! Will you sleep in? Will you play with your friends? Will you go somewhere? Each card describes the dream vacation of other third-grade students. Represent and solve the problems together using diagrams, equations using a letter for the unknown, and base ten blocks. Get the answer correct, and you might be the ﬁrst to reach your dream vacation! Give a set of Dream Vacation! Cards to each group. Hold a brief discussion about a dream vacation. Where would students want to go? Give a Student Journal to each student. Read the example problem on the Dream Vacation! Card titled “Hiking!” together as a class.

Engage

Explore

Explain

Elaborate

Evaluate

Discuss the following questions: a. DOK-1 What is Lisbeth’s dream vacation? It is hiking.

DOK-1 What do we need to ﬁnd out? We need to ﬁnd out how many hiking trails Lisbeth can explore.

DOK-1 What do we know about the hiking trails? There are four hiking trails close to her. There are twice as many farther away.

DOK-2 How can we organize this information? We could build or draw models.

11. 12. 13.

Allow students to share how they modeled the problem. Discuss the following question:

Tell students that sometimes problems will need two separate models to solve different parts of the problem. Students may need to use one model to figure out one piece of information before answering the final question. Have students write “Hiking” on the “Dream vacation” line on their Student Journals. Give students time to explore with manipulatives to build their models. Invite students to draw their models on their Student Journals. Discuss the following question: a. DOK-3 How could we represent what we did with an equation using a letter for the unknown? We could multiply four by two to show how many trails were at the state parks and then add another four to find the total number of trails. I used the letter s to stand for the state parks and the letter t to stand for the unknown total number of trails. Note: Students may need guidance on how to translate these steps into an equation and determine letters to use to represent the unknown. Show them how one step can be shown using parentheses: (4 × 2) + 4 = t. Students could also write 4 + 4 + 4 = t.

14.

Allow students to solve the problem using any strategy they choose (if they haven’t solved it already). Discuss the following question: a. DOK-3 How did you choose to solve the problem? We know our multiplication facts, so we knew 4 × 2 was 8 and then added 4 to get 12. We built an array to show 2 groups of 4 and then added 4 more.

15.

16.

17.

FACILITATION TIP Model the example problem with correct answers ﬁrst. Then, model how to use the Game Board with correct and incorrect answers.

Note that there is more than one right way to model a problem. Give students ﬂexibility in how they create their models as long as their models accurately represent what is happening in the problem.

a. DOK-3 What challenges did you run into, and what did you do about them? We had two unknowns on our ﬁrst one. We needed to ﬁnd the total number of trails and the number of trails far away. We turned the far-away trails part into its model, found that number, then found the total number of trails. 10.

Acceleration

Students will likely struggle since the problem requires two steps. Some may calculate the far-away trails mentally. a.

8. 9.

Intervention

FACILITATION TIP The race involves each student completing their Student Journal with the models, equations, and solutions.

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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FACILITATION TIP Be mindful and purposeful in choosing each group of students. Scaffold the Dream Vacation Cards as needed.

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.

Tell students they are going to continue finding out information for their dream vacations, but they are also going to have a race to see which group gets to their dream vacation first. Divide the class into groups. Display the Dream Vacation! Game Board using a document camera. Assign each group a game piece, and place game pieces on “Start!” Have students look at the Dream Vacation! Game Board. Discuss the rules. When a group finishes a problem, they will take their papers to the teacher to be checked. (The teacher can choose a random paper to check from the group each time to ensure equal participation and collaboration.)

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Multiplication and Division Problem Solving Explore 2 – Model and Solve Two-Step Problems a.

Every time a group completes a problem and gets the answer correct, they will roll the die and move their group’s game piece forward that number of spaces.

If their answer is not correct, they will roll the die and move their game piece back that number of spaces.

If they can’t go back the designated number of spaces, they should return to start.

If their answers are incorrect, they will need to work through the problem again until they get the correct answer.

e. When they do get the correct answer, they will not roll the die again, but they may move their game piece ahead one space. FACILITATION TIP If students are not correct, encourage them to ﬁgure out their mistakes with help from their group members.

f. 18. 19. 20. 21. 22.

FACILITATION TIP

23.

Have students use strategies to identify the factors, the missing factors, and what is occurring in the problem.

Help students see that accuracy is more important than speed in this activity.

Explain that since everyone got the first problem correct, each group can roll their die and move their game piece forward on the Dream Vacation! Game Board. Allow each group time to choose 1 student from the group to roll the die and move their game piece. Students can choose any Dream Vacation! Card for the next problem and work on solving the rest of the problems. Remind students that they do not need to solve the example card (“Hiking!”) again. To solve each problem, students must first represent it using a model and develop an equation using a letter for the unknown. They should write their answers as statements and, on their last 4 problems, explain their reasoning. This will ensure everyone verifies the answer before the group rolls the die and moves their game piece. 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? Answers will vary.

FACILITATION TIP Consider posting these guiding questions for students to refer to as they collaborate.

What information does the problem give you? Answers will vary.

What information is missing? Answers will vary.

d. How could you model what is happening in the problem? Models will vary.

24.

What equation can you use to represent the problem? Equations may vary.

What letter can you use to represent the unknown? Explain why you chose this letter. Letters may vary.

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

212

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat DOK-3 How has learning about multiplication and division models helped you with your problem solving? It has helped me work out problems in an easier way. I know now that I can use strip diagrams, equations, manipulatives, and pictures such as arrays and area models to help organize and solve word problems in a way that is easy to see. • DOK-3 How can you determine what operations to use to solve a problem? It helps to draw a picture of what is happening in the problem. Once I draw a model, I can get a better idea of what I need to do. If I’m looking for the number of groups or amount in each group, I need to divide. If I’m looking for the total of all equal groups, I need to multiply. • DOK-2 How can you model a problem with multiple steps? We can use more than one model if we need to use two different operations or if there are several steps in a problem. •

Post-Explore 1. 2. 3.

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.

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.

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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Multiplication and Division Problem Solving Explore 3 – Model and Solve One- and Two-Step Problems ACTIVITY PREPARATION Students represent and solve one- and two-step problems involving multiplication and division using diagrams, equations with a letter for the unknown, and a variety of problem-solving strategies.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. 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 Printed • • •

1 Student Journal (per student) 1 Set of Math Hunt Posters (per class) 1 Exit Ticket (per student)

Reusable •

Preparation • • • •

•

1 Projector (per class, optional) Manipulatives: • • •

Base ten blocks Two-color counters Tiles

• •

•

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 Math Hunt Posters. Hang the six Math Hunt Posters around the room. Note: Do not hang them around the room in the same order they are in the Math Hunt Posters document (they should be shuﬄed and hung out of order). Place the counters and base ten blocks in a central location so students can access them if needed. Put students in pairs. For students who need more support in recalling information, please see our Base Tens, Multiplication Array, and Grid Paper 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. (Two-Color Counters, Base Ten Blocks, and Color Tiles)

PROCEDURE AND FACILITATION FACILITATION TIP

Each partner should take turns reading the posters, determining the operations, determining the strategy, and working the problem. FACILITATION TIP

Post the different strategies and examples on the board for students to use as a reference. Review the strategies before beginning the Explore activity.

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Read the following scenario to the class: You are going on a math hunt! To begin, pairs will be assigned to a problem. Your task is to organize the problem with a model or strategy, write the equation, use the strategy of your choice to solve it, and write the answer as a statement. Once you have written your solution statement, look around the room to ﬁnd the poster that has your answer at the top. Move to that poster, and start all over again! Good luck! Have the students discuss different strategies used to solve multiplication and division problems. Have a class discussion about problem-solving strategies. Be sure that diagrams, arrays, area models, and equations using a letter for the unknown are mentioned. Discuss the following question: DOK-2 How can models and strategies help you when you work on word problems? They can help by giving me strategies that are organized and make sense. I am able to show the problem in more than one way. They both organize the information and help me see possible solutions. Tell students that some of the problems are just division or multiplication problems, but some problems also include addition and subtraction. Their equations should include a letter for the unknown and at least one multiplication or division function, rather than just addition or subtraction. © Accelerate Learning Inc. - All Rights Reserved

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Let students know there are counters available at each poster to help them solve the problems if needed. 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? Answers will vary. b. What information does the problem give you? Answers will vary.

What information is missing? Answers will vary.

How could you model what is happening in the problem? Models may vary.

What equation can you use to represent the problem? Equations may vary.

What letter can you use to represent the unknown? Explain why you chose this letter. Letters may vary.

Review the Student Journal. Make sure students know they need to write the name of the poster and at least one equation using a letter for the unknown, and they need to show the strategy or model they used to solve the problem. They should write their answers as statements and then explain their reasoning. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

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.

FACILITATION TIP Instruct students to complete a self-check with each poster with the list at the top of the Student Journal. You can also post the list on the board.

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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Math Chat DOK-2 What strategy did you use to solve the problem? I used different strategies. Sometimes, I drew a picture to ﬁnd the solution. Sometimes, I knew the answer because I know my basic facts. Other times, I decomposed the numbers. • DOK-3 How can a model or strategy help you solve word problems? These can help me organize numbers to ﬁgure out how to solve the problem and how the numbers relate to one another. • DOK-3 How can making arrays and area models help you solve division word problems? They are visual ways to see what equal groups look like in columns and rows. • DOK-3 Why is it important for you to understand how to draw the model and know the equation that goes with it? It is important to know the equation that goes with the model because the model helps you understand why the equation works. If you just had the equation, it would just be numbers and symbols with no meaning. The models give meaning to the equation. •

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Remind students of some real-world applications to being able to accurately and eﬃciently ﬁnd answers to two-step problems. Being a good math problem solver can help us negotiate with others well, get better jobs, and be able to provide solutions for our neighbors and families. FACILITATION TIP Reassure students that using these models build a foundation for more complex equations they will be solving in later grades.

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Multiplication and Division Problem Solving 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 and Solve One-Step Problems 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 and Solve Two-Step Problems 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

Model and Solve One- and Two-Step Problems 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

Jordy’s Collection

Machinist

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

Keep on Trucking

Solve Multistep Multiplication and Division Problems within 100

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

Fluency Builder

Food Bank

Multistep Multiplication and Division Problem Solving within 100

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

MULTIPLICATION AND DIVISION PROBLEM SOLVING

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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

MULTIPLICATION AND DIVISION PROBLEM SOLVING

Multiplication and Division Problem Solving

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 to solve multistep mathematical problems.

I can use letters to represent unknown quantities.

What prompts will be used?

What does mastery look like?

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I can use a variety of representations to explain my work and to verify that my answer is reasonable.

I can make use of arrays, number lines, equal groups, repeated addition, and equations to solve problems.

I can recognize that there is more than one way to solve a problem.

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SCOPE 1

Area in Square Units Scope Introduction SCOPE SUMMARY Students work with plane ﬁgures, covering rectangular shapes with square tiles (units) to develop the concept that area is a measure of covering a given surface with no gaps or overlaps and is an attribute of plane ﬁgures. This begins the development of “square units” for students to recognize, comprehend, and apply the concept of area measurement. Students continue their understanding by counting the unit squares to provide precise measures. Student Expectations

3.GSR.7.1 Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same unit, with no gaps or overlaps, and determine the total area (total number of units that covered the space).

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Second grade works with equal groups, arranging objects in rectangular arrays of up to ﬁve rows and ﬁve columns and writing equations to express the total as a sum of addends using repeated addition. This prepares students to explore the concept of not only multiplication but also area as students use color tiles to cover the inside of a space.

Fourth grade continues the concepts learned by applying area and perimeter formulas to rectangles in real-world mathematical problems. Students use models and concrete objects to determine the area and perimeter of various rectangles. Students will 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) (4 ) and the formula for the area of a rectangle (ll × w)) by using models. Students will also solve problems for scenarios where the dimensions of a rectangle or a composite ﬁgure are already given, and the students have to apply the formulas for area and perimeter to determine a solution.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they: •

can create area models with colored tiles or block.

•

determine the area of a friend’s model by either counting or multiplying the side lengths.

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: •

ﬁnd the area of a rectangular space by multiplying the number of rows by the number of square units in each row.

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. 220

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Recognize Unit Lengths and Tile the Area of Rectangles In this exploration, students will work in groups to solve a scenario about protecting library books. They will use square tiles at stations to measure the cover of a book and record their ﬁndings to make book covers. Students will: •

recognize unit length.

•

use square tile to determine an area using square units.

Explore 2

Explore 1

EXPLORE ACTIVITIES Count Area in Square Units In this exploration, students will work through a set of task cards. Students will: •

AREA IN SQUARE UNITS

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ﬁnd the area of different shapes by counting the square units

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 an Exit Ticket for assessment.

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Area in Square Units 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 create area models with colored tiles or blocks and determine the area of a friend’s model by either counting or multiplying the side lengths. This activity is intended to assess mastery of the following standard(s): 2.NR.3.2 Use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

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Materials Printed •

Reusable

1 Student Handout (per student)

•

Consumable

1 Handful of colored tiles (per student)

•

1 Sticky note (per student)

Preparation • • •

Separate the colored tiles so that there are enough for each student to create an area model. Print a Student Handout for each student. Prepare to project page 1 of the Student Handout.

Procedure and Facilitation Points 1. 2. 3. 4. 5. 6.

Project page 1 of the Student Handout, and give each student a Student Handout and a sticky note to write the number of tiles used. Read the scenario as a class, and answer questions about the directions if needed. Allow several minutes for students to count the tiles and design their spaces. Read the directions for page 2 aloud. Allow several minutes for students to look at their friends’ designs and sketch them. Allow students to ﬁgure out the areas however they choose. Facilitate a class discussion about how they chose to ﬁgure out the areas. 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. a.

I counted the tiles.

I multiplied the number of tiles on one side by the number of tiles across the bottom.

I skip counted the number of tiles because I knew there were ___ groups of ___.

FACILITATION TIP To facilitate distribution of the tiles, consider passing out small bags rather than having students grab a handful. They can still choose how many to use. FACILITATION TIP Determine an eﬃcient way for students to visit and sketch two other models. Perhaps, assign groups of three before Step 3 so that students don’t need to rotate and leave their tile model unattended. FACILITATION TIP Consider having students do this step independently and silently, so that in step 5, they can collaborate with students near them.

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

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Area in Square Units Hook – Tiling the Patio ACTIVITY PREPARATION Students ﬁnd the area of a rectangular area by counting the number of nonoverlapping square units that ﬁt together without gaps to cover the space.

Materials

Preparation

Printed • •

• • •

1 Student Handout (per pair) 1 Square Centimeters, printed/cut/bagged (per pair)

Reusable • • • • • •

•

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1 Resealable bag (per pair) 1 Pair of scissors (per teacher) 1 Example of a 12” × 12” square ﬂoor tile (per class) (If this is not possible, cut out a 12” × 12” piece of construction paper or cardboard to show students the size of the tiles for the patio.)

Plan to show the Phenomena Video. Print a Student Handout for every pair of students. Print, laminate (if desired), and cut out 1 cm squares in a color (not white). Put 100 squares in a baggie for each pair of students. Acquire a 12” × 12” ﬂoor tile. If this is not possible, make a 12” × 12” piece of construction paper or cardboard to show students the size of the tiles being used for the patio.

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

FACILITATION TIP

Instruct students that there should not be any overlapping tiles or gaps in the patio design.

5. 224

DOK-1 Refer to Student Handout and ask the students, “What shape is the patio?” Rectangle

DOK-1 Hold up the 12” × 12” tile (or the 12” × 12” piece of construction paper that was prepared). Ask students, “What shape is this?” Square

DOK-2 Ask students, “How would you lay tiles like this down to cover the ﬂoor so there are no gaps and no overlaps?” Allow students time to brainstorm strategies with their partners. Discuss possible strategies as a class. Students should not solve yet.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4. 5. 6.

7. 8.

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

DOK-1 Refer to the Student Handout and ask students, “What shape is the patio?” Rectangle

DOK-1 Hold up the 12” × 12” tile (or the 12” × 12” piece of construction paper that was prepared). Ask students, “What shape is this?” Square

DOK-2 Ask the students, “How would you lay tiles like this down to cover the ﬂoor so there are no gaps and no overlaps?” Allow students time to brainstorm strategies with their partners. Discuss possible strategies as a class.

Review the problem and pair up students. Give each pair of students a copy of the Student Handout and a bag of 100 tiles (1 cm squares). Instruct students that they need to ﬁgure out how many tiles the family needs to tile their patio so it is completely covered. Inform students that the rectangle on the Student Handout represents dimensions of the patio. Each 1 cm square in the baggie they were given represents a 12” × 12” tile for the ﬂoor. Give students about 10 minutes to lay the tile and solve the problem. Discuss the following questions with the class: a.

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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.

DOK-2 What strategies did you use to lay the tile? i. We put them in rows. We started at the top (or bottom) and formed rows until the whole rectangle was covered. ii. We put them in columns. We started at the left (or right) and formed columns until the whole rectangle was covered.

DOK-2 How did you prevent gaps or overlaps? After the rectangle was covered, we pushed the squares tightly together. We made sure the small squares were in both neat rows and neat columns.

DOK-1 How many tiles will it take to cover the patio ﬂoor? 80

DOK-2 How did you ﬁgure out the total once the squares were in place? i. We counted each tile and there were 80. ii. There were 8 rows of 10 tiles. We counted by tens eight times. 10-20-30-40-50-60-70-80

e. DOK-3 Do you think your family should buy exactly that number of tiles? Why or why not? No, I don’t think my family should buy exactly that number because some of the tiles might break. (Or → Yes, I do think so because it saves money not to buy extra tiles that will not be used.) f.

DOK-3 Would it be easier or harder to find how many tiles are needed in a circular room? Why? It would be more difficult. They will not fit exactly, so we will not be able to use whole numbers.

FACILITATION TIP Follow up by asking whether construction workers have time, money or supplies to lay out a “practice ﬂoor” like this activity represents. This activity is a perfect lead in to why students need to know how to eﬃciently calculate areas abstractly.

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Area in Square Units Explore 1 – Recognize Unit Lengths and Tile the Area of Rectangles ACTIVITY PREPARATION Students recognize a unit length and practice tiling areas of rectangles using square units.

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 Older Books Station Cards (per class) 1 Exit Ticket (per student)

Reusable • • •

1 Set of inch tiles (per station) 1 Pair of scissors (per group) 1 Set of crayons (per group, optional)

• •

Consumable •

•

1 Piece of 9 × 12 construction paper (per group)

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print out a set of Older Books Station Cards, and place them around the room. Make sure they are accessible enough to tile and manipulate. *When printing the Older Book Station Cards, ensure the printer is set to Print Scale 100% (not Scale to Fit Page) so measurements will be correct. Prepare a set of inch tiles at each station. For students who need more support in recalling information, please see our Grid Paper 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. (Color Tiles)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Begin by discussing area and what it means: a.

DOK-1 Invite students to discuss with their shoulder partners what they know about the word area and share an answer with the class. Area can be a space, like a carpet area or a play area.

DOK-1 Can it be measured? How? Yes! We can use rulers or yardsticks.

FACILITATION TIP

DOK-1 If we only have these tiles (show tiles), how can we use these to measure the area of a rectangle or square? We can cover the shape with the tiles and count the tiles to determine the side lengths and the area.

Use the Visual Glossary or Picture Vocabulary to clarify the deﬁnition of area. Take time to differentiate area from perimeter. Students will need repeated exposure of these terms to learn to ﬂuently use them in later standards. FACILITATION TIP Ask students how this type of measurement is different from perimeter. Emphasize that area is measured in square units, while perimeter is measured in regular units. Compare the size of one foot with the size of one square foot. Many classrooms have square-shaped tiles that are one foot by one foot, and they make a great reference point for conceptualizing one square foot. 226

Generate a list of real-world applications of area. Examples may include determining how many square feet of paint are needed to cover a wall or determining how many square tiles it would take to cover a ﬂoor.

4. 5.

Read the following scenario to the class: The school librarian discovers some old books in the back of a locked cabinet in the library. She sees that the books are in good shape but is worried that since they are older and fragile, they need to be covered for protection. Will you help her protect these books? Explain to the students that at each station, they will use the square tiles to measure the cover of the book and record their ﬁndings in their Student Journals, which will be their Book Cover Logs to use as they make the book covers. Give a Student Journal to each student, and assign each group to a station. Ask the groups to rotate after they are given a suﬃcient amount of time at each station.

Engage

Explore

Explain

Elaborate

Evaluate

Encourage students to use the tiles appropriately, lining them up with no gaps or overlaps.

Ensure students are counting each tile to come to the correct area measurement.

Discuss the following question:

Assign each group to a book to re-create the book cover using construction paper. a.

Give each group a piece of construction paper.

Have each group tile the book cover shape on the construction paper, trace it, and cut it out.

Optionally, have students decorate their book cover if time allows.

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

Math Chat • • •

Acceleration

Actively monitor each group’s discussion for misconceptions.

i. DOK-1 How are you ﬁnding the measurements with the square tiles? I am placing the tiles to cover the inside of the shape, and I am counting to ﬁnd the side lengths and the area. 7.

Intervention

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.

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FACILITATION TIP Consider saving Page 3 of the Student Journal to complete during the Math Chat all together.

DOK-1 What does the length of the shape tell us about the squares covering it? The length in inches matches the same number of squares covering it. DOK-1 What does the width of the shape tell us about the squares covering it? The width in inches matches the same number of squares covering it. DOK-1 What does the area of the shape tell us about the squares covering it? The number of squares covering the shape is the area.

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. On this Exit Ticket, determine ahead of time if you want to provide some constraints for Complete the Anchor Chart as a class. the Patch design. Students may want to Have each student complete their Interactive Notebook. create composite shapes or a patch that is 1 by 1.

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Area in Square Units Explore 2 – Count Area in Square Units ACTIVITY PREPARATION Students work through a set of task cards to ﬁnd the area of rectangles by counting the square units.

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 Set of Task Cards (per class) 1 Set of Station Printouts (per class) 1 Exit Ticket (per student)

Reusable • •

1 Set of inch square tiles (per station) 1 Sheet protector (per station)

Preparation • • • •

• • • • •

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 Task Cards, on card stock if possible. Print a set of Station Printouts, and laminate (if desired) or put in a sheet protector for durability. *When printing the Station Printouts, ensure the printer is set to Print Scale 100% (not Scale to Fit Page) so measurements will be correct. Place the Task Cards around the room in the form of a gallery walk. Place each Station Printout in an accessible place for students to tile next to the Task Card it matches. (For example, Task Card 1 should be next to Station Printout 1.) Place a set of inch tiles at each station. For students who need more support in recalling information, please see our Grid Paper 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. (Color Tiles)

PROCEDURE AND FACILITATION POINTS 1.

2. FACILITATION TIP For each Station card, provide multiple sticky notes with the titles of “length” and “width” on each. The students can begin with labeling the Station cards ﬁrst before building the model. 228

4. 5.

Invite the students to discuss the following questions: a.

DOK-1 What are we measuring when we ﬁnd the area? The amount of space inside a shape

DOK-1 What is a way of ﬁnding the area of a shape? Counting the square units inside the shape

DOK-1 Why do we call it a “square unit”? When we mark off the side lengths for the unit, they create a square.

Explain to students that they are going to be working through the Task Cards to ﬁnd the area by counting each square unit. Tell students that they will collaborate with their partners to use colored tiles to re-create the shapes in the scenarios, label the side lengths, count the tiles to determine the area, and record their ﬁndings on their Student Journals. Give a Student Journal to each student. Assign each pair to a Task Card, and then have the class rotate through until they have completed each Task Card. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

As students collaborate, monitor and assess understanding with the guiding points below: a.

Ensure that students are not counting the sides of the squares but each square shape inside the ﬁgure, as well as measuring the space within the shape rather than the distance around it.

Encourage students who are “free counting” to mark or label each square as they count to prevent any miscounting that may occur.

Intervention

Acceleration

FACILITATION TIP Model on the board how the total area is determined by the area of each smaller ﬁgures. Each smaller area is added together to ﬁnd the total area in square units.

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

Math Chat DOK-2 What are some observations you made as you were determining the area of each figure? We noticed that the rectangular shapes reminded us of arrays. They had rows and columns of tiles. • DOK-2 What were some challenges you saw in finding the areas with a large number of tiles? If an area is made up of a large number of tiles, it might be difficult to count accurately, and it would take a long time to count the total number of tiles in the shape. • DOK-3 Do you think there could be a different way to find the area based on your observations? For many of these shapes, we could multiply the side lengths like we do for arrays. The length represents the number of columns, and the width represents the number of rows. •

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Remind students of the many real-world applications of being able to accurately calculate area: landscaping, rooﬁng, painting, room capacity numbers, creative design, and many more. FACILITATION TIP For this Exit Ticket, consider allowing students to create composite ﬁgures for the second question if they are able.

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Area in Square Units 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

Recognize Unit Lengths and Tile the Area of Rectangles 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

Count Area in Square Units 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

230

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

Penny’s Pine Cone Project

Jamie Paul Durie

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

Robots Rule

Match Arrays with Area Models

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

Gardens Galore!

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

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AREA IN SQUARE UNITS

Area in Square Units 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?

AREA IN SQUARE UNITS

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What does mastery look like?

I can recognize area as an attribute of rectangular ﬁgures.

I can cover a rectangular space using the same-sized unit squares (squares with a side length of one unit).

I can count unit squares to determine area.

I can use multiplication to determine the area of a rectangular ﬁgure.

I can use addition to determine the area of a rectangular ﬁgure.

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SCOPE 1

Apply the Area Formula Scope Introduction SCOPE SUMMARY Students tile the area of different rectangles in real-world contexts, discovering that area can be determined by multiplying whole-number side lengths. The distributive property is applied to area models as students decompose rectilinear shapes and connect the operations of multiplication and addition to area, using this knowledge to solve real-world problems. Student Expectations

3.GSR.7.2 Determine the area of rectangles (or shapes composed of rectangles) presented in relevant problems by tiling and counting. 3.GSR.7.3 Discover and explain how area can be found by multiplying the dimensions of a rectangle.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Second grade works with equal groups, arranging objects in rectangular arrays up to ﬁve rows and ﬁve columns and writing equations to express the total as a sum of addends using repeated addition. This prepares students to explore the concept of not only multiplication but also area as students use color tiles to cover the inside of a space. In the previous scope, students explore the concept of area measurement by using concrete models to build a conceptual understanding of area in square units.

Fourth grade continues the concepts learned by applying area and perimeter formulas to rectangles in real-world mathematical problems. Students use models and concrete objects to determine the area and perimeter of various rectangles. Students will extend their knowledge base to determine the formulas for the perimeter of a rectangle (l (l + w + l + w OR 2l + 2w)) and a square (4s) (4 and the formula for the area of a rectangle (l (l × w) by using models. Students will also solve problems for scenarios where the dimensions of a rectangle or a composite ﬁgure are already given, and the students have to apply the formulas for area and perimeter to determine a solution.

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

determine the area of rectangles by counting to ﬁnd the total number of square units and describing the measurements using a number and the unit.

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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: •

ﬁnd the area of each rectangle by multiplying the length (in feet) by the width (in feet).

•

describe how area has an additive property.

•

add the area of each rectangle together to ﬁnd the sum, which is the total area of the “L-shaped kitchen island.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Relate Tiling to Multiplication In this exploration, groups of students will solve problems about crops and help determine how many total crops of corn can be planted in a garden. Students will: •

calculate the area of each section of the garden.

•

determine the area of a rectangle using wholenumber side lengths.

•

multiply the number of rows by the unit squares in each row.

Explore 2

Explore 1

EXPLORE ACTIVITIES Problem Solve for Area with Multiplication In this exploration, students will solve a scenario about determining the area of different drawn buildings. Students will: •

calculate the area of different drawn buildings by applying the area formula.

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Once students have solved the scenario, they discuss their learning with the class and ﬁnish with an Exit Ticket.

Area and the Distributive Property In this exploration, groups of students will tile a rectangular area. Students will: •

Explore 4

Explore 3

After completing the activity, students share their learning and conclude with an Exit Ticket.

decompose the dimensions of a rectangle using the distributive property of multiplication to determine the area.

Solve for Area in Composite Figures In this exploration, groups will work collaboratively to make a small quilt for a puppy to snuggle with at night. Students will: •

determine the area of composite ﬁgures.

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

Upon completion of the Explore activities, they will discuss their learning and complete an Exit Ticket for assessment.

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APPLY THE AREA FORMULA

Apply the Area Formula 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 determine the area of rectangles by counting to ﬁnd the total number of square units and describing the measurements using a number and the unit. This activity is intended to assess mastery of the following standard(s): 3.GSR.7.1 Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same unit, with no gaps or overlaps, and determine the total area (total number of units that covered the space).

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Materials Printed •

1 Student Handout (per student, group, or class)

Preparation •

Print a Student Handout for each student or group, or prepare to project the Student Handout for the class.

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

Distribute a Student Handout to each student or group, or project the Student Handout for the class. Instruct students to look at the areas and area pictures. The students will match the area picture with the correct area. With partners, groups, or the whole class, facilitate a discussion about the strategies students used to determine the areas of the rectangles. 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. a.

I counted the number of square units.

I multiplied the number of units on one side (width) by the number of units on the bottom (length).

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

FACILITATION TIP Consider projecting only one part of the Student Handout. Depending on your students, start with the pictures only or the areas to start. FACILITATION TIP Distinguishing between area and perimeter is an essential math skill needed for all subsequent geometry standards. Take time to illustrate. FACILITATION TIP As an extension, consider bringing perimeter into the discussion. You could add matching correct perimeters to the matching correct areas and challenge students to match both.

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Apply the Area Formula Hook – New Island in the Kitchen ACTIVITY PREPARATION Students find the area of an L-shaped kitchen island by decomposing it into two nonoverlapping rectilinear figures. Students will find the area of each rectangle by multiplying the length (in feet) by the width (in feet). Students will demonstrate an understanding that area is additive by adding the area of each rectangle together to find the sum, which is the total area of the L-shaped kitchen island.

Materials

Preparation

Printed •

• • •

1 L-Shaped Kitchen Island (per pair)

Reusable • • •

Plan to show the Phenomena Video. Print an L-Shaped Kitchen Island for each pair. Prepare to project L-Shaped Kitchen Island.

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1 Ruler (per pair)

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

FACILITATION TIP

Project images of different L-shaped kitchens for students to visualize.

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.

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4. 5.

Project L-Shaped Kitchen Island to the class. Discuss the following questions with the class: a.

DOK-3 How will making a model of the kitchen help us find the area? You will use the area formula (L × W) to find the area of both rectangular areas in the L. Then, you will add both of the areas to find the total area in square feet.

DOK-2 If the scale is 1 square inch on the paper is equal to 1 square foot in the kitchen, what will the answer in square inches be? It will be equivalent to the number of square feet the life-size island will be. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-3 If you could not use the area formula, what is another way to ﬁnd the area of the kitchen island? You could use tiles (1 square inch on the paper or 1 square foot on the ﬂoor) to mark out the area. Then, you would count the tiles to determine the number of square feet in the island.

Move on to complete the Explore activities.

Intervention

Acceleration

FACILITATION TIP Listen to see if students know the area formula or if they notice that there are 2 rectangles with different areas.

Part II: Post-Explore 1. 2.

3. 4. 5. 6.

7. 8.

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

DOK-3 How will making a model of the kitchen help us find the area? You will use the area formula (L × W) to find the area of both rectangular areas in the L. Then you will add both of the areas to find the total area in square feet.

DOK-3 If you could not use the area formula, what is another way to ﬁnd the area of the kitchen island? You could use tiles (1 square inch on the paper or 1 square foot on the ﬂoor) to mark out the area. Then you would count the tiles to determine the number of square feet in the island.

APPLY THE AREA FORMULA

Home

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.

Review the problem, and pair up students. Give each pair of students a ruler and an L-Shaped Kitchen Island. Instruct students that they need to figure out how many square feet the island is. Give students about five minutes to decompose the image into two rectangles, measure the length and width of the first rectangle in inches with the ruler, find its area, measure the length and width of the second rectangle, find its area, and add FACILITATION TIP the two areas together to find the total area (in square inches and then converted to square feet) of the proposed L-shaped kitchen island. Direct attention to the rulers and make sure students are measuring in inches, not Have one pair present their answer to the class. By a show of hands, determine centimeters. whether all groups got the same proposed area for their islands. Discuss the following questions with the class: a.

DOK-2 How did you ﬁnd the area of your kitchen after you made your model? i. We decomposed the L shape into two rectangles. (Some students may have chosen to use scissors to physically decompose it.) ii. Next, we used a ruler to measure the length and the width of each rectangle in inches.

FACILITATION TIP Have groups share with other groups their strategy to ﬁnd the area.

iii. For each rectangle, we multiplied the length by the width. This gave us the area of each rectangle. iv. b.

Then, we added the area of each rectangle together to ﬁnd the total area of the proposed L-shaped kitchen island.

DOK-2 How could you check your answer to see if you did the area calculations correctly? i. We could use repeated addition or we could use square-inch tiles placed (without overlapping and with no gaps) on the two rectangles to ﬁnd the area in square inches and then convert that value to square feet.

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APPLY THE AREA FORMULA

Apply the Area Formula Explore 1 – Relate Tiling to Multiplication ACTIVITY PREPARATION Students determine the area of a rectangle by connecting the whole-number side lengths to using multiplication of the number of rows by the unit squares in each row.

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.6 Attend to precision.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Corn Plants (per class) 1 Set of Garden Plans Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • •

15 Colored tiles (per group) 1 Resealable bag (per group)

•

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Corn Plants for the class and a set of Garden Plans Cards for each group. If students are not able to use the virtual manipulatives, prepare 15 colored tiles in a bag for each group. For students who need more support in recalling information, please see our Multiplication Array 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: Corn Plants 1. 2.

3. 4. FACILITATION TIP Remind students that when a rectangular array is formed, there are no gaps or overlaps and that each row and each column must contain the same number of tiles.

5. 6. 7.

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Give a Student Journal to each student and a set of 15 colored tiles to each group. Read the following scenario to the class: A farmer plants crops in equal rows. This picture shows the plan the farmer is making for the corn plants. The plan is not yet ﬁnished. Can you help determine the area and how many total corn plants can be planted in the garden? Display the image of the Corn Plants. Monitor and talk with students as needed to check for understanding by using the following guiding question: DOK-1 What do you notice? There is a row going up and down with six corn plants in it. There is a row going across that has ﬁve corn plants in it.

Tell students to use their tiles to create a model similar to the Corn Plants. They should make a row of six going up and down and then a row of ﬁve left to right. Students will draw this model on their Student Journals. After Part I, 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 many tiles did you use? I used 10 tiles. DOK-1 Do you have enough tiles to cover the entire space? No DOK-1 Each corn plant is planted in a 1 ft. space. If the farmer plants six corn plants in a row going down the side of his garden, about how many feet long is the garden? The garden is about 6 feet long. Students should label this measurement on their Student Journals. DOK-1 If the farmer plants five corn plants in a row across the bottom of the garden, about how many feet wide is the garden? Students should label this measurement on their Student Journals. The garden is about 5 feet wide. DOK-1 What do we know about the farmer’s garden? It is 6 feet long and 5 feet wide. DOK-1 What shape is the garden? It is a rectangle. DOK-1 What do we know about the sides of rectangles? A rectangle has two pairs of equal sides. If we know the length of one side, we know the opposite side is the same length. DOK-1 What is the length and width of the missing sides? Students should label these measurements on their Student Journals. The missing sides are 6 feet long and 5 feet wide. DOK-1 How many rows is the farmer going to plant? The farmer is going to plant six rows. DOK-1 How many corn plants can the farmer plant in each row? The farmer can plant five in each row. DOK-3 We do not have enough tiles to model his garden in complete rows. How could you figure out how many corn plants the farmer can plant in the garden? Students might suggest drawing lines to create squares in equal rows. They might use mental math to determine how much six groups of five equals or how much five groups of six equals.

11.

FACILITATION TIP Precision in language is essential for effective mathematical discourse. Review the terms length and width. Length refers to the longer side of a rectangle, and width refers to the shorter side of a rectangle. FACILITATION TIP If students have diﬃculty observing that there are 5 or 6 rows, ask them to rotate their Student Journals 90 degrees so that the position of the sides is reversed. FACILITATION TIP Feature student strategies such as skip counting and repeated addition.

Students should see that you can make six groups of five or five groups of six to find how many corn plants can be planted in the farmer’s garden. Discuss the following question: a.

9. 10.

APPLY THE AREA FORMULA

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DOK-2 What operation can we use to determine the total? We can use multiplication.

Explain that the entire space inside the garden is called the “area.” Students will record the equation they could use to ﬁnd the area of the farmer’s garden. They will multiply the number of rows by how many corn plants are in each row. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How many corn plants can the farmer plant in his garden? The farmer can plant 30 plants.

DOK-1 What is the area of the garden? The area of the garden is 6 feet × 5 feet = 30 square feet. i. Explain that when we are measuring in units, we have to put “squared” or “sq.” in front of the units in our answer because each piece we’re talking about is a square.

FACILITATION TIP If students use repeated addition, challenge them to think of a more eﬃcient method of calculation. Discuss why multiplication is faster than repeated addition. 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.

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APPLY THE AREA FORMULA

Apply the Area Formula Explore 1 – Relate Tiling to Multiplication Part II: Garden Plans 1. 2.

Pass out a set of Garden Plans Cards to each group. Students will work with partners or small groups to complete this portion of the activity. Students will ﬁgure out the area of each section of the garden. Students can use the tiles if necessary. a.

3. 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.

Note that it is intentional that students do not have enough tiles to build the whole area model. This is to drive students to use multiplication to calculate the area of a rectangle instead of counting squares.

Students should draw a model of each section and record an equation that could help them determine the area of the space. 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 the figures? They were all rectangles. I could not completely fill them with tiles. DOK-3 What did you have to do to figure out the area of each figure? I had to count the rows and how many were in each row. I multiplied those numbers since I knew I was going to have ___ rows of ___, or ___ groups of ____. DOK-3 How can you find the area of a rectangle if there is not a figure shown? I can multiply the length by the width. I can draw a figure if I need 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. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

APPLY THE AREA FORMULA

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APPLY THE AREA FORMULA

Apply the Area Formula Explore 2 – Problem Solve for Area with Multiplication ACTIVITY PREPARATION Students determine the area of different drawn buildings by applying the area formula.

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.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 •

1 Set of colored tiles (per group) •

Plan to divide the class into 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 Scenario Cards for each group of students. Prepare 1 set of colored tiles per group. Have extra ready if needed. For students who need more support in recalling information, please see our Multiplication Array 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 1.

FACILITATION TIP Assign roles to each group that can be rotated: reading the scenarios to the group, identifying the length and width, creating the model with the colored tiles, and writing the expression.

2. 3. 4. 5.

FACILITATION TIP Groups can compare their answers to other groups for speciﬁc problems. Then, have students discuss their strategies in the Math Chat. 244

Read the following scenario to the class: You and your family have decided to take a little vacation to the mathematical world of Rectangula! Your family has visited Rectangula many times, but it has gotten so much busier and is growing so quickly. As you walk down Main Street in the city, you notice there is so much to do! With your group, you will be discovering lots of things about this bustling city! Give a Student Journal to each student. Distribute the Scenario Cards and colored tiles to each group. Student groups will read the Scenario Cards, and each student will solve each scenario following the instructions on their Student Journals. As students collaborate, actively monitor and assess their work for misconceptions: a.

Ensure students are multiplying and not adding, as if to ﬁnd the perimeter.

Encourage students who are struggling with multiplication facts to use a strategy to solve, such as skip counting, making a T-chart of multiples, or using the provided tiles to make an array/model of the scenario.

Engage

Explore

Explain

Elaborate

Evaluate

Math Chat • •

•

1. 2. 3.

DOK-3 Did you need the lengths of all four sides of the shapes to find the area? Explain. No, I only needed the length and the width of the shape to find the area. DOK-2 What steps did you take to solve the problems? Since all the figures were rectangles, I was able to multiply the length times the width to figure out the area inside the figures. DOK-2 Why is area measured in square units? Why are they called that? The area of a shape is the number of squares needed to cover the inside completely; a square unit is a square with side lengths of one square unit. 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 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.

APPLY THE AREA FORMULA

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APPLY THE AREA FORMULA

Apply the Area Formula Explore 3 – Area and the Distributive Property ACTIVITY PREPARATION Students tile a rectangular area and decompose the dimensions of a rectangle using the distributive property of multiplication to determine the area.

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.6 Attend to precision.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Exploration Sites (per class) 1 Exit Ticket (per student)

• • •

Reusable • •

100 colored tiles (per group) 1 Ball of yarn (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 Exploration Sites on card stock, with the option to laminate for durability. Cut a piece of yarn 14 inches long for each station. Place a set of counters and a piece of yarn at each station. For students who need more support in recalling information, please see our Multiplication Array 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 FACILITATION TIP

Show images or short videos of exploring the deep sea to provide context to the activities.

FACILITATION TIP

2. 3.

Direct attention to the key on the Exploration cards for students to determine the square unit.

4. 5. 6. 7.

FACILITATION TIP Groups answers will vary. Expressions should match how the group divided the Exploration areas. 246

Read the following scenario to the class: As a deep-sea explorer, you are one of the luckiest people on Earth! You get to see a world that is unexplored by most people. In your expeditions, you scour the depths of the ocean to find long-lost treasure and undiscovered or rare species and study incredible underwater plants and landforms. You are planning for an upcoming expedition and have scoped out six exploration sites. However, because the exploration is so detailed and timeconsuming, you have to break each exploration site into two days in order to have enough oxygen underwater. Are you ready to dive in? Explain that at each exploration site, there is a layout of the site. Emphasize that some sites may be in square feet, and others may be measured in square meters. Motivate the students to use the tiles to model the site after the layout. Challenge them to discuss and collaborate to find the best way to break the exploration site into two days using the yarn as a separation for the two parts. Tell students they must sketch an area model labeling the dimensions reflecting how the area will be broken down into two parts. Explain that because it is important to have enough oxygen, all plans must be thoroughly recorded. Tell students to write an expression that represents the area covered each day, as well as how they will use those products to determine the total area of the exploration site. © Accelerate Learning Inc. - All Rights Reserved

9. 10.

11.

Engage

Explore

Explain

Elaborate

Evaluate

Allow students to collaborate and discuss different options to break down the exploration area. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What are the dimensions of the exploration area? Answers may vary depending on the exploration site. Students should name the number of feet/meters for the width and length of the area.

DOK-3 How can this help you determine which dimension to break apart? Answers may vary. 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 obtaining an answer easier because I’m using different numbers.

DOK-2 Does breaking it apart change the total area being explored? How do you know? It does not change. The total area is still being explored; it is just being broken apart into smaller pieces.

Intervention

Acceleration

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.

APPLY THE AREA FORMULA

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

Math Chat DOK-3 How did you determine how to break down the area? Was there more than one way? 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 obtaining an answer easier because I’m using different numbers. Yes, there were multiple ways of breaking down the dimensions. • DOK-3 How is this skill useful? This skill is useful when we need to multiply larger numbers; we can break it apart and multiply smaller, more familiar factors and add the products to get the answer. •

Explain that this process is called the “distributive property,” and it states that numbers can be decomposed, or broken apart, and “distributed” to each of the decomposed numbers to multiply to obtain the same answer as multiplying the original two factors. •

DOK-2 Does breaking it apart change the total area being explored? How do you know? No, breaking up the site into parts did not change the total area. This is because the dimensions and size of the site did not change, only how we explored it.

FACILITATION TIP Reassure students that using this skill supports their ability to visualize complex problems in more than one way. They will use this model in later math standards. It will also help them problem solve in many careers (landscaping, rooﬁng, ﬂooring, painting, creative design).

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 having students complete this Exit Ticket, consider providing some constraints for students regarding the shape and size of the two different areas.

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APPLY THE AREA FORMULA

Apply the Area Formula Explore 4 – Solve for Area in Composite Figures ACTIVITY PREPARATION Students determine the area of composite ﬁgures.

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.6 Attend to precision.

Materials

Preparation

Printed

Part I: A Quilt for Your Puppy

• • •

1 Student Journal (per student) 1 Set of Fabric Scraps (per group) 1 Exit Ticket (per student)

• • •

Reusable • • •

1 Pair of scissors (per teacher) 1 Calculator (per group) 1 Ruler (per group)

• Set 1 •

Consumable • •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Measure and cut out rectangles from colored card stock. There will be six sets of three rectangles. Place each set in a resealable bag, and label each bag with its corresponding set number.

Rectangle 1: 9 in. by 6 in.

•

Rectangle 2: 6 in. by 4 in.

•

Rectangle 3: 3 in. by 4 in.

•

Rectangle 2: 10 in. by 3 in.

•

Rectangle 3: 8 in. by 2 in.

•

Rectangle 2: 7 in. by 6 in.

•

Rectangle 3: 6 in. by 2 in.

•

Rectangle 2: 7 in. by 4 in.

•

Rectangle 3: 9 in. by 2 in.

•

Rectangle 2: 11 in. by 5 in.

•

Rectangle 3: 11 in. by 8 in.

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Rectangle 2: 6 in. by 6 in.

•

Rectangle 3: 6 in. by 5 in.

• Set 2

6 Resealable bags (per class) 18 Sheets of colored card stock (per class)

•

Rectangle 1: 10 in. by 5 in.

• Set 3 •

Rectangle 1: 9 in. by 3 in.

• Set 4 •

Rectangle 1: 7 in. by 5 in.

• Set 5 •

Rectangle 1: 11 in. by 4 in.

• Set 6 •

Rectangle 1: 11 in. by 7 in.

Part II: Collage of Love • •

•

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Print a set of Fabric Scraps for each group. Cut the cards apart on the dotted lines. For students who need more support in recalling information, please see our Multiplication Array 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)

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS Part I: A Quilt for Your Puppy 1.

2. 3. 4. 5.

6. 7. 8. 9. 10.

11.

Read the following scenario to the class: You are making a small quilt for your puppy to snuggle with at night. You have already gone to the store and selected the fabric. The lady at the store cut the fabric into three pieces. You want to know how big your quilt is going to be, so you need to measure each piece and assemble them into one large quilt. Give each student a Student Journal. Give each group a set of rectangles (set 1, 2, 3, 4, 5, or 6) and a ruler. They will need a calculator for the last question in Part I of their Student Journals. Students will begin by measuring the length and width of their three rectangles. Tell students ahead of time that they will be measuring in inches. Explain that they will be sketching a model of their three rectangles on their Student Journals. Emphasize that these are not to scale, but only representations. Have students find the area of each individual rectangle. Students will then arrange their rectangle pieces to make one larger rectangle. This represents the quilt. No ends should be overlapping or sticking out. Ask students to draw a model of their larger rectangle on their Student Journals and label their measurements. Give students time to find the area of their entire quilt. They should add the three areas of the smaller rectangles to find out the area of the largest rectangle. Encourage students to collaborate to complete Part I of their Student Journals. Students will need a calculator to check their work for one of the questions in their Student Journals. Answers for each set of rectangles are listed below: a.

Set 1

APPLY THE AREA FORMULA

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FACILITATION TIP Alternatively, students might add the side lengths ﬁrst and then ﬁnd the area of the composed rectangle. Make note of all strategies students apply, and refer to them during the Math Chat.

FACILITATION TIP Challenge early ﬁnishers to explore whether there is more than one way to arrange the set of rectangles and whether this affects the total area.

i. Areas of rectangles: 54 sq. in., 24 sq. in., 12 sq. in. ii. Area of large composite rectangle: 90 sq. in. b.

Set 2 i. Areas of rectangles: 50 sq. in., 30 sq. in., 16 sq. in. ii. Area of large composite rectangle: 96 sq. in.

Set 3 i. Areas of rectangles: 27 sq. in., 42 sq. in., 12 sq. in. ii. Area of large composite rectangle: 81 sq. in.

Set 4 i. Areas of rectangles: 35 sq. in., 28 sq. in., 18 sq. in. ii. Area of large composite rectangle: 81 sq. in.

e. Set 5

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.

i. Areas of rectangles: 44 sq. in., 55 sq. in., 88 sq. in. ii. Area of large composite rectangle: 187 sq. in. f.

Set 6 i. Areas of rectangles: 77 sq. in., 36 sq. in., 30 sq. in. ii. Area of large composite rectangle: 143 sq. in.

12.

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

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APPLY THE AREA FORMULA

Apply the Area Formula Explore 4 – Solve for Area in Composite Figures Math Chat DOK-2 How did you ﬁnd the area of each rectangle? We multiplied the length times the width. • DOK-1 When you put the three rectangles together, what shape was made? A larger rectangle was made. • DOK-3 How could you ﬁnd the area of your quilt? Students should suggest adding the three areas of the rectangles. •

Part II: Collage of Love Students will continue working in their groups from Part I. 1.

FACILITATION TIP

Tactile and visual learners may beneﬁt from building the ﬁgures with one-inch tiles.

Read the following scenario to the class: After making your puppy’s quilt, you have a few scraps left over. You have always said your pets are like family, so you decide to make and frame a collage from the scraps to match your puppy’s quilt to hang in your room. In order to make the collage, you will need smaller rectangles. Decompose the scraps to create your collage of love! Give each group one ﬁgure from Fabric Scraps. Tell them this is their piece of scrap fabric. Explain that this is a scale model of the actual piece of fabric. a.

Students will observe their ﬁgures. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP Students will likely decompose the figure into rectangles and find the sum of the decomposed areas. Challenge early finishers to consider an alternative approach by composing a larger rectangle. (Find the area of the larger rectangle, find the area of the rectangular-shaped extra space, and subtract the area of the extra space from the area of the larger rectangle.)

4. 5.

250

DOK-1 What shape is your ﬁgure? Students might suggest it mostly looks like a rectangle, but there is a section that sticks out. They might suggest it looks like several shapes put together.

DOK-1 Does it look like your ﬁgure could be made up of more than one shape? Yes.

DOK-1 What shapes make up your ﬁgure? Students should suggest that their ﬁgure looks like several rectangles.

DOK-2 How can you ﬁnd the area of your ﬁgure? Allow students time to discuss this with their groups.

Students will complete Part II of their Student Journals. After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

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.

Optionally, you can create the actual size of the ﬁgures from Fabric Scraps on butcher paper.

DOK-1 Can we find the area of shapes that are not perfect rectangles? Yes DOK-2 How did your group find the area of your figure? We had to section off the figure into more than one rectangle. We then found the length and width of each rectangle and then the area. Then, we could add all the areas to find the total area of the shape. Allow groups to share how they decomposed the figures. Emphasize that there is more than one way to solve these problems.

• •

DOK-3 How can we find the area of a rectangle if we cannot see how many individual units there are? We can multiply the length by the width. DOK-2 How can knowing how many rows and how many are in each row help you find the area of a space? We can multiply the number of rows and how many are in each row to find out the area.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Prior to having students complete this Exit Ticket, determine if they are allowed to use any method and how they are to show their thinking.

APPLY THE AREA FORMULA

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251

APPLY THE AREA FORMULA

Apply the Area Formula 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

Relate Tiling to Multiplication 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 for Area with Multiplication 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 and the Distributive Property

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 for Area in Composite Figures

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

252

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 Great Performance

Interior Designer

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

A Wild Weather Day

Area – Models and Number Sentences

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

PhET Interactive Simulation

This Place is a Zoo!

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

APPLY THE AREA FORMULA

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253

Students who are still acquiring the concept and need remediation

APPLY THE AREA FORMULA

Apply the Area Formula

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

254

 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?

APPLY THE AREA FORMULA

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I can ﬁnd the area of a rectangle by tiling it and by multiplying the dimensions.

I can use the dimensions of a rectangle to determine the number of square units within it.

I can decompose ﬁgures (into nonoverlapping rectangles) to determine area.

255

SCOPE 1

Perimeter Scope Introduction SCOPE SUMMARY Students understand that the perimeter of a ﬁgure is found by measuring the length of each side and adding the lengths together. They are tasked with ﬁnding the perimeter of polygons when all side lengths are given, as well as when a side length is missing. Students also use knowledge from the previous third-grade standards regarding area to create rectangles that have the same perimeter and different areas or different perimeters and the same area. Student Expectations

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. 3.GSR.8.2 Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students learn how to express the length of an object using nonstandard units, and they understand that the length measurement of something is the number of same-size units that span the object from end to end with no gaps or overlaps. Second-grade students add to their understanding by using tools, such as rulers, yardsticks, and measuring tapes. It is here that they learn to measure different objects and determine their difference in length. Students then use this knowledge to describe this difference in measurement in terms of standard length units. Prior to this standard, third-grade students learn about the concept of area.

Fourth grade continues the concepts learned by applying area and perimeter formulas to rectangles in real-world mathematical problems. Students use models and concrete objects to determine the areas and perimeters of various rectangles. Students will extend their knowledge base to determine the formulas for the perimeter of a rectangle (l (l + w + l + w OR 2l + 2w)) and a square (4s) (4 and the formula for the area of a rectangle (l (l × w) by using models. Students will also solve problems for scenarios where the dimensions of a rectangle or a composite ﬁgure are already given, and the students have to apply the formulas for area and perimeter to determine a solution.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

measure the length and width of a notebook.

•

measure the length and width of two other objects of their choice.

•

use a ruler in inches.

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: •

measure to ﬁnd the perimeter of a shape.

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

PERIMETER

Home

In this exploration, students will explore a scenario in which they must use their mathematical skills to determine which order belongs to which business based on its needs. Students in groups will: •

solve for the perimeter of rectangles by adding the lengths of all sides.

•

use measurement tools.

Explore 2

Solve for Perimeter

Find the Missing Length In this exploration, students will solve a scenario about helping a zoo accurately determine the perimeter of each animal enclosure so that it can place the correct order for barrier materials. In groups, students will: •

determine the perimeter of composite ﬁgures composed of non-overlapping rectangles with whole-number side lengths.

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

Once students have solved the scenario, they discuss their learning with the class and ﬁnish with an Exit Ticket.

Rectangles with the Same Perimeter and Different Area

Rectangles with the Same Area and Different Perimeter

In this exploration, groups of students will pretend they are helping a university frame art pieces for a gallery. Students will: •

determine the size of frame and backing material each art piece needs.

•

determine the total amount of framing and backing materials.

•

use manipulatives such as rulers and tiles.

Explore 4

Explore 3

Explore 1

EXPLORE ACTIVITIES

In this ﬁnal exploration, groups will design a garden that has an area of 10 square feet and design different pods for small, medium, and large dogs for an animal shelter. Students will: •

solve problems in which rectangles have the same area and but different perimeters.

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

Upon completion of the Explore activities, they will discuss their learning and complete an Exit Ticket for assessment. Notes

257

PERIMETER

Perimeter Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

258

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PERIMETER

Home

ACCESSING PRIOR KNOWLEDGE Students measure the length and width of a notebook and then two objects of their choice. They will measure the length and width with a ruler in inches. This activity is intended to assess mastery of the following standard(s): 2.MDR.5.2 Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.

Materials

Preparation

Printed •

• • •

1 Student Handout (per student)

Reusable • •

Print a Student Handout for each student. Have a 1 ft. ruler with inches for each student. Students will need to have one of their notebooks out for this activity.

1 Ruler (per student) 1 Notebook or other book that students already have in their desks (per student)

Procedure and Facilitation Points 1.

Distribute a Student Handout to each student.

Let students know they will be measuring the length and width of their notebooks.

Refer back to the Student Handout to discuss where the length and width are located on the notebooks.

Ask students how they would use the ruler to correctly complete the measurements before they complete them. To measure in inches, I would make sure the 0 on the ruler is lined up with the end of the notebook. I would look to see what line on the inch side is closest to the end of the notebook.

Students will work in partners or groups as they measure their notebooks. Once they have a measurement in inches, they will have a peer check to see if they agree with their answer. I think you might be wrong on this measurement. See, you didn’t line up the ruler correctly. Let me help you line up the end of the notebook with the 0 at the end of the ruler.

Student pairs or groups will look for two more rectangular objects around the room to measure. They will measure the lengths and widths in inches.

Facilitate a class discussion about their 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.

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

FACILITATION TIP Students should each measure a notebook (or a book) of the same size so that they may compare measurements. FACILITATION TIP Set up a T-chart on the board with the columns Inches and Centimeters. Have each student record the measurements they get on the T-chart. Prompt students to check whether they see a discrepancy with the measurement(s) they obtained and to check the measurement again if necessary. Model proper use of the measuring tool as needed.

259

PERIMETER

Perimeter Hook – Soccer Ball Shapes ACTIVITY PREPARATION Students measure to ﬁnd the perimeter of a shape.

Materials

Preparation

Printed •

• • • •

1 Soccer Ball Shapes (per group)

Reusable • • • •

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1 Ruler (per group) 1 Pair of scissors (per group)

Plan to show the Phenomena Video. Print a Soccer Ball Shapes for each group. Cut 20–30 inches of yarn or string for each group. Prepare to project Soccer Ball Shapes.

Consumable •

20–30 in. Yarn or string (per group)

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

2. FACILITATION TIP

Be prepared with a few different models or actual soccer balls to show students. Have them make some observations about the ﬁgures on the physical soccer ball(s) before showing the video.

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.

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 situation. Discuss the following questions with the class: a. DOK-1 What do we know? We know the machine cuts out the shapes. We know we need to ﬁnd out how many inches the machine cuts for each shape. b.

3. 4. 260

DOK-1 What shapes do you see s on this soccer ball? Hexagons and pentagons

DOK-1 What shapes do you see on this soccer ball? Hexagons and pentagons

Engage

Explore

Explain

Elaborate

Evaluate

Ask the groups to cut a piece of yarn that is the exact length of one side of the hexagon and another piece of yarn that is the exact length of one side of the pentagon. Discuss the following questions with the class: a. DOK-1 How many sides do the hexagons have? The hexagons have six sides.

7. 8.

DOK-1 How many sides do the pentagons have? The pentagons have ﬁve sides.

DOK-2 What do you notice about the sides of each shape? They are all the same length.

DOK-1 If we are ﬁnding the distance around each shape, what attribute are we measuring? We are measuring the perimeter.

Ask the groups to ﬁnd the perimeters of the pentagons and hexagons on the soccer ball. Discuss the following questions with the class: a. DOK-2 Ask each group what method they used to ﬁnd the perimeters and what they found for the perimeter. Some groups may have measured the yarn they cut and multiplied it by the number of sides. Some groups may have measured each side. Some groups may have measured one side and multiplied by the number of sides. b.

DOK-1 These hexagons and a pentagons are called regular shapes because all the sides are the same length. How can you ﬁnd the perimeter of a regular shape? Find the length of one side, and then multiply by the number of sides. DOK-1 How can you ﬁnd n the perimeter of an irregular shape (a shape with sides of different lengths)? Add up the lengths of all the sides.

Intervention

Acceleration

FACILITATION TIP

PERIMETER

Home

Take time to be sure your string and scissors are a good match for accurate cutting. Some yarn is diﬃcult to cut precisely with school scissors.

FACILITATION TIP Decide beforehand when you want to distribute the rulers. It might be helpful for students to have them before Step 5 when they are cutting yarn.

FACILITATION TIP Using the precise language of regular and irregular shapes is an important skill in math. Take time to illustrate, deﬁne and clarify regular and irregular as they relate to geometry. Post on your word wall or anchor chart.

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PERIMETER

Perimeter Explore 1 – Solve for Perimeter ACTIVITY PREPARATION Students solve for the perimeter of polygons by adding the lengths of all sides.

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. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials Printed

Reusable

1 Student Journal (per student) 1 Exit Ticket (per student)

• •

Consumable

1 Set of counters (per group) 1 Projector (per class, optional)

• •

1 Roll of masking tape (per class) 15 Strawberry milk containers (per class, optional)

Preparation • •

Plan to divide the class into groups of 4 to complete this activity. Before class begins, tape the given dimensions of the geometric ﬁgures below with masking or painter’s tape on a ﬂoor or a wall. These will represent the tables or desks their carpentry shop has built. Note that if your classroom is not big enough, you may also mark an outside surface with sidewalk chalk. • • •

• • • • •

(Order A) Rectangle: 3 yd. × 2 yd. (Order B) Square: 6 in. × 6 in. (Order C) Triangle: each side is 36 in.

• • •

(Order D) Hexagon: each side is 4 ft. (Order E) Rectangle: 36 in. × 24 in. (Order F) Trapezoid: 2 ft., 2 ft., 2 ft., 3 ft.

Print a Student Journal and an Exit Ticket for each student. Print a set of Order Cards for each group. Cut them apart and laminate them (optional). Select a different Order Card for each group, and staple or paper clip it to the outside of the plastic bag. Place the rest of the Order Cards in the plastic bag. Place the rulers and tape measures or yardsticks in a central location that students can easily access as they need. 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. (Color Tiles)

PROCEDURE AND FACILITATION FACILITATION TIP Point out that units of measure vary. Measurements are provided in centimeters, inches, feet, and yards. Discuss the importance of paying attention to units because units play an important role in communicating size. FACILITATION TIP Make time to preview some of the unique vocabulary on the Order Cards. 262

2. 3. 4.

Read the following scenario to the class: You and your team now have your very own carpentry shop! Lately, business has been booming, and you have been receiving orders from a variety of different businesses and people who have many different needs. There have been so many orders that they all accidentally got mixed up! You must use your mathematical skills to determine which order belongs to which business based on their needs. Distribute the Student Journals, and give each group an Order Card bag. Explain to students that the Order Card attached to the outside of the bag is the polygon they will look for ﬁrst. Tell students they will collaborate to ﬁnd the order, draw and label the polygon, and answer the questions on their Student Journals. © Accelerate Learning Inc. - All Rights Reserved

5. 6. 7. 8. 9. 10. 11. 12. 13.

Engage

Explore

Explain

Elaborate

Evaluate

Then, they may choose any of the other Order Cards in the bag to complete next. Discuss the proper use of rulers or yardsticks and expectations for group work. You may have groups work by moving to a new polygon every 5–10 minutes or allow them to move at their own pace. Have groups read the Order Card attached to the outside of their bags and then walk around and look for the polygon that matches the order. Challenge students to use the clues and specifications on the Order Cards as a guide to help them solve which table or desk belongs to which order. As students work, walk around and encourage them to think about how to calculate the distance around the shape efficiently. Guide them to think about how they can use opposite equal sides to cut down on measuring time. Emphasize that they will be determining total distance around the figure. Introduce the distance around a figure as the perimeter. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-3 How did you determine which tool to use for measuring? We looked at the lengths of the sides of each polygon. If the sides were very long, it made more sense to use a longer tool, which made our work faster.

14.

DOK-3 How did you know how many sides to measure? If the polygon had equal sides (for example, a square, which has all equal sides, or a rectangle with equal opposite sides), we were able to measure one side and then multiply or add it repeatedly by the number of equal sides.

DOK-3 What clues did you use to decide which table or desk went with each order? We looked at the clues on the Order Cards and thought about the sizes and shapes the tables would be. We also used logic to determine which table or desk went with each order. For example, a dollhouse-furniture store was not going to be selling a large table with sides measured in yards.

Intervention

Acceleration

FACILITATION TIP

PERIMETER

Home

Have students locate each unit of length and be sure that students know which side of the ruler to use. Remind students of the importance of starting at zero and measuring straight from end to end on each side.

FACILITATION TIP Ask students why perimeter and area measure different things. (Perimeter is the number of units that border the edge of a shape, and area is the number of square units that cover the inside of a shape.)

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

263

PERIMETER

Perimeter Explore 1 – Solve for Perimeter Math Chat Ask students to share how they solved for the perimeter of each polygon. Encourage them to use accountable talk during the discussion by using the following sentence stems: • • •

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.

I agree with ____________ because _________________. I respectfully disagree with ______________ because ______________. I liked the way you solved __________________; it was different from/the same as ________________ because ____________________.

Could you tell me more about how you solved ________________? Highlight different ways students solved the same problems. Encourage students to talk about the challenges they faced as they solved for the perimeter and decided how to use which unit of measurement. DOK-3 When did it make sense to use a yardstick instead of a ruler and vice versa? On polygons in which the length of the sides was large, it made more sense to use the yardstick. If we had used a ruler to measure it, it would have taken a lot longer. For polygons with smaller sides, a yardstick would not have made sense because it would be much too long. • DOK-3 Which perimeters were easiest to measure? Why? The easiest perimeters to measure were the ones for polygons with equal sides. In this case, the square’s sides were all equal, so we could measure one side and add it four times or multiply it by four. Rectangles have opposite parallel sides, which means we could measure, add the length and width sides together, and then double the amount (or add them again). • DOK-3 What strategies did you use to make your work more eﬃcient? We worked as a team. Each person measured one side, which made it faster. For polygons with equal sides, we used repeated addition or multiplication of those equal sides to make our calculations faster. •

Post-Explore FACILITATION TIP When you preview this Exit Ticket with students, read the scenario with them and allow time for questions. Reassure students that the given measurements in many math assessments are often not similar to their own experiences.

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.

264

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes

PERIMETER

Home

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265

PERIMETER

Perimeter Explore 2 – Find the Missing Length ACTIVITY PREPARATION Students work together to determine the perimeter of a polygon or a missing length when given the perimeter and remaining side lengths in problems.

Standards for Mathematical Practice • • • • • •

Materials Printed • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

Preparation • • • •

Reusable • • • • • •

• •

14 1 ft. lengths of ribbon (per class) 100 Craft sticks (per class) 200 Small paper clips (per class) 1 Pack of toothpicks (per class) 200 1 in. squares (plastic or construction paper) (per class) 200 Centimeter cubes, stacking cubes, or base ten single cubes (per class) 1 Marker (per station) 1 Ruler (per class)

Consumable •

•

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Station Cards, and cut them apart. Laminate them for future use (optional). Decide where to set up the six stations. Most stations will need a large area. If the classroom is not large enough to accommodate all of the stations, consider using a multipurpose room, gym, hallway, etc. Prepare materials for each station as follows: • • • • • •

• •

1 Pad of sticky notes (per station)

Station 1: 14 1 ft. lengths of ribbon, sticky notes, 1 marker, and Station 1 card Station 2: 100 craft sticks, sticky notes, 1 marker, and Station 2 card Station 3: 200 small paper clips, sticky notes, 1 marker, 1 ruler, paper, and Station 3 card Station 4: 1 pack of toothpicks, sticky notes, 1 marker, and Station 4 card Station 5: 200 1 in. by 1 in. plastic or construction paper squares, sticky notes, 1 marker, and Station 5 card Station 6: 200 centimeter cubes, stacking cubes, or base-ten single cubes, sticky notes, 1 marker, and Station 6 card

PROCEDURE AND FACILITATION FACILITATION TIP Generate a list of real-world applications of perimeter. Examples may include determining how much framing is needed for a painting or how much fencing is needed to mark the border of a garden. 266

Explain that each group will be going to six different stations. At each station, students will read the Station Card and use the dimensions on the card to build the ﬁgure described with the objects provided.

4. 5. 6. 7.

Explore

Explain

Elaborate

Evaluate

Tell students that each object represents one unit of measurement as described on the Station Card. a.

Engage

For example, each craft stick in Station 2 represents 1 foot, each toothpick in Station 4 represents 1 mile, and so on.

Have students use sticky notes to label the length of each side. (Note that after groups are finished at their first station, they should save the unused sticky notes for use by the remaining groups.) Students will then collaborate to answer the corresponding questions on their Student Journals. Tell students they will have a set amount of time at each station. When the time is up, they will clean up the stations and stack the sticky notes neatly. Assign each group to a station. Monitor and check for understanding. As you walk around, make sure students are counting and labeling the outsides of their figures. Guide students toward being more efficient by asking the following question:

Intervention

Acceleration

FACILITATION TIP

PERIMETER

Home

Take some time to preview the Station Cards for unique vocabulary before students begin collaborating.

FACILITATION TIP Explore 1 focused on the perimeter of rectangles. Students may beneﬁt from seeing examples of perimeters of other types of shapes. Consider projecting a triangle, square, or octagon and asking student volunteers to trace along the sides that make up the perimeter.

a. DOK-2 What operation could help in finding the remaining length without counting each of the objects? We can use addition to figure out how much of the total perimeter is already being applied to the figure. To determine what we still need, we can subtract that amount from the total. 8. 9.

As students get more comfortable, challenge them to make drawings of the ﬁgures and use computation instead of building them with the materials. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP

Challenge students to consider whether there is a more efficient way to solve that Math Chat involves multiplication. Students may Briefly review one or two answers to Station Cards, and highlight different ways the observe that there are 2 sets of equal side students used to get the answer. lengths. To calculate perimeter, students • DOK-2 How were you able to find the missing side? If we knew the total perimeter, can add each size length and double the sum or double each side length and find the we added the sides we knew and then subtracted that sum from the total sum. perimeter to find the missing side. Another way is by subtracting each side from the perimeter individually; the difference that remains after subtracting all is the length of the missing side. If the figure was congruent to another figure, we used the side lengths from the other figure. If the figure was a rectangle, we could use the other sides that were congruent. • DOK-2 What observations did you make about the shapes of the figures? They were all closed figures with straight sides. Some had equal sides, and some did not. STEMscopes Tip • DOK-2 What were some challenges you faced? One of the challenges we faced The Standards-Based Assessment is was remembering to count all the sides, especially for the figures that weren’t found within the Evaluate section for regular rectangles or squares. Grades 2–5. Students demonstrate • DOK-3 What were some discoveries you made? A discovery we made was that mastery of the concepts covered as we began taking away lengths from the total perimeter, we noticed that the in the scope using multiple-choice number we started with began getting smaller. This let us know that we were and gridded response questions using subtraction. Opposite equal sides made our computation a lot easier. We aligned to the scope standard(s). This also discovered that you can solve for the missing side by just adding up all the assessment can be assigned and side lengths and subtracting the sum from the total perimeter or subtracting one scored digitally, printed, or edited to length at a time from the total perimeter. meet students’ individual needs. • DOK-2 Without using the objects, how could you solve for the missing side of a figure if you are given the perimeter? Since we have the total perimeter, we can either add the given sides and subtract from the total to see how much we have left or subtract each side individually until we are left with the remaining side. 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 pre-assessment for students before this Explore activity. 267

PERIMETER

Perimeter Explore 3 – Rectangles with the Same Perimeter and Different Area ACTIVITY PREPARATION Students ﬁnd the perimeter of rectangles and notice that rectangles can have the same perimeter but different areas.

Standards for Mathematical Practice • • • • • •

Materials

Preparation

Printed • • •

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

Reusable • • •

1 Set of color tiles (per group) 2 Resealable bags (per group) 1 Dry-erase marker (per group)

• • • • • •

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. For each group, print a set of Room Cards on card stock, laminate them for durability (optional), cut them apart, and place them in a resealable bag. Prepare a set of color tiles for each group in a resealable bag. Have extras available in a central location. 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. (Color Tiles)

PROCEDURE AND FACILITATION 1. 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.

2. 3. 4. 5.

6. 7. FACILITATION TIP Draw and label each shape on a piece of chart paper for student reference. Mark congruent sides using the same type of tick marks. 268

Read the following scenario to the class: Your parents have hired Home Warehouse to redo the floors in your home. The carpet in your house needs to be replaced, but your parents have decided to put tile down instead. There are 6 rooms that will need to have new tile installed. Once the tile has been put on the floor, your parents also want to add molding to the perimeter of the ceiling to make the room look nicer. Your job is to take measurements of the rooms needing tile and molding to calculate how much material is needed to complete the job. Give a Student Journal to each student. Give a dry-erase marker, a set of color tiles, and a set of Room Cards to each group. Explain to students that they will be creating models of each room’s floor. Clarify that each room will be a rectangle, but each one will be a different size. The color tiles represent the tile flooring and the outer edges of the rectangle represent the perimeter for the ceiling molding. Invite groups to read the first Room Card for the hallway together. Read the card to the class. Remind students that each inch of the tiles represents a foot for the problem. Discuss the following questions: a. DOK-1 What do you think I should do with my tiles to represent that the hallway is 13 feet long? I will count out 13 tiles and place them in a line. b.

DOK-2 How will you represent that the hallway is 3 feet wide? I will count out 2 tiles and add them to the end or beginning but going next to the 13 tiles. The shape should look like an L shape. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 Why don’t don we add on 3 tiles to represent the width? We don’t add on 3 tiles because the row with 13 tiles for the length represents the first tile for the width. DOK-1 Are these all the tiles I need to find the area? No, these are not the only tiles we need for the area. We need to make sure we fill in each row so we have 3 rows of 13 tiles.

e. DOK-1 How do we find the area for the tiles in the hallway? Answers will vary. We find the area by counting all the tiles individually. I could also count one row and find that there are 13 tiles. Since I know there are 3 rows, I can add 13 + 13 + 13 and find that my area is 39 square feet. We can also multiply the length, which is 13, by the width, which is 3. f.

10. 11. 12. 13.

DOK-1 How can we use the color tiles to ﬁnd the perimeter for the ceiling molding of the hallway and each room? Well, I know that perimeter is the outside of the shape, and each edge on the outside represents 1 foot of ceiling molding. There are 13 edges of my tiles on the top and bottom of the shape and 3 edges on the left and right side of my shape. To ﬁnd the perimeter, I know that I must add up all the sides, so I will add 13 + 13 + 3 + 3, which equals 32. Each inch represents a foot for my problem, so the perimeter for the ceiling molding in the hallway is 32 feet.

Instruct students to sketch the model of their hallway on their Student Journals and to record their work and answers for how they calculated the area and the perimeter. Encourage groups to collaborate as they continue working through the Room Cards and using their tiles to help them calculate area and perimeter. Instruct groups to record their ﬁndings on their Student Journals. Walk around the classroom, and monitor for understanding. Ask guiding questions for struggling students like the ones from the whole-group lesson. 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 from this activity? I noticed that each room had the same number of edges around the outside of the shape but a different number of floor tiles. DOK-2 What does that tell us about each room’s area and perimeter? This tells us that each room had the same perimeter but different areas. DOK-1 Did you use the same number of square tiles for each room? No. Some rooms needed more tiles, and some needed fewer tiles. DOK-1 How did you find the area of each room? We found the area of each room by multiplying the length by the width. I could also find the area by counting each tile individually. DOK-3 Why do you think the perimeter was the same for each rectangle but the area was different? Note: Recognize that this is a tough idea for students to understand, and simply discuss why the students think this is. A possible idea they may mention is that the counting is different. When counting the area, you are counting whole tiles, but when finding perimeter, you are only counting the edges of the tiles.

Intervention

Acceleration

PERIMETER

Home

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.

FACILITATION TIP Challenge students to consider the formula for the perimeter of a square. Explain that a square does not have a length or width, because all of its sides are the same length. (Using the variable s to represent the side length, P = 4s.) FACILITATION TIP For this hands on activity, students may need to be in partners rather than groups. Manipulating and counting the tiles is an important part of the learning process in this Explore activity.

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. For this Exit Ticket, determine your criteria for success and clarify before distributing Complete the Anchor Chart as a class. to students. The reﬂection questions may Have each student complete their Interactive Notebook. need complete sentences and correctly spelled vocabulary to be accurate.

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PERIMETER

Perimeter Explore 4 – Rectangles with the Same Area and Different Perimeter ACTIVITY PREPARATION Students solve problems in which rectangles have the same area and different perimeters.

Standards for Mathematical Practice • • • • • •

Materials Printed • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable • •

20 Color tiles (per pair) 1 Resealable bag (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. Prepare 20 color tiles in a resealable bag for each pair of students. 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. (Color Tiles)

PROCEDURE AND FACILITATION Part I FACILITATION TIP

Encourage partners to create different garden models with only the requirement of 10 square feet.

2. 3. 4. 5. FACILITATION TIP Have students conduct a short Gallery Walk with guiding questions of: “What is the area of each garden model? What is the perimeter of each garden model?”

6. 7.

Read the following scenario to the class: Your parents have entrusted you with creating a new space for a vegetable garden. Since there is limited room in your backyard, your parents want to keep the garden to a total of 10 square feet, and it must be rectangular so it can ﬁt along the fence. Your mom wants to lay a perimeter of bricks around the garden that you choose. How could you design the garden so it has an area of 10 square feet? Is there more than one way? How many bricks will your mom need? Distribute color tiles to each pair of students. Explain that the tiles are simply a model of the area of the garden. Each tile counts as one square foot. Task them with determining a shape for their garden with their partners and ﬁnding the perimeter the bricks would border. Give students time to construct a rectangle with 10 square tiles. Walk around to assist struggling students. Ask students to share their designs. Discuss the following questions: a. DOK-2 What did you notice about every rectangle? Why? All the areas were the same. This is because we had 10 square units that represented the 10 square feet of garden. We used all of them for each rectangle. b.

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DOK-2 What rectangle did you create that would need the least number of bricks to go around the perimeter? Answers should include the following: The smallest perimeter we created was 14 units when one side of the rectangle was 2 units and the other side was 5 units. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

DOK-2 What rectangle did you create that would need the greatest number of bricks to go around the perimeter? Answers should include the following: The greatest perimeter was created when one side of the rectangle was 1 unit and the other side of the rectangle was 10 units.

Part II 1. 2.

Intervention

Give a Student Journal to each student. Read the following scenario to the class: You and your best friend are opening an animal shelter for homeless dogs awaiting adoption! Each dog will need to have the same amount of space inside their kennel (living area) as dogs of similar size. Due to size differences, some dogs will need more space than others. You will design different pods for small, medium, and large dogs. Each of these 3 pods contains kennels that have the same area within that pod but do not need the same amount of fencing. Each size dog will need a different amount of space within the kennel; this amount is indicated in your Student Journals. To simplify things, each animal’s space should be rectangular so they line up more easily. You want to make a fence around each kennel, so it is important to know the perimeter around the kennel. Discuss the following questions:

PERIMETER

Home

FACILITATION TIP Direct attention to the area for each pod on the Student Journal. Students may need to list factors or use square blocks to determine a possible pod design.

a. DOK-1 What does it mean to have an area of a certain number of square feet? That is the amount of space inside the shape in square units. b. 4.

6. 7.

DOK-1 How do we ﬁnd the perimeter? We ﬁnd the perimeter by adding up the side lengths.

Explain to students that they will collaborate with their partners to determine at least two ways they could design kennels for each size pod, depending on the area and noting the perimeter. Instruct them to record their designs in their Student Journals after they have used the color tiles to design the kennels each pod contains. The areas for the kennels for all three dog sizes are indicated in their Student Journals. Walk around the classroom to assist struggling students. 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 from this activity? I noticed that each room had the same number of tiles but a different number of edges around the outside of the shape. DOK-1 What does that tell us about each room’s area and perimeter? This tells us that each room had the same area but different perimeters. DOK-1 Did you use the same number of square tiles for each of the kennels for the same-sized dogs? Yes, they just compose rectangles with different lengths and widths. DOK-1 How did you find the perimeter of each room? We found the perimeter of each room by adding up the four sides on the outside of the shape. DOK-1 How did you find the area of each room? We found the area of each room by multiplying the length and the width. We could also find the area by counting each tile individually. DOK-2 Why do you think the perimeter was different for each rectangle but the area was the same? Recognize that this is a tough idea for students to understand, and simply discuss why the students think this is. A possible idea they may mention is that the counting is different. When counting the area, you are counting whole tiles, but when finding perimeter, you are only counting the edges of the tiles.

FACILITATION TIP To prevent one partner completing all the work, have each partner create their model and then check each other’s work before completing the Student Journal.

FACILITATION TIP Have each set of partners share their pod designs with another set of partners. The students can then discuss their noticing’s about area and perimeter. 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.

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PERIMETER

Perimeter Explore 4 – Rectangles with the Same Area and Different Perimeter Post-Explore 1. 2. 3. 4.

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

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes

PERIMETER

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PERIMETER

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

Solve for Perimeter 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

Find the Missing Length 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

Rectangles with Same Perimeter and Different Area

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

Rectangles with Same Area and Different Perimeter

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

274

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PERIMETER

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

A Gift for Aunt Maggie

Tony DeRose

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

Yasmine’s New Style

Problem Solving with 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

Dandy Designer Picture Frame Company

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

275

PERIMETER

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

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 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

PERIMETER

Home

What prompts will be used?

What does mastery look like?

I can determine the perimeter of a polygon.

I can explain that perimeter represents the distance around a polygon.

I can determine an unknown side length of a polygon when given the perimeter.

I can investigate and describe how rectangles with the same perimeter can have different areas.

I can investigate and describe how rectangles with the same area can have different perimeters.

277

SCOPE 1

Lines and Angles Scope Introduction SCOPE SUMMARY Students are expected to understand the concepts of and be able to describe and identify perpendicular and parallel line segments, right angles, and lines of symmetry within various polygons as well as real-world examples. When given a two-dimensional figure, students are able to identify each of these attributes that are unique to the shape. Students also draw lines of symmetry in two-dimensional figures while also identifying line-symmetric two-dimensional figures. Student Expectations

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. 3.GSR.6.3 Identify lines of symmetry in polygons.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students recognize and draw speciﬁc types of shapes, such as triangles, quadrilaterals, pentagons, and hexagons, as well as 3-D solids, including rectangular prisms and cones. Second graders are also introduced to lines of symmetry.

In fourth grade, students will be 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 will be investigating, identifying, and drawing each of the attributes that are unique to the shape.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

deﬁne attributes of different ﬁgures.

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.

identify lines of symmetry in a twodimensional ﬁgure.

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

278

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Identify Lines and Right Angles In this exploration, students will identify perpendicular line segments, parallel line segments, and right angles in polygons. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES Identify Lines of Symmetry In this exploration, students will create a greeting card. Students will: •

determine which shape would meet the criteria to make a frame for a painting.

LINES AND ANGLES

Home

identify and draw one or more lines of symmetry, if they exist, for a two-dimensional shape.

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 an Exit Ticket for assessment. Notes

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LINES AND ANGLES

Lines and Angles Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

280

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students answer true or false statements about deﬁning attributes of different ﬁgures. This activity is intended to assess mastery of the following standard(s):

LINES AND ANGLES

Home

2.GSR.7.1 Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes. 2.GSR.7.2 Identify at least one line of symmetry in everyday objects to describe each object as a whole.

Materials Printed • •

1 Set of Figure Cards (per class) 1 Set of True/False Cards (per student or per class)

•

1 True/False Statements (per class)

Preparation • • •

Be prepared to project the Figure Cards. Print one set of True/False Cards to hang on opposite sides of the classroom, or print one True/False Card (double-sided) per student. Print one copy of True/False Statements to read aloud to students.

Procedure and Facilitation Points 1.

2. 3. 4.

5. 6.

Hang True and False signs on opposite sides of the classroom. If you prefer for students to do this activity individually from their desks, then print one True/False Card (double-sided) for each student. Display Figure 1 on the screen for each student to see. Read each numbered statement from True/False Statements. Ask students to go to the side of the classroom and stand near the answer they agree with. Alternatively, students can answer individually from their seats by holding up either the True side or the False side of the card. Repeat steps 2–4 for ﬁgures 2–4. Facilitate a class discussion about 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. If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP If time allows, try the following extension activity: Display all of the figures. Invite one student to describe a shape they are thinking of and to call on their classmates to guess their 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. FACILITATION TIP Ask students if they can name each figure. If so, have them write the name of each figure on the displayed copy.

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LINES AND ANGLES

Lines and Angles Hook – Darling … it MUST have Symmetry! ACTIVITY PREPARATION Students identify lines of symmetry in a two-dimensional ﬁgure.

Materials

Preparation

Reusable • • •

•

Plan to show the Phenomena Video.

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1 Set of colored pencils (per student)

Consumable •

1 Piece of blank drawing paper (per student)

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 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.

FACILITATION TIP Take some time to prepare some additional engaging real-world images of symmetry to share with students during this discussion.

DOK-1 What is symmetry? It is okay if students do not know. It is when things look the same on both sides.

DOK-2 Why might a lot of architects and artists use symmetry in their designs? Answers will vary. Examples include that a lot of people like the way symmetric things look.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2. FACILITATION TIP

If students are still unsure about what symmetry is, take time to share images from the Picture Vocabulary.

DOK-1 What is symmetry? It is okay if students do not know. It is when things look the same on both sides.

DOK-2 Why might a lot of architects and artists use symmetry in their designs? Answers will vary. Examples include that a lot of people like the way symmetric things look.

3. 282

After students have completed all the Explore activities for this topic, show the Phenomena Video again and repeat the situation. Discuss the following questions with the class:

4. 5. 6.

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Let the students draw or build their design. Ask the students to draw their lines of symmetry with a different color of pencil. Tell students when they are ﬁnished drawing or building their design, they can request approval for their design. You can pretend to be the movie star client and either approve or reject their design based on the provided criteria. If any student shows you a design that does not have symmetry, you can have them identify the shapes without symmetry and modify their creation. Discuss the following questions with the class: a.

DOK-1 What shapes did you use in your design? Answers will vary. Examples include rectangles, squares, and triangles.

DOK-1 Do some of the components of your design also have symmetry? Answers will vary. Examples include square windows and triangular roofs.

Intervention

Acceleration

FACILITATION TIP To focus the design and draw stage, consider providing some constraints for students. Consider folding the paper in half before they begin drawing. Then, provide some shapes or ﬁgures that they must include on both sides.

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Lines and Angles Explore 1 – Identify Lines and Right Angles ACTIVITY PREPARATION Students will identify perpendicular line segments, parallel line segments, and right angles in polygons and determine which shape would meet the criteria to make a frame for a painting.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of 2-D Shapes (per pair) 1 Exit Ticket (per student)

•

Reusable • • •

•

5 Gallon-size resealable bags (per class) 1 Index card (per student) 4 Crayons (different colors) (per student)

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Provide an index card and 4 different-colored crayons for each student. Print one set of 2-D Shapes for each pair of students. Cut out each shape, and put each set in a large resealable bag. For students who need more support in recalling information, please see our Shapes Supplemental Aids element in the Intervention section.

Consumable •

1 Sheet of drawing paper (per student)

PROCEDURE AND FACILITATION POINTS Part I: Creating Frames FACILITATION TIP

Read this scenario a few times together with students. Project the text, and guide them to locate the math vocabulary. Underline or highlight: frame, parallel, perpendicular, line, angles, and right angles. FACILITATION TIP

2. 3.

Explain what attributes students should focus on. Consider listing them for students to view as they explore the shapes.

FACILITATION TIP These are most likely new vocabulary terms (parallel, right angle, perpendicular, line segment) for students. Have students write the words, deﬁnitions, and draw sketches on their Student Journal.

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Read the following scenario to the class: Alani has been taking art lessons after school. Her favorite type of medium to use is watercolor paint. She painted several paintings and wants to have them framed. Her dad told her he will make simple frames for the paintings. To easily make the frames, the paintings must have parallel line segments, perpendicular line segments and right angles. Alani has traced the shape of her paintings on paper. Help Alani decide which paintings she can give her dad to frame. Give each pair a set of 2-D Shapes. Explain to students that each of the polygons is an example of the shape of Alani’s paintings. Tell students that they will collaborate with their partners to name the attributes of each shape. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What attributes does the shape have? Answers may vary. The square has 4 sides and 4 vertices. The vertices form a right angle.

DOK-1 What does it mean if there are parallel line segments? The lines will not touch, and they will be the same distance apart.

DOK-1 How do you identify a right angle? The angle forms the corner of a square like the edge of a book.

5. 6.

7. 8. 9.

10.

11.

12.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Give each student a Student Journal and an index card. Explain to students that they are to use their index cards, which have a corner like a square, and work with their partners to determine whether the shape has right angles. (Demonstrate if needed.) Allow time for students to ﬁnd a shape that has a right angle. Demonstrate how to trace over 2 opposite lines with the same color to see if they ever touch and if they appear to stay the same distance from each other. FACILITATION TIP Give students time to work together to determine if one of the shapes has parallel line segments, perpendicular line segments, or right angle(s). Instruct them to Post and project these criteria for students record their ﬁndings on their Student Journals. to refer to as they collaborate to determine if the shapes would work for Alani’s dad. Discuss the following questions: a.

DOK-1 What attributes do the paintings need to have? They need to have parallel line segments, perpendicular line segments and right angles.

DOK-2 How do you determine whether the shape has a right angle? We can hold the corner of an index card at the vertex of the shape. If it matches the index card corner, it is a right angle.

DOK-2 How do you determine whether the shape has parallel line segments? We can trace 2 opposite sides of the shape and see if they touch. If they don’t touch and are the same distance from each other, they are parallel.

Have students continue working with their partners to determine whether the shapes match the criteria to frame Alani’s paintings. Tell them to record the attributes on their Students Journals. Tell them the shapes are labeled with a letter to correspond with the shapes on their Student Journals and will help with identiﬁcation when discussing the activity as a whole group. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How do you determine whether the shape has perpendicular line segments? We can use the index card to see if the two lines that were touching formed a right angle.

DOK-1 Which shapes meet the criteria for the frames? Shapes A and G meet all the criteria for the frames.

DOK-2 Would a hexagon make a good frame? Explain your answer. Yes, but it would be hard to make. Alani’s dad does not want to make a frame that doesn’t have right angles, perpendicular line segments, or parallel line segments.

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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.

Part II: Lines and Angles Are All Around 1. 2. 3. 4. 5.

Direct students’ attention to Part II of the Student Journal. Have students look around the classroom for examples of parallel line segments, perpendicular line segments, or right angles. Tell students to discuss with their partners their ﬁndings and draw an example of each in the table on their Student Journals. Actively monitor discussions for misconceptions as students are working. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

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Lines and Angles Explore 1 – Identify Lines and Right Angles Math Chat •

FACILITATION TIP

•

One trick to help students visualize parallel lines when they read the word is that the two letter l’s in the middle look like train tracks.

•

FACILITATION TIP

•

One trick that may help students remember the deﬁnition of parallel is that it has two parallel lines in the letters (the two l’s).

•

DOK-1 What examples of perpendicular line segments do you see in the real world? Explain. I see windows and a door that have lines that touch to form perpendicular lines. DOK-1 What examples of parallel lines do you see in the real world? Explain. I see windows and a door that have parallel lines because the opposite lines do not touch. DOK-2 What did you notice about perpendicular line segments in relation to right angles? In order for the line segments to be perpendicular, the lines that touch must have right angles. DOK-2 Compare parallel lines to perpendicular lines. How are they the same and how are they different? They are both straight lines that can be used to form 2-D shapes. Parallel lines never touch. Perpendicular lines touch and form a right angle. DOK-3 What would our classroom look like if it did not have any right angles or perpendicular line segments? It would have furniture and doors with curved lines. The windows would have to be round.

Post-Explore FACILITATION TIP

For this Exit Ticket, project the qualiﬁcations for the frames so that students can refer to them while they complete the assessment.

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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Lines and Angles Explore 2 – Identify Lines of Symmetry ACTIVITY PREPARATION Students create a greeting card by identifying and drawing one or more lines of symmetry, if they exist, for a two-dimensional shape.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 5 Sets of 2-D Shapes (per class) 1 Exit Ticket (per student)

•

Reusable • • • •

5 Gallon-size resealable bags (per class) 1 Ruler (per student, as needed) Colored pencils or markers (per group) 1 Pair of scissors (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 2-D Shapes for each group of students. Cut out each shape, and put each set in a large resealable bag. For students who need more support in recalling information, please see our Shapes Supplemental Aids element in the Intervention section.

Consumable •

1 Sheet of drawing paper (per student)

PROCEDURE AND FACILITATION POINTS 1.

2. FACILITATION TIP

Hold up an actual greeting card to use as a visual reference.

FACILITATION TIP

Emphasize that students are only tracing folds that result in equal-sized halves. 5.

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Read the following scenario to the class: Today, you will be a greeting card design supervisor. Your team has submitted multiple options to be used for a greeting card. Look at their designs, and decide which one to use for your company’s newest card. Then, you will create a prototype of the card. The card can be a birthday card, a get-well-soon card, a thank-you card, or just a card to say hello! Give each student a Student Journal and each group a set of 2-D Shapes. Rulers may be needed to help students draw straight lines. Discuss the following questions: a.

DOK-1 What do all cards usually have in common? They are folded in half. There is a message on the front and a message on the inside.

DOK-2 What is the same about both halves of a card? They are the same size. The edges match up.

Explain to students that they are to work with their group members to fold each shape in half. When they fold the shape in half and both halves are congruent, have them use a marker to trace the folds. Tell them they can use a ruler to help draw straight lines on their folds. Have them continue folding each shape in half until there are no more possible ways to fold and create equal halves. Have students look at the folds they have traced and record similar lines on the shapes on their Student Journals. Tell them the shapes are labeled with a letter to correspond with the shapes on their Student Journals and to help with identiﬁcation when discussing the activity as a whole group. © Accelerate Learning Inc. - All Rights Reserved

10. 11.

Explore

Explain

Elaborate

Evaluate

Explain that a line that divides a shape into congruent halves is called a “line of symmetry.” Symmetry is when both sides are exactly the same. Symmetry is like a mirror image, so if the halves are folded to be on top of each other, they will match up perfectly. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How do you know if that shape has one or more lines of symmetry? We fold the paper in different directions to see if the shape can be folded into two equal/congruent halves.

DOK-2 Is there another shape not shown here that might make a good greeting card? Why? Answers will vary. A circle, equilateral triangle, or square would make good greeting cards because they can all be folded into congruent halves.

c. 8. 9.

Engage

DOK-2 Would a regular trapezoid make a good greeting card? Explain your answer. Yes, because a regular trapezoid has 1 line of symmetry.

Give each student a sheet of drawing paper and a pair of scissors. Have students choose a shape from the ones provided to make a greeting card. Remind them that the shape must be able to be folded in half with at least one line of symmetry. Because the shapes have traced folds, have students use the shapes they want to use as their greeting cards as templates. Have them trace the shapes onto their sheets of drawing paper and cut them out. Have them fold their shapes in half to create one line of symmetry. Have students decorate their cards however they wish. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • • • •

DOK-1 What do we call the line that divides a shape into congruent, yet mirrored, halves? Line of symmetry DOK-1 Which shapes had the most lines of symmetry? Shapes D, E, G, and H DOK-1 Which shapes had the fewest lines of symmetry? Shape C DOK-1 Did any shape have no lines of symmetry? If so, which one or ones? Yes, shapes A, B, and F DOK-2 We discussed greeting cards being folded in half. Which shapes could be used as a greeting card? Shapes C, D, E, G, and H

Post-Explore 1. 2. 3. 4.

Intervention

Acceleration

FACILITATION TIP Explain that lines of symmetry are imaginary and that mathematicians draw them using a dotted line. Encourage students to use dotted lines when drawing lines of symmetry on their Student Journal.

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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.

FACILITATION TIP Post the deﬁnition and examples of line of symmetry on your word wall, anchor chart and/or Student Journals. Refer to the Picture Vocabulary.

FACILITATION TIP Before students complete this Exit Ticket, determine your criteria for success. On the ﬁnal question, students may draw a shape that has more than three lines of symmetry while only labeling three lines.

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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

Identify Lines and Right 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 Lines of Symmetry 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

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

Peppy’s Pizza Parlor

Designing Parking Spots

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

Service Dog Training House

Name 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

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

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Lines and 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

What prompts will be used?

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What does mastery look like?

I can identify speciﬁc attributes (perpendicular line segments, parallel line segments, and right angles) in polygons.

I can identify lines of symmetry in polygons.

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SCOPE 1

Two- and Three-Dimensional Figures Scope Introduction SCOPE SUMMARY

Student Expectations

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.

Students build on their prior knowledge of two-dimensional figures to classify them based on their parallel and perpendicular lines, right angles, and lines of symmetry. In addition, students explore quadrilaterals, including rhombuses, kites, parallelograms, trapezoids, rectangles, and squares, to compare and contrast their attributes using formal geometric language. While exploring these polygons, students begin to notice that a two-dimensional figure can fit into multiple categories based on its attributes. Students then extend their understanding of two-dimensional shapes to assist them in analyzing three-dimensional solids, including triangular and rectangular prisms, cubes, and square pyramids. This understanding allows students to identify the attributes of a 3-D solid, such as number of faces, edges, and vertices, and describe quadrilaterals as faces of these figures using formal geometric language.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In fourth grade, students continue developing their understanding of twodimensional ﬁgures by classifying and sorting 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. They use side lengths to identify and construct equilateral, isosceles, and scalene triangles and use angle sizes to identify and draw right, acute, and obtuse triangles. Students 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).

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

classify and sort three-dimensional objects and describe them using formal geometric language.

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: •

identify two- and three-dimensional ﬁgures.

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. 294

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Classify Two-Dimensional Shapes In this exploration, students will classify polygons based on attributes using formal geometric language. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

classify shapes that includes quadrilaterals, such as parallelograms, rectangles, rhombuses, squares, trapezoids, and kites, and pentagons and hexagons by their attributes.

In this exploration, students will compare and contrast quadrilaterals based on attributes and using formal geometric language. Students will: •

classify shapes as parallelograms, rectangles, rhombuses, squares, kites, and trapezoids.

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 their learning and an Exit Ticket.

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 their learning.

Explore 3

Compare and Contrast Quadrilaterals

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Three-Dimensional Solids In this exploration, students will analyze three-dimensional solids. Students will: •

describing the attributes of 3-D objects as triangular and rectangular prisms, cubes, and square pyramids.

•

describe quadrilaterals as faces of these ﬁgures, using formal geometric language.

As students solve the scenario, they discuss their learning with the class and conclude with an Exit Ticket for assessment; then, revisit the Hook to solve. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

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Two- and Three-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 classify and sort three-dimensional objects and describe them using formal geometric language. This activity is intended to assess mastery of the following standard(s): 2.GSR.7.1 Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes.

Materials Printed •

1 Student Handout (per student or per pair)

Preparation •

TWO- AND THREE-DIMENSIONAL FIGURES

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Print a Student Handout for each student or pair, or prepare to project the Student Handout for the class.

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

Distribute a Student Handout to each student or each pair, or project the Student Handout for the class. Instruct students to look at the three-dimensional pictures. Students will match the three-dimensional pictures with the correct geometric names. With partners, groups, or the whole class, facilitate a discussion about the different attributes of each shape. 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. Ask the following questions: a.

How else can a cube be classiﬁed? A rectangular prism

Which shapes have two bases? Cylinder

Which have more than two bases? Cube and rectangular prism

Which have fewer than two bases? Sphere

FACILITATION TIP Take time to locate a set of 3-D solids. After showing students the three-dimensional pictures and allowing a limited time for discussion, show students the 3-D solids and allow for more discussion.

FACILITATION TIP List these vocabulary terms with images on your word wall or anchor chart. Take time to have students chorally read the words together in whole group, small groups, and with partners.

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

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Two- and Three-Dimensional Figures Hook – Catch a Thief ACTIVITY PREPARATION Students identify two- and three-dimensional ﬁgures.

Materials

Preparation

Printed •

• •

1 Clues (per class)

Reusable • • •

Plan to show the Phenomena Video. Print Clues double-sided or assemble single-sided sheets by taping them together. • Pictures of buildings should go on the front, and the clues should go on the back.

1 Set of geometric solids: cone, cylinder, sphere, triangular prism, rectangular prism, cube (per class) 1 Phenomena Video (per class) 1 Projector or document camera (per class)

• •

Laminate if desired. Prepare to project Clues.

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

2. FACILITATION TIP

Project the scenario and read it with students. Guide students to ﬁnd the math term and underline or highlight it.

FACILITATION TIP

Take time to check for understanding on questions 4a and 4b before preceding with the Explore activities.

DOK-2 What is the difference between a two-dimensional shape and a three-dimensional solid? A two-dimensional shape is ﬂat like a piece of paper. A three-dimensional solid is not ﬂat; it’s like a box.

DOK-1 Hold up one of the geometric solids. Ask the students, “If you are looking at it straight on, what shape do you see on the face of the solid?” Answers will vary depending on what shape you hold up.

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.

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5. 6.

Tell students they will be able to catch the criminal after they have completed all the Explore activities for this topic. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities, show the Phenomena Video again and repeat the situation. Discuss the following questions with the class: a.

Engage

Explore

Explain

Elaborate

Evaluate

Place the building pictures at the front of the classroom. You can arrange them in any order, but make sure the sides with the pictures of buildings are facing the students. Tell students that they will use their knowledge of shapes to help catch the thief. Remind them that the ﬁrst clue was that the suspect ﬂed into a building with a sphere on top. Call on a student to choose which one looks like a building with a sphere on top. Flip over the card the student chose. a.

If the student was incorrect, it will have a message on the back to try again.

If the student was correct, it will have the next clue.

There are three clues (and three correct pictures students will need to identify). The third correct identiﬁcation will have a picture of the thief on the back.

Discuss the attributes of two- and three-dimensional ﬁgures shown in the building pictures:

Intervention

Acceleration

FACILITATION TIP To create more engagement, have students do a secret vote (heads down, hands up) to choose the building and subsequent clues. 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.

DOK-1 How many faces does a triangular prism have? It has ﬁve faces.

FACILITATION TIP

DOK-1 How many faces does a rectangular prism have? It has six faces.

DOK-1 What shapes could you classify a square as? You could classify a square as a square, rhombus, rectangle, parallelogram, quadrilateral, and polygon. A square is a special rhombus and a special rectangle. A rhombus is a special parallelogram. A rectangle is a special parallelogram. A parallelogram is a type of quadrilateral. A quadrilateral is a type of polygon.

Post these questions as you lead the discussion. Depending on your students, consider teaching them how to draw some of these 3-D ﬁgures.

DOK-1 Are all parallelograms a type of rhombus? No, only a parallelogram with four equal sides is called a rhombus. However, all rhombuses are a type of parallelogram.

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e. DOK-1 What type of shape is a diamond? It is a rhombus, because it is a parallelogram with four equal sides. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Two- and Three-Dimensional Figures Explore 1 – Classify Two-Dimensional Shapes ACTIVITY PREPARATION Students classify polygons, including quadrilaterals, such as parallelograms, rectangles, rhombuses, squares, trapezoids, and kites, and pentagons and hexagons based on attributes, using formal geometric language.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• • • • •

1 Student Journal (per student) 1 Set of 2-D Shapes (per group) 1 Exit Ticket (per student)

Reusable • •

1 Index card (per student) 1 Pair of scissors (per student)

•

Plan to divide the class into groups of 4 or 5 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Provide an index card and a pair of scissors for each student. Print one set of 2-D Shapes for each group of students. For students who need more support in recalling information, please see our Shapes 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. (Geoboard)

PROCEDURE AND FACILITATION POINTS Part I: Shape Hunt 1.

FACILITATION TIP

Encourage students by saying if they can ﬁnd two shapes in the classroom while seated, they will be invited to go on the shape hunt.

FACILITATION TIP Have students use their arms, elbows, knees, and hands to form right angles. 4.

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Read the following scenario to the class: This morning when I was driving to school, I noticed there were shapes all around. I saw a shape with 8 equal sides when I stopped at the corner. Do you know what shape I saw? (Pause) Yes, you are correct. The shape I saw was an octagon. It was the stop sign. Invite students to work with partners to locate 2 shapes in the classroom, name the shapes, and tell the attributes of each shape. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What attributes does the shape have? The square has 4 sides and 4 vertices. The vertices form a right angle.

DOK-1 Where in our classroom do you see a rectangle? Our classroom door is a rectangle.

DOK-2 How can an index card help you when identifying attributes of shapes? I can hold the corner of my index card at the vertex of the shape. If it matches the index card corner, it is a right angle. Note that this would be a great opportunity to model for students how to identify angles smaller and larger than a right angle using the index card.

After students have found their 2 shapes and discussed attributes of the shapes with their partners, read the rest of the scenario: Who thinks they can ﬁnd more shapes around our classroom? Well, I don’t know about you, but I’m ready to go on a shape hunt. Let’s go! © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Distribute Student Journals and index cards to students. Students may work in groups of 4 or 5. Point out the word bank at the bottom of the first page of the Student Journal. Explain to students that they will go on a shape hunt to find an example of each of the shapes on their Student Journals. They will record the attributes in the box under each shape. If they don’t see the shape in the classroom, they will still fill in the attributes. As students are working with their groups, discuss the following questions: a.

DOK-2 What type of angle(s) does this shape have? How do you know? This shape has right (acute, obtuse) angles because it forms a square at the vertex.

DOK-2 How do you identify parallel or perpendicular lines in polygons? Point to ones you see. If the shape has lines that do not intersect and they are the same distance from each other, they are parallel. If they intersect and form a right angle, they are perpendicular.

DOK-2 What do you notice about kites and rhombuses? They both have 4 sides, but the sides on a kite are not all equal. They have 2 pairs of sides, and each pair is made of two adjacent sides that are equal.

DOK-1 How can you tell if there are any lines of symmetry? We can fold the shape in half so there are two equal, congruent sides.

Intervention

Acceleration

FACILITATION TIP For this activity, consider using partners so students can hunt in some common spaces like the cafeteria, gym, or hallways. FACILITATION TIP Struggling students will need help ﬁlling in all of the attributes. Modify by having students focus on recording only one or two attributes (like parallel lines or right angles) at ﬁrst. FACILITATION TIP Review or teach these vocabulary terms (acute, obtuse, parallel, perpendicular, kite, rhombus) before the shape hunt so students can look for these attributes and use the vocabulary successfully.

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Part II: Classifying Shapes 1. 2.

Tell students that they found so many shapes that the shapes need to be classiﬁed by their attributes. Give a set of 2-D Shapes to each group. Have students cut out the shapes and group them by common attributes. Then, have students draw how they classiﬁed the shapes on their Students Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How are these two shapes alike? How are they different? They both have 2 sets of parallel lines. They both are polygons.

DOK-2 Why did you group these shapes together? They all have right angles. They all have parallel sides.

DOK-2 How can you classify the shapes another way? I can classify them by ones that have acute angles.

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

Math Chat • • • • • • •

DOK-1 Describe the different shapes you found today. Answers will vary, but they should include the shapes that are on their Student Journals. DOK-2 What makes triangles different from parallelograms? Triangles don’t have any parallel lines. Parallelograms have two sets of parallel lines. DOK-2 How can you draw a triangle with perpendicular lines? You could draw a right triangle, which has perpendicular lines. DOK-1 What is an example of a shape with zero right angles? A regular pentagon, hexagon, octagon, parallelogram, rhombus, kite and trapezoid DOK-1 What is an example of a shape with 3 sets of parallel lines? A regular hexagon DOK-2 What do you notice about the lines on the shapes with right angles? They have at least one set of perpendicular lines. DOK-2 What are 2 ways you classified your shapes? I classified them by shapes that have 0 parallel lines and ones that have parallel lines. I also classified them by the type of angles.

FACILITATION TIP To save time, have the 2-D shapes pre-cut or use purchased sets.

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.

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Two- and Three-Dimensional Figures Explore 1 – Classify Two-Dimensional 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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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Two- and Three-Dimensional Figures Explore 2 – Compare and Contrast Quadrilaterals ACTIVITY PREPARATION Students compare and contrast quadrilaterals, including parallelograms, rectangles, rhombuses, squares, kites, and trapezoids, based on attributes and using formal geometric language.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. 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 Ruler (per student) 1 Pair of scissors (per class)

•

Consumable • • •

•

1 Roll of clear tape (per group) Construction paper, various colors (per group) 6 Poster boards or chart papers (per group)

•

Plan to divide the class into groups of 4 or 5 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Cut the construction paper into 1 in. wide strips. The length of the construction paper should vary from 4 inches to 12 inches. Each group should have at least 75 strips of various lengths. Write “Order 1,” “Order 2,” “Order 3,” “Order 4,” and “Order 5” at the top of each group’s poster board or chart paper. For students who need more support in recalling information, please see our Shapes and 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. (Geoboard)

PROCEDURE AND FACILITATION POINTS Part I: Customer Orders FACILITATION TIP

Read this scenario with students while projecting a print version. Guide students to ﬁnd the math terms and highlight or underline them. 2. FACILITATION TIP

DOK-1 What is a shape with three or more sides called? It is a polygon.

Print and project these questions during the discussion and record accurate answers. Provide time for students to practice saying the words out loud (large group, small group, partners, and individually) so they become ﬂuent and comfortable using precise mathematical language.

DOK-1 What is the name for any four-sided shape? Its name is a quadrilateral.

DOK-2 Can all quadrilaterals be called polygons? Why or why not? Yes, because a quadrilateral is a shape with three or more sides.

DOK-2 Can all polygons be called quadrilaterals? Why or why not? No, polygons can have any number of sides, but quadrilaterals can only have four sides.

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Read the following scenario to the class: Fabulous Funky Frames just opened in your neighborhood, and the orders are pouring in! They need your help to build some of the most fabulous funky frames possible! They would like you to make two different frames for each order so the customer can choose the one they like best. All of the frames should be quadrilaterals. Be as funky as you want, but make sure the customers get what they want! Discuss the following questions:

5. 6. 7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Tell students you just got a customer order. The customer would like a quadrilateral frame with one right angle. Demonstrate how to build a frame using the paper strips. Ask the following questions: a.

DOK-1 How do I make a right angle? You put two strips together to form an angle. It should look like the corner of a square.

DOK-2 How can you make other corners that are not right angles? What are they called? We can put the strips together so the angles are larger or smaller than a right angle. The smaller angles are acute and the larger are obtuse.

DOK-1 What is the corner where the sides meet to form the right angle called? It is called a vertex.

DOK-1 What are all of the corners called? All of the corners are called vertices.

FACILITATION TIP Have students use arms, hands, elbows, and ﬁngers to make different angles.

Tell students that after they build their frames, they will tape them onto the poster board or chart paper to display for the customer. Distribute the Student Journals and rulers to students and the paper strips, tape, and poster board or chart paper to groups. Students should construct the two frames for each order and then draw the two frames on their Student Journals, using the rulers. As students are creating their frames, monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What did you have to make sure this frame had? Answers will vary. Two sets of parallel lines, no right angles, etc.

DOK-2 How is a ____ the same or different from a _____? Answers will vary. A square and rectangle both have 4 sides, 2 sets of parallel lines, 4 sets of perpendicular lines, and 4 right angles. But a rectangle does not have 4 equal sides.

DOK-1 How were you able to make this frame match what the customer wanted? Answers will vary. The customer wanted two sets of parallel lines, so I laid the four strips on the table and made the top and the bottom parallel, and then I made the other two sides parallel, and then I taped the vertices together.

DOK-2 Were there any frames that could ﬁll more than one order? Yes! Some of the frames that had all four equal sides could also ﬁll the order that wanted two sets of parallel sides.

e. DOK-1 Explain why all quadrilaterals have four vertices. All quadrilaterals have four sides. When I put the four sides together, they form four corners, or vertices.

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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.

Part II: Leftover Frames 1.

Tell students that the customers chose the frames they wanted. Now Fabulous Funky Frames wants to sell the remaining frames on their website. Before they can, though, they have to compare the frames in order to group them with other frames of similar attributes. They will also need to name the group so customers can easily search for the frames they want. They need your help to group and name the leftover frames. Have students compare the frames and group according to the listed attributes. Then, they will draw the frames in the correct box and name each group with a keyword. Be sure to remind students to include all of the frames that meet the title. Some frames will go in more than one group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

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Two- and Three-Dimensional Figures Explore 2 – Compare and Contrast Quadrilaterals Math Chat •

•

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.

•

DOK-2 What did you notice about parallelograms, rectangles, rhombuses, and squares? All the shapes are quadrilaterals. All the shapes are also parallelograms. All the shapes have four vertices. All squares are rectangles, but not all rectangles are squares. Rhombuses are different from rectangles because they don’t have right angles. DOK-3 What makes trapezoids and kites different from parallelograms? Trapezoids only have one set of parallel lines. Kites don’t have any parallel lines and have two pairs of adjacent sides that are equal in length. Parallelograms have two sets of parallel lines. DOK-3 How is a square the same or different from a rectangle? A square and rectangle both have 4 sides, 2 sets of parallel lines, 4 sets of perpendicular lines, and 4 right angles. But a rectangle does not have 4 equal sides. DOK-3 How is a rhombus the same or different from a kite? A kite and rhombus both have 4 sides, but a kite does not have 4 equal sides. It has 2 pairs of adjacent congruent sides. DOK-1 Which shapes have acute angles? How do you know? A kite, rhombus, trapezoid, and parallelogram have acute angles.

Have students review the frames on the poster board or chart paper they created for customers in Part I. Have them write all of the categories that apply to each frame near or inside the frame. a.

Order 1: Trapezoids

Order 2: Square, rectangle

Order 3: Parallelogram, rhombus

Order 4: Rhombus, square

e. Order 5: Kite, rhombus 5.

Display the frames on the poster boards or chart papers. Have students take a gallery walk to look at other groups’ frames and categories.

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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Two- and Three-Dimensional Figures Explore 3 – Three-Dimensional Solids ACTIVITY PREPARATION Students analyze three-dimensional solids, including triangular and rectangular prisms, cubes, and square pyramids to identify their attributes and describe quadrilaterals as faces of these ﬁgures, using formal geometric language.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • • •

• • • •

1 Student Journal (per student) 1 Cityscape (per group) 1 Set of Three-Dimensional Net Templates (per group, optional) 1 Exit Ticket (per student)

• Square pyramids: Gather examples such as a cheese grater, pyramid toy, perfume bottle, paper weight, etc. • Rectangular prisms: Gather toothpaste boxes, tissue boxes, juice boxes, cubes, wood blocks, dominoes, small candy or chocolate boxes, dice, plastic food containers, etc. • Triangular prisms: Gather triangular-shaped chocolate bars, light prisms, wood pieces, etc. (If materials cannot be gathered, print the set of three-dimensional net templates and construct the three-dimensional ﬁgures for each group using glue and tape.)

Reusable • • • • •

Square pyramids of various sizes and shapes (per group) Rectangular and triangular prisms of various sizes and shapes (per group) 1 Container (per group) 1 Pair of scissors (per class) 1 Projector or document camera (per class, optional)

• •

Consumable • • •

Plan to divide the class into groups of 4 or 5 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Cityscape for each group. If possible, also project it onto the board. Collect a variety of three-dimensional solids for each group. Suggestions include the following solids:

6 Index cards (per group) 1 Bottle of glue (per class, optional) 1 Roll of tape (per class, optional)

•

Place a variety of three-dimensional solids in a container for each group. Student groups will need an area where they can build their cities. Students can work on the ﬂoor, at tables, or at several desks grouped together. For students who need more support in recalling information, please see our 3-D Objects Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS Part I: Viewing a City 1.

FACILITATION TIP Take time to ﬁnd some real-world images of 3-D cities. Consider video games, connecting block toys, and other engaging examples. 308

Give a Cityscape to each group, and project it on the board, if possible. Ask the following questions: a.

DOK-1 What shapes do you see in this picture? The buildings are rectangular prisms. A couple of buildings are shaped like cubes. The roofs of some of the buildings are triangular prisms and square pyramids.

DOK-2 If we were looking at this actual city and not a picture of it, these shapes would be three-dimensional. What makes a shape threedimensional? It is a shape that is not ﬂat. It takes up space with how wide it is, how long it is, and how deep it is. © Accelerate Learning Inc. - All Rights Reserved

3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

• • • •

Students may struggle counting the faces and edges since they can’t see some of the faces. Have them reﬂect on what an edge really is (where two faces meet). If needed, have them refer to their threedimensional solids.

Discuss the shape of the faces. Ask the following question: Which 2-D shapes does this solid contain?

DOK-1 What is a face on a three-dimensional solid? The face of a threedimensional solid is a ﬂat surface. DOK-1 What is an edge on a three-dimensional solid? It is where two faces meet. DOK-1 What are the vertices of a three-dimensional solid? They are where two or more edges meet. DOK-2 What is similar about the faces of cubes and rectangular prisms? They both have square faces. DOK-2 What is the difference between cubes and rectangular prisms? Cubes have to have equal-sized edges and faces, but rectangular prisms do not.

Part II: Building a City

2. 3. 4.

FACILITATION TIP Many schools have sets of 3-D solids. Provide students some time to manipulate these solids. They can touch and count the edges, vertices, and faces.

Repeat with the other shapes listed on the Student Journal. After Part I, invite the class to a Math Chat to share their observations and learning.

Rectangular prisms have rectangular faces.

Acceleration

Give a Student Journal to each student. Have groups circle the red roof of the house on the bottom of the cityscape picture. Student groups should identify the number of faces, vertices, and edges on the roof and record the information on their Student Journals.

Math Chat •

Intervention

Read the following scenario to the class: Congratulations! The mayor has noticed your ability to identify three-dimensional shapes and has chosen you to be on your city’s building committee! The city has purchased a large area of land and would like to develop it with unique and interesting buildings that will attract tourists and future homeowners. The land has been divided into sections, and each section has to be developed with buildings that meet speciﬁc building codes. You have been asked to create a model of the future city to present to the city council for their approval. Read the building codes on the Student Journal. Distribute the container with the three-dimensional objects to each group. Students will create city structures using the three-dimensional objects and will use the index cards to label the sectors with the three-dimensional solid names and their attributes. Once students have created their city structures, they should draw them on their Student Journals. Students should label the three-dimensional structures in their drawings and list their attributes. After Part II, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP

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Use the Print Files Math Chat to project these questions and record answers as you guide the discussion.

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.

FACILITATION TIP If students are not able to draw the three-dimensional shapes accurately, consider allowing them to photograph their cityscapes. FACILITATION TIP To simplify the drawing section, consider using page 2 to demonstrate how to draw the 3-D ﬁgures. Model for students how to draw a 3-D cube, prism, and/or pyramid.

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Two- and Three-Dimensional Figures Explore 3 – Three-Dimensional Solids Math Chat DOK-2 How can the chart from the ﬁrst page of your Student Journal help you with creating your structures? If we use our chart, it will help us know which object we can use in each section. We can make sure we are using the correct object by checking the number of faces, edges, and vertices. • DOK-2 Why do you think you are being asked to draw and label the city after you complete it? We are being asked so we can have a blueprint of our city plan. • DOK-2 Why would it help you to know all the total vertices, edges, and faces of each three-dimensional object in your structure? It would help us identify each attribute and include it in the correct category. • DOK-1 What shapes are the faces of a rectangular prism? They are the shapes of a rectangle and a square. • STEMscopes Tip 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 problem-solving skills within a realworld context.

Post-Explore 1. 2. 3. 4.

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Two- and Three-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 Two-Dimensional Shapes 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 and Contrast Quadrilaterals 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

Three-Dimensional Solids 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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Explain

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Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Puzzling Pieces

Painter

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

Magnets, Magnets Everywhere!

Match Attributes to 2-D and 3-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

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Problem-Based Task Building Prisms 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

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Two- and Three-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 polygons based on their properties.

What prompts will be used?

What does mastery look like?

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I can analyze specific threedimensional figures and describe quadrilaterals as faces of these figures.

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SCOPE 1

Represent and Compare Fractions Scope Introduction SCOPE SUMMARY

Student Expectations

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. 3.NR.4.2 Compare two unit fractions by ﬂexibly using a variety of tools and strategies. 3.NR.4.3 Represent fractions, including fractions greater than one, in multiple ways.

Students build on their prior knowledge of fractions by drawing and describing a unit fraction as one equal part of a whole. They then compare unit fractions using fraction tiles and fraction circles and explain that a whole is the sum of unit fractions. Students work to dive deeper into their understanding of unit fractions and how a sum of unit fractions makes a whole by drawing fractional models and writing a numerical equation involving addition. They then represent fractions, including fractions greater than one, in different ways using concrete objects, diagrams, and number lines. These representations are applied to fraction problems relating parts to a whole and parts to a set.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

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. Students recognize that a whole is composed of two-halves, three-thirds, or four-fourths, and they recognize that equal-size parts of identical wholes may not have the same shape.

In fourth grade, students will 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, will be used to justify the decompositions. Fourth graders also work on comparing two fractions with the same numerator and the same denominator, as well as comparing fractions with different numerators and/or different denominators. Students compare fractions using models, number lines, and benchmark fractions. These tools and strategies help students recognize and reason about the sizes of fractional parts and the fact that comparisons are only valid when the two fractions refer to the same whole.

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

partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names.

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: •

compose a fraction from unit fractions.

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. 316

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Represent and Compare Unit Fractions In this exploration, students will describe and compare unit fractions and explain that a whole is the sum of unit fractions. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

build all of the whole puzzles and identiﬁed the unit fraction for each puzzle piece.

Parts of a Whole In this exploration, students will represent fractions, including fractions greater than one in different ways, using concrete objects as part of a whole. Students will: •

write and name their fractions as parts over a whole.

•

determine the different unit fractions within the object or set of objects.

•

model the parts that make up the whole for different stations.

Parts of a Set In this exploration, students will represent fractions of a set in different ways using concrete objects as pieces of a set. Students will: •

create models of fractions using manipulatives.

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

In this exploration, students will explain that unit fractions represent parts of a whole and understand that a fraction of the whole is the sum of the unit fractions. Students will:

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 their learning and Exit Ticket.

Explore 4

Explore 3

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 their learning.

Combine Fractional Parts

REPRESENT AND COMPARE FRACTIONS

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Diagrams and Number Lines In this exploration, students will represent fractions, including fractions greater than one, using number lines and diagrams. Students will: •

write answers to fraction problems in three different ways: a diagram, number line, and sentence.

After solving the scenario, students discuss their learning with the class, complete an Exit Ticket for assessment; then, revisit the Hook to solve.

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Represent and Compare Fractions 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 represent and compare fractional parts. This activity is intended to assess mastery of the following standard(s): 2.GSR.7.3 Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (“halves,” “thirds,” “fourths”, “half of,” “third of,” “quarter of,” etc.).

Preparation

Materials Printed •

•

Print a Student Handout for each student or group, or prepare to project the Student Handout for the class.

1 Student Handout (per student, group, or class)

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

Distribute a Student Handout to each student or group, or project the Student Handout for the class. Instruct students to look at the fractional pictures and the descriptions. Students match the fractional picture with the correct descriptions. With partners, groups, or the whole class, students facilitate a discussion about the relationship between the number of partitions and the sizes of the parts. 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. a.

As the number of parts becomes larger, the equal parts of the whole become smaller.

As the number of parts becomes fewer, the size of the equal parts becomes larger.

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

REPRESENT AND COMPARE FRACTIONS

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FACILITATION TIP Add the number form to the word form to each fraction description on the Student Handout. Consider coloring in one section of each picture so that the descriptions match. FACILITATION TIP First, show the fractional pictures only and allow students to discuss what they notice. Next, reveal the descriptions and have students discuss again and match. FACILITATION TIP Use precise language when discussing the numbers involved with fractions. Begin to use numerator and denominator.

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Represent and Compare Fractions Hook – Slices of Vitamin C ACTIVITY PREPARATION Students will compose a fraction from unit fractions.

Materials

Preparation

Printed •

• • •

1 Orange Slices (per class)

Reusable • •

1 Phenomena Video (per class) 1 Projector or document camera (per class)

Plan to show the Phenomena Video. Print Orange Slices, and prepare to project it for the class. If your school permits and no allergies are present in your classroom, you could use actual oranges. If the oranges you use have a number of slices other than eight, adjust your discussion accordingly.

Consumable •

1 Orange (per group) (optional, if permitted)

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

FACILITATION TIP Project this scenario. Decide whether you want to tell students how many friends are sharing the orange. To further engage students, bring in some apples and an apple slicer to demonstrate and allow students to eat an apple slice.

3. 4.

DOK-1 What fraction of the orange is each wedge? Each wedge is 1 equal part of 8.

DOK-2 How do you know? There are eight pieces in the whole. There are eight equal parts, so each person would get one equal part of eight.

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.

Part II: Post-Explore 1. 2.

3. 4. 320

Move on to complete the Explore activities.

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

DOK-1 What fraction of the orange is each wedge? Each wedge is 1 equal part of 8.

DOK-2 How do you know? There are eight pieces in the whole. There are eight equal parts, so each person would get one equal part of eight.

Engage

Explore

Explain

Evaluate

Ask students to share the orange slices among their group members equally. Students in the Group

Elaborate

Solution 4 1

2 1

Two Students

Each student gets _8_ (_8_ + _8_ + _8_ + _8_)

Three Students

Each student gets _8_, with _8_ remaining (_8_ + _8_)

Four Students

Each student gets _8_ (_8_ + _8_)

Five Students

__ remaining Each student gets _8_, with __ 8

Intervention

Acceleration

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.

FACILITATION TIP

Discuss the following questions with the class: a.

DOK-1 What is a unit fraction? It is a fraction with a numerator of 1. It represents one equal part of a whole.

DOK-1 Did you recognize any unit fractions in the activity? Yes, each wedge represented a unit fraction.

DOK-2 How did you ﬁnd the fraction of the wedges eaten? We passed

REPRESENT AND COMPARE FRACTIONS

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If unit fraction is not yet on your word wall or anchor chart, take time to add it now.

them out to each person in our group. We added up each wedge as a 1

unit fraction. If we had 2 wedges each, we knew it was _8_ + _8_ = _8_.

DOK-3 If you are in a group where you had leftover orange wedges, how did you know what fraction was eaten and what fraction was left over? In our group, we passed them out so we each had an equal number. Since there are ﬁve people in our group, each person only got one 1 wedge, which is _8_. We took the wedges eaten from the whole orange, 8 8 1 1 1 1 1 3 which was _8_. So, _8_ _8_ _8_ _8_ _8_ _8_ = _8_ left over.

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Represent and Compare Fractions Explore 1 – Represent and Compare Unit Fractions ACTIVITY PREPARATION Students describe and compare unit fractions and explain that a whole is the sum of unit fractions.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

1 Student Journal (per student) 1 Set of Mystery Puzzles (per group) 1 Set of Puzzle Contest Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • • •

• •

1 Resealable bag (per group) 1 Set of fraction circles (per group) 1 Set of fraction tiles (per group)

• •

Consumable •

5 Sheets of white card stock (per group)

•

Plan to have students work in groups to complete this activity. Print a set of Mystery Puzzles on card stock for each group. Cut the pieces out. There should be 23 pieces total. If desired, laminate the pieces for future use. Print a set of Puzzle Contest Cards for each group. Cut the pieces out. If desired, laminate the pieces for future use. Mix up the Mystery Puzzle pieces. Place the 23 pieces in a resealable bag for each group. Have fraction circles and fraction tiles available for students to use as manipulatives to come up with evidence. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips 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. (Fraction Circles and Fraction Tiles)

PROCEDURE AND FACILITATION POINTS Part I: Mystery Puzzles FACILITATION TIP Many schools have fraction manipulative sets available. Consider giving students time to experiment with a set before beginning this Explore activity. FACILITATION TIP Project this scenario and read it through a few times with students. Guide them to locate the math words/phrases: whole, ﬁve different, what fraction of. 322

1. 2.

3. 4.

Place students in groups of four to five. Read the following scenario to the class: A resale shop has received a bag full of puzzle pieces from someone who told them the pieces belong to five different puzzles. The resale shop has asked you to sort the pieces into whole puzzles and identify what fraction of the whole puzzle each piece represents. Give each group a bag of Mystery Puzzle pieces. Instruct students to take the pieces out of the bag and place them in a pile on the desk. Tell students they should find matching pieces of the mystery units from the pile, put the pieces together to build a whole puzzle, and identify what fraction of the whole puzzle each mystery piece represents. As students are finding matching pieces, encourage conversation. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a.

DOK-2 How do you know those mystery pieces belong together? They are the same size.

DOK-1 What is one piece? One piece is one part of the whole.

DOK-1 You have made a whole out of your pieces. How many pieces do you have? What fraction does each mystery piece equal? Answers will vary. I have eight pieces. Each piece equals one-eighth of the whole.

DOK-2 You have found two pieces of matching mystery units. How many more pieces do you think you need to ﬁnd to make a whole? How do you know? Answers will vary. We need four more pieces to make a whole. When we put the two pieces together, we can see that there is enough space for four more pieces that are the same size.

After students find all the pieces necessary to build each whole puzzle, have them use the whole circles provided on their Student Journals to generate their report to the shop owner. Students should name each puzzle and split up the circle into the same number of pieces as the original puzzle. Students should also label each piece of their drawing with the fraction of the whole puzzle it represents. After students have built all of the whole puzzles and identified the unit fraction for each puzzle piece, challenge them to work together to develop a definition of a unit fraction. Guide students to identify a unit fraction as one part of the whole and that a whole is divided into two or more unit fractions. After Part I, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Post these discussion questions before students begin collaborating. Read them with students to provide a focus for their building time.

REPRESENT AND COMPARE FRACTIONS

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FACILITATION TIP Use Picture Vocabulary to reinforce these deﬁnitions for key fraction terms.

Math Chat •

DOK-2 What is always the same about the numerator and denominator in a unit fraction? The numerator always has the digit 1 because each piece is one unit of the whole thing. The denominator is always the total number of units in the whole.

Part II: Puzzle Contest 1.

2. 3.

4. 5. 6.

Read the following scenario to the class: Now that the resale shop has sorted the ﬁve different puzzles, the workers want to have a contest to see who can complete a puzzle more quickly. Each day during the week, the workers take turns putting a puzzle together. Place students in groups of two to four. Let students know that today they will compare fractions in order to see who has the largest portion of the puzzle completed. To be accurate, they must use the manipulatives as tools to justify their answers. In each situation, the answer must be presented as words, using symbols in two ways (> and <) and using drawings of how they used the manipulatives. Encourage them to talk about observations they make about the numerators and denominators as they are modeling the fractions. As students are working, walk around, encouraging conversation focusing on the inverse relationship between the numbers and the size of the pieces of the whole. For students struggling to see the connection, help them place the manipulatives for each fraction right under each other. a.

DOK-1 What do you notice about these two fractions? I notice they both have the same number of “parts” out of the whole; this means they will both have the same numerator.

DOK-2 What is different about these two fractions? They have different denominators.

FACILITATION TIP Use some total physical response strategies to help students learn the difference between numerator and denominator. (Saying “D” for “down on the bottom” might help some students).

FACILITATION TIP Review these symbols. Have students say the phrases “is less than” and “is greater than” between several whole numbers to review. Students need to be ﬂuent with these symbols to compare more complex values as they progress to future math standards.

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Represent and Compare Fractions Explore 1 – Classify Two-Dimensional Shapes c.

DOK-2 What do you notice about the size of the pieces in fractions with a larger denominator? The pieces get smaller.

DOK-2 Why would the greater-number denominator give you smaller pieces? We can see that if we put all the pieces for each whole together, the whole is the same size. So if we take that whole and cut it up into equal parts, the fewer times we cut it, the bigger the pieces are. The more times we have to cut it to make more equal pieces, the smaller those pieces get.

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 A follow up to this question about sharing might be about how often younger students are confused by the denominators in fractions. Ask students, “Why might your little siblings be tricked if asked, ‘Would you rather have one-fourth or one-eighth of this candy bar?’” This common misconception is related to the value of the denominator numeral. FACILITATION TIP When previewing this Exit Ticket with students, show them that it is two sided. Some students may need empty rectangles provided on the back side so they can draw equivalent models.

8. 9.

After students have ﬁnished, have a few students come up and share their answers. After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What are some observations you made about these fractions? We noticed that each pair of fractions had the same numerator, but their denominators were different. An interesting thing we also observed is that the greater the number in the denominator was, the smaller the sizes of the pieces were. • DOK-2 What does the denominator do to the whole? Why is that important to the size of the pieces of the whole? The denominator equally partitions the whole. It does not change the size of the whole but changes only the size of the piece. It is important because the more times you have to cut it to get more pieces, the smaller those pieces get. • DOK-3 If you wanted a greater piece of something such as your favorite snack, would you share with more people or fewer people? What would either scenario do to the fraction? If we wanted to get a greater piece of something, we would want to share it with fewer people. If we shared it with more people, the number in the denominator would be a greater number, but the size of the pieces would be smaller. If we shared it with fewer people, the denominator would be a lesser number, but the size of the pieces would be larger. •

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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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT AND COMPARE FRACTIONS

Home

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Represent and Compare Fractions Explore 2 – Combine Fractional Parts ACTIVITY PREPARATION Students explain that unit fractions represent parts of a whole and understand that a fraction of the whole is the sum of the unit fractions.

Standards for Mathematical Practice •

MP.3 Construct viable arguments and critique the reasoning of others.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

Reusable • • •

• •

Preparation • • • •

1 Dry-erase marker (per student) 1 Dry-erase board/erasable surface (per group) 1 Dry-erase eraser (per student)

6 Plastic eggs in an egg carton (excess egg slots can be cut off) (per class)

Station 2: • •

2 Miniature toy cars (make sure they can be pulled by magnets) (per class) 2 Magnets (per class)

•

Station 3: • •

1 Basket/container (per class) 3 Plastic balls (per class)

Station 4: •

Students will use their dry-erase boards to draw the pizza described on the Station Card.

Plan to divide the class into groups of 4 or 5 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print Station Cards on card stock, cut them apart, laminate them (optional), and place 1 at each station. Arrange the materials for each station as described. • Station 1: Place the plastic eggs in an egg carton. Cut off any excess egg slots, if necessary. • Station 2: Make 2 separate circular “race tracks” with a START/ FINISH line with the masking tape, and place 1 magnet and car at each track. • Station 3: Place the basket, bucket, or container on the ﬂoor, and mark a START line from where students will be throwing the balls into the container. • Station 4: Students will use their dry-erase boards to draw the pizza described on the Station Card. • Station 5: Put 4 play $1 bills and play quarters at the station.

Station 1: •

MP.4 Model with mathematics. MP.6 Attend to precision.

•

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).

Station 5: • •

4 Play 1-dollar bills (per class) 4 Play quarters (per class)

Consumable • •

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3 Sheets of white card stock (per class) 1 Roll of masking tape (per class)

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS 1.

2. 3.

4. 5.

Discuss the following questions: a.

DOK-1 Have you had cake on your birthday? How do you serve that cake? We usually cut the cake into equal pieces to share with all the guests.

DOK-1 Does each person eat a whole cake? No, each person eats 1 piece of the whole cake.

DOK-1 Ask students to remind their shoulder partners what a unit fraction is based on the deﬁnition that was agreed upon as a class during Explore 1. A unit fraction is one part of a whole. A whole is divided into 2 or more unit fractions.

Tell students that they are surrounded by unit fractions every day and that today, they will be seeing them in different ways. Explain to students that they will be doing fractional activities at 5 different stations. At each station, they must look for the different unit fractions within the object or set of objects they are exploring. Students should read each Station Card and use the objects along with their dry-erase boards to model the parts that make up the whole. Encourage students to work together in their groups to decompose the wholes into unit fractions and make a numerical equation that represents the whole. As students revolve through the different stations, monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How many equal pieces is this whole partitioned into? This whole is partitioned into (2, 3, 4, 6, 8) equal pieces.

DOK-2 How would you decompose this whole into its fractional units? To decompose this whole into its fractional units, I would break it apart into 2 one-halves, 3 one-thirds, 4 one-fourths, 6 one-sixths, 8 oneeighths.

DOK-1 If I am combining several amounts together, what operation am I doing? I am doing addition.

DOK-1 When we compose the whole, how would you describe it in a numerical equation? To compose the fractional parts of a whole using a numerical equation, I would add all the unit fractions together to get the 1

6. 7. 8.

sum (for example, _3_ + _3_ + _3_ = _3_).

Students should record their models and equations on their Student Journals. Students should complete the challenge at each station, if there is one. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What are some observations you made through the activities? Some of the observations we made during the activities is that each whole is made up of equal individual (unit) pieces. Those parts are all equal in size and part of the same whole. • DOK-1 After having interacted with these fractions in their individual units, how can we deﬁne a unit fraction? A unit fraction is one part of a whole. A fraction is made up of 2 or more unit fractions. For example, a whole partitioned into 6 equal pieces is made up of 6 one-sixths. • DOK-1 What value does each piece of the whole have? Each piece of the whole is one out of ___ number of pieces of the whole. They are all equal in value. •

REPRESENT AND COMPARE FRACTIONS

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FACILITATION TIP The concept of fractions as part of a group may be new for many students. Take time to differentiate and demonstrate fractions of a whole and fractions as a part of a group. FACILITATION TIP Preview the Station Cards for unique vocabulary and consider reading them aloud to students before they rotate to stations. FACILITATION TIP Project and read these questions with students before they begin the stations. Encourage them to ask and answer these questions as they collaborate with their partner.

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.

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Represent and Compare Fractions Explore 2 – Combine Fractional Parts •

• •

DOK-2 What can you tell me about the fractional pieces in relation to the whole? Even though each piece is one out of ___, when we put them all together, the whole becomes the sum of all of these individual units put together. DOK-1 What do you notice about the fractions that represent each whole? The numerator is the same digit as the denominator. DOK-2 What do you notice about the fractions that represent each piece of the whole? The numerator is always a 1, and the denominator is always the total number of units in the whole.

Post-Explore FACILITATION TIP When you preview this Exit Ticket with students, take time to answer questions. Some students may be uncertain about how to draw a rainbow with equal parts (the bottom semi-circle may be visually smaller than the top semi-circle).

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

REPRESENT AND COMPARE FRACTIONS

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Represent and Compare Fractions Explore 3 – Parts of a Whole ACTIVITY PREPARATION Students will represent fractions, including fractions greater than one in different ways, using concrete objects as part of a whole.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. 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 • • • • • •

•

1 Set of linking cubes (per group) 1 Set of colored tiles (per group) 1 Set of fraction circles (per group) 1 Resealable bag (per group) 1 Paper plate (per group) 1 Bin or container (per group)

•

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket per student. Print one set of Scenario Cards per group, cut the Scenario Cards out, and place them in a resealable bag. Cards need to be used in order. Prepare a bin of linking cubes, colored tiles, and fraction circles per group. 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. (Linking Cubes, Color Tiles, and Fraction Circles)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Take time to ﬁnd some real-world images of 3-D cities. Consider video games, connecting block toys, and other engaging examples.

2. 3. 4. 5. 6.

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Read the following scenario to the class: What a treat! You and your family are going to dinner at a nice restaurant! Your friends will want to know every detail about your dinner. Tell students they will be modeling and recording the details about eight different parts of their dinner. Let students know that each group will have a paper plate and manipulatives to help them represent each part of their dinner and answer questions. Have students read Card 1: The Windows and create a model of the situation using any of the manipulatives available. Have students draw their models on their Student Journals and shade in the parts of the window that were washed. Discuss the following questions: a.

DOK-1 How many window panes were already washed? Five window panes were washed.

DOK-2 How did you show this with your model? We used red tiles for the washed panes and blue tiles for the unwashed panes.

DOK-1 How many window panes were there total? There were a total of eight window panes.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

e. We need a way to show part of a whole. We can write a fraction to show others how much of the whole thing we are talking about! i. Guide students in writing the fraction. The top number is called the numerator, and it shows how many pieces you’re looking for. The bottom number is called the denominator, and it shows how many pieces are in the whole thing. f.

9. 10. 11.

Students should record this information on their Student Journals by completing the statement and writing the fraction that shows the number of window panes that have been washed.

After a group completes the third card, discuss the following questions: a.

DOK-1 How many apples did the family share? They had a total of three apples.

DOK-1 How is each apple partitioned? Each apple is partitioned into halves.

DOK-1 How many pieces of apple did the family eat? They ate ﬁve pieces.

DOK-2 How can we write this as a fraction? We can write it as ﬁvehalves.

Guide students on how to write the fraction that is greater than one by counting each piece, “one-half, two-halves, three-halves, four-halves, ﬁve-halves.” Discuss 5 how they can read the fraction another way. For example, _2_ could be read as “two and one-half”. Students should continue to model the situations described on each card and record their work on their Student Journals. As students work, walk around to assist students who are struggling. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat

FACILITATION TIP Consider modeling Card 3 to the whole class before they begin collaborating. Mixed numbers is likely a new concept.

REPRESENT AND COMPARE FRACTIONS

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FACILITATION TIP Encourage students to use rectangles in their models whenever they can. Drawing accurately divided rectangles is simpler than drawing circles. When students model multiplication and division with fractions, they will use rectangles rather than circles.

After students have ﬁnished the activity and Student Journal, invite the class to share their ﬁndings for each scenario. DOK-1 What did the top number in the fraction tell you? The top number showed how many parts we were looking for. • DOK-1 What did the bottom number in the fraction tell you? The bottom number showed how many pieces there were in the whole thing. •

Explain the following to the class: We have special names for these numbers. The top number is called the numerator, and the bottom number is called the denominator. DOK-2 How are fractions helpful? Fractions can help us describe a piece of something. They gives us a way to use numbers to show parts of a whole. • DOK-2 What are some other situations in which you could use a fraction? Answers will vary but could include pieces of pie, slices of oranges, strips of paper, etc. •

FACILITATION TIP Take time to reinforce ﬂuency with these vocabulary words. Post them on your word wall, use physical responses to show understanding, and provide multiple opportunities to read and say the words aloud. FACILITATION TIP

Post-Explore 1. 2. 3.

Be prepared with some additional engaging Have students complete the Exit Ticket to formatively assess their understanding images of fractions in the real world. of the concept. FACILITATION TIP Complete the Anchor Chart as a class. Before students complete this Exit Ticket, Have each student complete their Interactive Notebook. give them time to practice saying and writing the deﬁnitions of numerator and denominator in their own words (Picture Vocabulary).

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Represent and Compare Fractions Explore 4 – Parts of a Set ACTIVITY PREPARATION Students represent fractions of a set in different ways using concrete objects as pieces of a set.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. 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)

• •

Reusable • •

•

1 Set of color tiles (per group) 1 Set of two-color counters (per group)

•

Consumable •

•

4 Sheets of card stock (per class)

Plan to divide the class into groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print one set of Station Cards on card stock and cut the cards out. Prepare a bin of color tiles and two-color counters for each station. For students who need more support in recalling information, please see our Grid Paper 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. (Color Tiles and Two-Color Counters)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP These Station Cards and the Student Journal provide excellent opportunities for students to practice carefully reading math problems. Encourage students to read the Station Cards aloud together and look for clue words.

1. 2.

Tell students that they will be spending the day at an amusement park! Students will rotate with their groups to eight different stations. At each station, they will need to model what is happening and record their work on their Student Journals. a.

As students work, walk around to assist students who may need support.

FACILITATION TIP When you preview the Station Cards, consider appropriate supports for your students. Several stations require students to ﬁnd combined sub totals. Note the word “not” and sort out extra numerals that don’t impact the solutions.

Optional: Complete Stations 1 and 2 as a whole group, discuss, and then have students rotate among the remaining six stations.

Students may need support with creating the models. Help students see how the manipulatives could be used to represent what is being described; for example, you could lay out eight counters with the yellow side up, turning over three of them to represent how three of the eight roller coaster cars are empty.

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

Math Chat After students have ﬁnished the activity and Student Journal, invite groups to share their ﬁndings for each station. Prompt students to discuss how some of their models look different but are representing the same fraction. 332

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 How did your group determine which number belonged as a denominator? As a numerator? To determine the denominator, we referred to the scenario to see how many total pieces there were in the set. This number tells us how many equal parts there are in the whole and, therefore, goes under the fraction bar, making it the denominator. To ﬁnd the numerator, we found the number of parts the question was asking for. • DOK-2 Think of a time when using fractions could be helpful. Answers will vary but could include sharing colored candies with a friend, describing the amount of quarters you have in your coin collection, etc. •

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. When previewing this Exit Ticket, consider Complete the Anchor Chart as a class. how your students may interpret the facial expression and body language of the Have each student complete their Interactive Notebook. children in the image.

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Represent and Compare Fractions Explore 5 – Diagrams and Number Lines ACTIVITY PREPARATION Students represent fractions, including fractions greater than one, using number lines and diagrams.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials Printed • • • • • •

Reusable

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Set of Fabric Stamp Designs (per class) 1 Silly Animal Noises Game Board (per class) 1 Vote Spinner (per class) 1 Exit Ticket (per student)

• • • • • • • • • • •

Consumable

1 Set of fraction tiles (per group) 1 Bag of tangrams (per class) 1 Plastic egg (per class) 2 Timers (per class) 1 Number cube or die (per class) 1 Game marker or token (per class) 1 Flyswatter (per class) 1 “Fly” (cube, plastic object, etc.) (per class) 1 Blindfold (per class) 1 Paper clip (per class) 1 Ball (can be a dodgeball, volleyball, plastic ball, etc.) (per class)

• • • • •

1 Roll of masking tape (per class) 1 Half-full water bottle (16–20 oz.) (per class) 3 Empty 2-liter bottle “bowling pins” (per class) 6 Sheets of card stock (per class) Butcher paper (optional)

Preparation • • • •

Plan to have students work in groups to complete this activity. Gather all materials. Print a Student Journal and an Exit Ticket for each student. Print the set of Station Cards on card stock, laminate them (optional), cut them apart, and tape them around the room. •

•

• • • •

Station 1: Make a number line out of masking tape on the ﬂoor. If possible, make the number line 8 feet long, and divide it into 16 sections. Place a 0 at the beginning of the number line, a 1 in the middle, and a 2 at the end. Alternatively, make an 8-foot number line divided into eight sections between 0 and 1 and 8 sections between 1 and 2 on butcher paper. Station 2: This station should be located at a table that students can walk around. If a table is not available, several desks can be pushed together to create an area that students can walk around. Alternatively, a section of ﬂoor could be marked off with masking tape, and students would walk on the tape line. Station 3: Print the Fabric Stamp Designs. Station 5: Print the Silly Animal Noises Game Board on card stock. Optionally, laminate it for future use.

Station 1 • •

•

Station 2 •

•

1 timer

•

Station 5 • • •

•

1 Vote Spinner, a pencil, and a paper clip

Station 8 • • •

•

3 bottles as bowling pins: 2 in the back row, 1 in t he front 1 ball (can be a dodgeball, volleyball, plastic ball, etc.)

Station 7 •

•

1 die 1 Silly Animal Noises Game Board 1 game marker

Station 6 •

•

1 half-full water bottle

1 “ﬂy” 1 blindfold 1 ﬂyswatter

For students who need more support in recalling information, please see our Assorted Number Lines 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. (Fraction Tiles and Number Lines)

Station 3 • • •

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Masking tape number line from 0 to 2 divided into eighths on the ﬂoor 1 plastic egg

Station 4 •

You can do rotations all in 1 day or over several days. Set up the following materials at the corresponding stations: •

•

1 bag of tangrams (If tangrams are not available, cut out the pieces of an additional set of Fabric Stamp Designs for students to use to build the shapes.) 1 timer 1 Fabric Stamp Designs

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS 1.

2. 3. 4.

Tell students that each station will have a challenge for them to complete. Read through each scenario, and demonstrate how to do each challenge. Explain that they will have 5–7 minutes at each station to complete the challenge and write their answer in three different ways (diagram, number line, and sentence). Take some time to review proper use of materials. Set the timer for the predetermined time, and have students begin their ﬁrst activity. Monitor actively. At each station, students will complete the following steps: a. Act out the situation described at the station and keep track of results. b. Trace the “whole” fraction tile in the box on their Student Journals for that station. Note that a couple of stations will have more than one whole. c. Trade out the whole fraction tile(s) for one that is divided into the number of equal pieces needed based on the situation. d. Use the pieces to create sections in the drawing so the bar is divided up into the right number of equal parts. e. Build the fraction that represents the results using these fraction pieces and shade in that part of the drawing. (Students should label the parts of their drawing.) f. Cut out and glue one of the number line models directly below the drawing so the 0 and 1 or the 0 and 2 line up with the edges of the drawing.

FACILITATION TIP For these stations, consider having an older student or adult at each station to support students. Reading the challenge, completing the challenge, and recording data may take longer than 5–7 minutes otherwise.

REPRESENT AND COMPARE FRACTIONS

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FACILITATION TIP Print and post these steps at each station to guide students. FACILITATION TIP Consider adding some rectangles or labeled number lines to the Student Journal for struggling students. Another modiﬁcation may be to skip Step f and allow students to draw rather than cut and glue.

g. Divide up the number line the same way the model is divided. h. To ﬁnd the point on the number line that represents the fraction, let each shaded piece equal one “hop” on the number line. i. Place a point on the number line where they land after the last hop.

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Represent and Compare Fractions Explore 5 – Diagrams and Number Lines 5.

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

As students model their answers on number lines, encourage them to trace the hops on the number lines to help solidify that they will count the hops, not the tick marks. a.

STEMscopes Tip 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.

DOK-1 How do you determine how many equal pieces you will partition your number line and diagram into? The number of equal parts is determined by the number of turns, pieces, or objects in the scenario. These pieces will also tell us what the denominator is.

Demonstrate how the denominator of the fraction would be wrong if you were to count the tick marks instead of the hops, or sections, of the number line.

When class is ﬁnished, share and highlight different answers, emphasizing how each group wrote fractions with the same denominator that helped them partition both the number line and diagram. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat Note that for many of these stations, each group will have different answers. Take this opportunity to encourage students to share their scenario results and how they decided to show their results. •

•

DOK-2 If each student got different results for each of these scenarios, how did you decide how many equal pieces each diagram was broken into? Even though our results were all different, the total number of turns, pieces, and objects was the same for everyone. This told us the fraction’s denominator, and the numerator was our actual result of the activity. DOK-1 How did you decide how to equally partition your number line? To determine how many equal pieces our number line and diagram were broken into, we looked at the scenarios and saw the number of equal turns, pieces, and objects. The total number of equal objects or pieces told us how to partition our number line and diagram. DOK-2 How do you place fractions on a number line? What challenges did you encounter? To place a fraction on a number line, we count the hops, not the tick marks, on the line to find the numerator. The total number of hops was the denominator. DOK-2 How did you place fractions greater than 1 on the number line? To place a fraction greater than 1 on a number line, we count the hops by eighths. Then, we find the whole number and the fractional part after the whole number (for example, count one-eighth, two-eighths, three-eighths ... ten-eighths.) DOK-2 What are some similarities you found between the number line and the diagram? Did you use one to help with the other? Some similarities are that the “whole” was the same size. This helped us understand that they both modeled the same fraction in two different ways. The diagram helped us line up the tick marks on the number line and find the fraction more easily.

Post-Explore

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FACILITATION TIP

This Exit Ticket could be used as a preassessment before this Explore activity as well as after. When previewing with students, be sure they are aware that it is two sided.

2. 3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Represent and 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

Represent and Compare 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

Combine Fractional Parts 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

Parts of a Whole

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

Parts of a Set

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

Show What You Know, Part 5 Diagrams and Number Lines 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

Susie’s Decorating Project

Duff Goldman

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

The New City Park

Compare Fractions – Area Models and Number Lines

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

Fluency Builder

Astro Cuisine

Match Fraction Models with Fraction Words and 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

REPRESENT AND COMPARE FRACTIONS

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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

REPRESENT AND COMPARE FRACTIONS

Represent and Compare Fractions

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?

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I can explain how multiple copies of a unit fraction form a non-unit fraction.

I can compare two unit fractions by using a variety of tools and strategies.

I can represent fractions, including fractions greater than one, in multiple ways.

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SCOPE 1

Equivalent Fractions Scope Introduction SCOPE SUMMARY Students acquire an understanding of equivalent fractions. They explain the equivalence of fractions and compare fractions by reasoning about their size or their location on a number line. Using a visual model to justify, they generate simple equivalent fractions such as __1 = __2. 2 4 They are able to explain whole numbers as fractions and realize fractions are equivalent to whole numbers. Student Expectations

3.NR.4.4 Recognize and generate simple equivalent fractions.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Second-grade students partition circles and rectangles into equal shares using fractional language. Third grade uses concrete models; students investigate and grasp the relationship between unit fractions and the whole. This lays the groundwork for students to work with equivalent fractions.

Fourth-grade students will extend their understanding of fraction equivalence with attention given to how the number and size of the parts differ, even though the two fractions themselves are the same size. They will compare fractions with different numerators and denominators by creating common denominators or making comparisons to a benchmark fraction such as __1 . 2

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

partition rectangles into halves, thirds, and fourths.

•

partition pie models in various ways.

•

describe their strategies in order to best share pie pieces.

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 recognize equivalent fractions with denominators of 2, 4, 8, 3, and 6.

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

Model Equivalence with Visual Models In this exploration, groups of students will solve a scenario involving how to equally cut fruit and ﬁnd different ways to describe the amounts of fruit in fruit salad. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

determine equivalent fractions using a variety of objects and manipulatives.

Explore 3

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

Model Equivalence with Number Lines In this exploration, groups of students will decide how to fairly share different foods with their family members during a reunion. Students will: •

use number lines to determine equivalent fractions.

•

fold number lines to identify fractions of a whole to locate equivalent fractions among the different denominations.

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Once students have solved the scenario, they discuss their learning with the class, and conclude with an Exit Ticket.

Whole Numbers as Fractions In the ﬁnal exploration, students are identifying the different ways whole windows are partitioned for their window washing service. Students will: •

express whole numbers as fractions using concrete objects, pictorial models, and number lines.

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

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Equivalent Fractions 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 1

Students partition a visual model of a pie into unit fractions of __2 and __4. Students use those units to compose a greater fraction. This activity is intended to assess mastery of the following standard(s):

2.GSR.7.3 Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (“halves,” “thirds,” “fourths”, “half of,” “third of,” “quarter of,” etc.).

Preparation

Materials Printed • •

EQUIVALENT FRACTIONS

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Place students in groups of two. Print a Student Handout for each student. Print a Pie Model for each pair.

• • •

1 Student Handout (per student) 1 Pie Model (per pair)

Reusable •

1 Pair of scissors (per teacher)

Procedure and Facilitation Points 1. 2. 3. 4. 5. 6.

Distribute a Pie Model to each pair and a Student Handout to each student. Give students time to decide how they will make one cut in the pie so that it can be shared equally between two people. Encourage students to fold their Pie Models to see. Students should then draw the line of the fold on the picture on their Student Handouts. Invite students to determine the best way to share between 4 people. Allow students time to work in pairs to answer questions. Facilitate a class discussion about their 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. Ask the following questions: a.

What did the numerator show? How many equal-sized pieces of pie we are talking about

What did the denominator show? How many equal-sized pieces the pie was divided into

What is a unit fraction? A fraction with a one as the numerator. It is always one equal part of the whole.

What was the unit fraction in the ﬁrst scenario? __2

A better word to use consistently in this activity is partition. Divide implies separating into groups of equal size, but partition means decomposing a ﬁgure into equal-sized units.

FACILITATION TIP Model on the board with a picture of the pie partitioned into 4 equal pieces along with the fraction labeled with numerator and denominator.

e. What was the unit fraction in the second scenario? __4 f.

FACILITATION TIP

Which unit fraction represents a larger piece of the pie? __2

When you added unit fractions together, what did you notice? Answers will vary. The numerator got larger, but the denominator stayed the same.

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

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Equivalent Fractions Hook – Can’t Stop, Won’t Stop … Reading ACTIVITY PREPARATION Students represent and recognize equivalent fractions with denominators of 2, 4, 8, 3, and 6.

Materials

Preparation

Printed •

• •

1 Can’t Stop, Won’t Stop … Reading (per class)

Reusable • • •

1 Bowl or bag for fractions (per class) 1 Phenomena Video (per class) 1 Projector or document camera (per class)

• •

Plan to show the Phenomena Video. Print one Can’t Stop, Won’t Stop … Reading. There are 24 different fractions with matching number lines and wholes. You should have one fraction with a matching number line and whole for each student. Cut out the fractions, number lines, and wholes. Prepare to project Can’t Stop, Won’t Stop … Reading.

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

FACILITATION TIP

To make connections of part to whole, have a chapter book that students like or have read as a visual aid. 4.

FACILITATION TIP

Use the Picture Vocabulary or draw a fraction on the board with labeled parts.

DOK-1 If you have read 1 equal part of the 8 chapters in one book and 6 1 1 chapters of the other, what fraction of the books have you read? __8, __6

DOK-1 If you have read 2 equal parts of 8 chapters and 6 chapters, what 2 2 fraction of the books have you read? __8, __6

DOK-1 If you have read 3 equal parts of the 8 chapters and 6 chapters, chapters 3 3 what fraction of the books have you read? __8, __6

DOK-1 If you have read 4 equal parts of the 8 chapters and 6 chapters, 4 __ 4 what fraction of the books have you read?__ , 8 6

FACILITATION TIP For a quick review of fractions, challenge students with various examples of numbers of chapters read from different books.

e. DOK-2 If you have read half of the chapters in each book, how many chapters have you read? 4 in the book with 8 chapters, and 3 in the book with 6 chapters f.

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DOK-2 How much of the books have you read if you are done with __4 of 2 the book with 8 chapters and __3 of the book with 6 chapters? 6 chapters in the book with 8 chapters, and 4 chapters in the book with 6 chapters

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 situation. Discuss the following questions with the class: a. b. c. d.

DOK-1 If you have read 1 equal part of the 8 chapters in one book and 6 1 1 chapters of the other, what hat fraction of the books have you read? __8, __6

DOK-1 If you have read 2 equal parts of 8 chapters and 6 chapters, what 2 2 fraction of the books have you read? __8, __6 DOK-1 If you have read 3 equal parts of the 8 chapters and 6 chapters, 3 3 what fraction of the books have you read? __8, __6 DOK-1 If you have read 4 equal parts of the 8 chapters and 6 chapters, 4 4 what fraction of the books have you read? __8, __6

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.

EQUIVALENT FRACTIONS

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e. DOK-2 If you have read half of the chapters in each book, how many chapters have you read? 4 in the book with 8 chapters, and 3 in the book with 6 chapters f.

3. 4.

Review the problem and allow students to solve it. Have students draw one fraction out of a bowl or bag. Show each number line and have students come get the number line that matches the fraction they drew. Show each whole, and have them come get one that matches their fraction. FACILITATION TIP Have the students organize themselves into groups based on what fraction of the books they have read. Tell students that there were 24 in the bag or bowl, but Reduce the set of cards if the number of there should be only 12 groups—some of the fractions represent the same part of students is fewer than 24. the books. If the students are struggling to discover that there are some equivalent fractions, remind them to use their number lines and wholes to look for other fractions that represent the same amount of the books read.

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Equivalent Fractions Hook – Can’t Stop, Won’t Stop … Reading 7.

Discuss the following question with the class: a.

DOK-3 How do you know that each set of fractions belonged together in the same group? The groups are listed below: i.

1 __

FACILITATION TIP

ii.

2 __ 1 __

Direct students’ attention to how the wholes are represented in two different ways and how students can match the size of the fractions.

, We knew that we represented the same amount of the 8 8 4 chapters because fourths partitioned in half make eighths.

iii.

3 __

iv.

3 __ 2 __ 4 __ 1 __

, , , We could see on our number lines and wholes that each of 4 8 6 2 our fractions is equivalent to a half. 2 is half of 4, 4 is half of 8, and 3 is half of 6.

5 __

vi.

3 __ 6 __

, Our number lines showed the same distance from 0, so we knew 4 8 that we had equivalent fractions.

vii.

7 __

viii.

8 __ 3 __ 6 4 __ __

, , , All of the number lines had the dot at 1 whole. All of our 4 8 3 6 wholes were completely shaded. All of our fractions represent that the whole book had been read.

ix.

1 __ 2 __

2 __ 4 __

xi.

1 __

xii.

5 __

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.

, Thirds split in half make sixths, so these fractions represent the 3 6 same amount of the book read. ,

3 6

Our wholes showed the same amount, so they are equivalent.

6 6

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

EQUIVALENT FRACTIONS

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Equivalent Fractions Explore 1 – Model Equivalence with Visual Models ACTIVITY PREPARATION Students determine equivalent fractions using a variety of visual models.

Standards for Mathematical Practices • • •

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

Part I: Apples and Oranges

• • • •

1 Student Journal (per student) 1 Set of Fraction Cards (per student) 1 Set of Ingredient Cards (per class) 1 Exit Ticket (per student)

• • • •

Reusable

Part II: Lolita’s Fraction Salad • •

Part I: Apples and Oranges • •

1 Set of fraction circles (per group) 1 Pair of scissors (per student)

•

Part II: Lolita’s Fraction Salad • • • •

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 set of Fraction Cards for each student. Prepare fraction circles for each group.

3 Bags of fraction bars (per class) 2 Bags of fraction circles (per class) 5 Plastic bins (per class) 1 Glue stick (per student)

•

Print a set of Ingredient Cards, and cut out the cards. In each bin, place a bag of fraction manipulatives and one Ingredient Card. For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips 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. (Fraction Circles and Fraction Tiles)

PROCEDURE AND FACILITATION POINTS Part I: Apples and Oranges 1.

FACILITATION TIP

Have students write numerator and denominator on sticky notes. Then, have students write a fraction on a sheet of paper and label the parts with the sticky notes. FACILITATION TIP Virtual Manipulatives and Supplemental Aids: Fraction Circles will be helpful manipulatives for students.

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Read the following scenario to the class: Akari and Mila like to share their fruit at lunch. Akari brings an apple, and Mila brings an orange. The apple and the orange are the same size. Their moms slice their fruit into different numbers of equal parts each day. The girls then ﬁgure out how to equally trade their fruit. DOK-1 Ask students to turn to their shoulder partners, deﬁne what a fraction is, and share answers. a.

DOK-3 Ask the following general question: a.

A fraction is a part of a whole. It is made up of a numerator on the top, which says how many equal pieces you have of something, and the bottom number is the denominator. A denominator tells you the total number of equal pieces the whole is broken up into.

Can two fractions that have different digits be equal? Accept all answers, and allow students to explain their reasoning.

7. 8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

Ask students if they have ever shared something such as food with a friend or family member. Allow students to share what they think is a fair trade when sharing food. Explain to students that they are going to try to ﬁnd a fair way to trade the fruit slices. The fractions will represent how much fruit each girl is going to share. Even though each girl’s fruit might be divided into a different number of slices, students will have to ﬁgure out how many slices each girl will share so they are giving an equal amount to the other person.

Intervention

Acceleration

FACILITATION TIP Model for students how to slice fruit in different ways. Show students slices that are equal and slices that are not equal.

EQUIVALENT FRACTIONS

Home

Tell students to build __4 using their fraction circles. This represents the amount of an apple Akari is going to share with Mila. Students will now cut up the Fraction Cards. They will build each fraction using their fraction circles. Discuss the following questions: 1

a. DOK-1 Look at each fraction you built. Compare them to the __4 model of 1 the fruit Akari is going to share. Are any of your other models equal to __4? 2 1 __ __ How can you tell? Yes, 8 is equal to 4! I can tell because if I put one model on top of the other, they cover the same area or space. b. 10. 11. 12. 13.

14.

DOK-1 What fraction could possibly pos be an equivalent amount Mila then 2 shared with Akari? An equivalent amount could be __8.

FACILITATION TIP

Cut some Fraction Circles into various slices for students to use as needed to determine Students will take the fraction card showing 2/8 and glue it on their Student Journals. They will draw a model of their fraction circles on their Student Journals. the equal fractions. Challenge students to collaborate with partners or small groups to determine how Akari and Mila shared their fruit the rest of the days. Explain that there will be 4 fractions left over. As students explore with their manipulatives, listen in on conversations they are having, looking out for misconceptions. a.

Make sure they understand that the same-size whole is broken up into a different number of equal pieces.

Ensure that they are covering the same area displayed in the fraction by pieces that are the same size.

For students who are struggling, help them by displaying a whole first and finding the first fraction and then exploring different fractions that may cover the same area.

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

Math Chat DOK-2 Can two fractions with different digits be equal? Yes, you can divide up the pieces into smaller equal pieces. This will create a new fraction, but the fraction is still covering the same area, or space. • DOK-2 Find an equivalent fraction for each of your left over cards using fraction circles. Explain how you found the equivalent fraction for the leftover cards. We put the fraction circles/tiles on top of several different fractions. I noticed that the denominators for equivalent fractions are related, and sometimes they’re doubled or halved. •

FACILITATION TIP Use different manipulatives to model as needed for struggling students.

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.

Part II: Lolita’s Fraction Salad 1. 2.

Give one bin to each group. Read the following scenario to the class: Lolita has created the most delicious exotic fruit salad recipe! She listed how much of each ingredient is needed to re-create her salad. Unfortunately, different people may have different tools to measure food! We need to ﬁnd different ways to describe these amounts so people can measure them using the tools they have.

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Equivalent Fractions Explore 1 – Classify Two-Dimensional Shapes 3. 4. 5. 6. 7.

Ask students to look over the Ingredient Card they have in their bin. Students should start by building the fractional part described on the card. Students will then use the remaining fraction circles or bars to ﬁnd as many different ways as possible to represent the same amount of that ingredient. Students should record the equivalent fractions on their Student Journals. Rotate bins so each group ﬁnds equivalent fractions for each ingredient. DOK-1 After students have explored the fractions with all different manipulatives, ask students to share their observations on the fractions they modeled. a.

8. 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.

We noticed that even though all the fractions had different digits, they were the same size and were equal.

Tell students that fractions that have different digits but cover an equal area are called “equivalent fractions.” After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat •

DOK-3 These fractions all look different when written as numbers but are still equivalent. Why is that? All of these fractions may look different when written as numbers because their wholes are partitioned into a different number of equal 1 pieces, yet they are equivalent because they all represent __2 of a whole.

•

DOK-2 What number patterns do you notice in the numerators and denominators 1 of fractions that are equal to __2? A number pattern that we notice is that the number in the denominator is double the number in the numerator.

•

DOK-2 Using the patterns you have noticed, what other fractions are equivalent 1 5 __ 2 3 to __2? __ , , __, etc. 10 4 6

•

DOK-1 What other denominators did you use to find fractions that are equivalent 2 2 to __3? We couldn’t find a set of fourths or eighths to equal __3. We were able to find an equivalent fraction using sixths.

•

DOK-2 What fractions were equivalent to __6? Explain why. We were able to make equivalent fractions with each size piece! Six-sixths is equal to one whole, so we could make one whole no matter what size the pieces were.

Post-Explore FACILITATION TIP

On this Exit Ticket, reassure students that the models that they draw can be simple ﬂat, 2-D images. Consider providing blank rectangle shapes already drawn on the Exit Ticket for struggling students.

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

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Equivalent Fractions Explore 2 – Model Equivalence with Number Lines ACTIVITY PREPARATION Students determine whether a set of fractions is equivalent using a number line.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. 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 Number Line (per student) 1 Set of Scenario Cards (per class) 1 Exit Ticket (per student)

•

Reusable •

•

1 Pair of scissors (per student)

•

Consumable • •

5 2” × 11” strips of parchment paper (per student) 1 Pack of crayons or colored pencils (per student)

•

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Number Line for each student. Laminate it for long-term use if desired. Cut enough parchment paper for each student to have 5 2″ × 11″ strips. Print a set of Scenario Cards on card stock, cut them apart, and tape them around the room. For students who need more support in recalling information, please see our Open Number Line 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. (Number Lines)

PROCEDURE AND FACILITATION POINTS Part I 1. 2.

FACILITATION TIP

3. 4.

Ensure that students understand how the number lines are equal in size and divided differently. Have students point to the number line that is divided into halves, thirds, and eighths.

Distribute the number line and 5 parchment paper strips to each student. Students will put the Number Line under each piece of parchment paper. Ask students to lay the strip on top of the Number Line and trace it onto each piece of parchment paper, each with a different color. Explain that each piece will be folded into a different number of equal parts. Model folding the Number Lines in the following ways: a.

Halves

Thirds

Fourths

Sixths

e. Eighths 5.

Ask students to put a dark mark on their Number Lines where they see folds, like on a number line. a.

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Engage

Explore

Explain

Elaborate

Evaluate

Strip folded pieces into thirds: They should have marks labeled __3 and __3.

Strip folded pieces into fourths: They should have marks labeled __4, __4, 3 and __4.

Strip folded pieces into sixths: They should have marks labeled __6, __6, __6, 5 4 __ , and __6. 6

1 2

1 2 3

DOK-1 Ask students to turn and talk to their partners about what they notice about these ﬁve strips. They are all the same size. They are all equal to one whole. They are divided into a different number of pieces. They all show a part of a number line between 0 and 1. Tell students to put the parchment paper divided into halves on top of the fourths paper. Discuss the following questions: a. b.

9. 10. 11. 12. 13. 14. 15.

Acceleration

e. Strip folded pieces into eighths: They should have marks labeled __8, __8, __8, 5 6 4 __ 7 __ , , __, and __8. 8 8 8 6.

Intervention

DOK-1 What do you notice? The spot where __2 is labeled is the same as 2 where I labeled __4 on my other paper.

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.

EQUIVALENT FRACTIONS

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DOK-2 What can we conclude about these two fractions? They are the same point on the number line. They are equal.

Tell students to put the parchment paper divided into sixths on top of the thirds paper. Discuss the following questions: a.

DOK-2 What do you notice? Some of the fractions line up at the same distance.

DOK-1 Which fractions are equal? The fraction __3 is equal to __6; __3 is equal 4 to __6.

2 2

Tell students that as a class, they will explore how using a number line can show how fractions can be equivalent. Begin by working through the process as a whole group. Project the Number Line onto the board. 6 Ask students to ﬁnd the strip of parchment paper that could show __8. Model how to lay it on top of the Number Line.

FACILITATION TIP Have students circle the numbers in each scenario. Have them write the fraction on sticky notes, labeling the numerator and denominator.

Challenge them to discuss with their elbow elbow partners and decide where the tick 6 marks should be on the Number Line and put a dot on __8. Invite a student to share how they used it to mark the Number Line. See the model below: STEMscopes Tip

16. 17. 18.

Pose this challenge: Using your fraction strips, ﬁnd a different way to represent this distance on the Number Line. Give students time to discuss and explore with their fraction strips. Invite a student to demonstrate with a different color how they showed the same distance on the Number Line using a different fraction. See the model below:

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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Equivalent Fractions Explore 2 – Combine Fractional Parts 19.

Discuss the following questions:

Preview the Scenario Cards for any unique vocabulary that you may need to pre-teach to your students. 2. 3.

4. 5. 6.

DOK-1 What fraction is equivalent to __8? The fraction __4 is equivalent.

DOK-1 Are there any other fractions that are equivalent on your number 2 1 4 2 line? Yes, __8 is equal to __4, and __8 is equal to __4.

Part II FACILITATION TIP

Read the following scenario to the class: It’s time again for your family’s yearly reunion! It’s a great time to see and play with family members you don’t get to see often and share delicious family favorites! You realize when you show up to the picnic that whoa … your family has grown. This means that there are certain dishes that will have to be shared a little differently this year. Luckily, you have the tools and knowledge to help with this! Explain that at each station is a family dish that will be shared differently because the number of people has changed. Encourage students to work cooperatively to ﬁnd a new way to split the same dish in a different way. Assign student groups to begin at a food station. Give students enough time to work through each station and record in their Student Journals. Monitor and talk with students as needed to check for understanding. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-2 How can number lines be used to show equivalent fractions? You can partition the distance between two whole numbers into different equal amounts. Some fractions will be at the same point on the number line, so they are equivalent. DOK-2 What do you notice about the relationship between halves and fourths? (Repeat the question for fourths and eighths as well as thirds and sixths.) It takes two-fourths to make one-half. Every time I have one-half, I know I can also think of it as two-fourths. DOK-3 How can this be applied to your everyday life? When we have to share something with more or fewer people, we can change the way the whole is partitioned and still share the same amount. Those pieces might just be smaller or bigger in size.

Post-Explore FACILITATION TIP This Exit Ticket requires colored markers to complete successfully (purple, red and blue).

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

EQUIVALENT FRACTIONS

Home

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Equivalent Fractions Explore 3 – Whole Numbers as Fractions ACTIVITY PREPARATION Students express whole numbers as fractions using concrete objects, pictorial models, and number lines.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Window Jobs Cards (per class) 1 Exit Ticket (per student)

•

Reusable • • • • • •

6 Sets of fraction circles (per class) 6 Sets of fraction tiles (per class) 12 Tubs or containers (per class, optional) 1 Dry-erase marker (per group) 1 Small dry-erase board (per group) 1 Projector or document camera (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 Window Jobs Cards on card stock, laminate them if desired for long-term use, and post them around the room. Place 1 set of fraction circles and 1 set of fraction tiles at each station. • Optionally, put each manipulative in a tub/container at the stations.

•

For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips 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. (Fraction Circles and Fraction Tiles)

PROCEDURE AND FACILITATION POINTS 1. 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.

2. 3.

Read the following scenario to the class: Congratulations on getting the job at Whole Window Washers! As a company, you pride yourself on washing whole windows, with quick service and competitively low prices. Because of this, business is booming. Part of your job is to keep a precise record of how many whole windows you wash in order to get paid for your spotless work. The business uses precise fraction notations for quality control to ensure the whole window was washed, as this is their promise. So, welcome to the Whole Window Washers’ Orientation. Divide the class into groups. Pose the following questions, and allow students to discuss with their groups before sharing (accept all answers): a.

DOK-1 What are fractions? Answers may vary. Fractions are numbers that represent part of a whole.

DOK-1 What are the parts of a fraction, and what do they mean? There are two numbers that make up a fraction. The numerator is the number above the fraction bar, which represents the number of parts being shaded, pointed out, or highlighted in some way. The denominator is the number underneath the fraction bar. This number tells us how many equal parts the whole is partitioned into.

DOK-2 How could this relate to windows and wholes? Answers will vary. Maybe a whole window is broken into equal pieces. Maybe we are washing a whole window that has separate parts.

FACILITATION TIP Consider modeling Card 3 to the whole class before they begin collaborating. Mixed numbers is likely a new concept. 358

4. 5.

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Distribute dry-erase markers and white boards to students (if white boards are not available, students could draw on their desks using the dry-erase markers). Explain that for this next part of the orientation, they will work with their teams to determine how whole windows are represented as fractions based on what they know. Draw a window with no divisions or partitions on a white board, or project a picture on a screen. DOK-1 Ask students to discuss what they notice and what they wonder, with fractions in mind, with their teams. Invite them to share after a minute or so. Answers may vary: a.

That’s a whole window.

I don’t see that it is broken into equal parts.

I’m not sure how we could represent that as a fraction.

Is it one equal piece?

Intervention

Acceleration

EQUIVALENT FRACTIONS

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e. I wonder if we can make a fraction. f.

Is it a denominator or one?

Ask students to draw a model of this window with a blank fraction next to it and a number line underneath using their dry-erase markers.

Explain that yes, this can be represented as a fraction. Guide students to the 1

realization that this window is __1 using the following guiding questions and having them discuss with their teams: a.

Although it is not partitioned, there is still a number that represents the number of parts in this whole.

DOK-1 How many parts are in the whole window? There is just one part that is not broken up into smaller pieces.

DOK-1 Where could we show that in the fraction next to our model? How do you know? The denominator tells us how many pieces there are, so we could put a 1 under the fraction bar.

d. DOK-1 What if we washed the whole window? How many pieces would we wash? If we washed the whole window, we would be washing 1 piece. e. Ask students to shade in the fraction and draw a “jump” on the number line for the amount of window that is washed. f.

DOK-2 Where could we show that in the fraction next to our model? How do you know? If the numerator tells us the number of pieces that are highlighted, then we would also put a 1 at the top.

10.

Now, show three of the same window on the board or screen.

11.

Repeat the same line of questioning and models until students can understand 3 that they would be washing __1 windows.

12.

13. 14.

Explain that the windows each represent one whole that has one part. The total number of parts is represented at the bottom of a fraction. The number of parts they wash is represented at the top. Draw a window with 4 partitions on a white board, or project a picture on a screen. DOK-1 Ask students to discuss what they notice and what they wonder, with fractions in mind, with their teams. Invite them to share after a minute or so. a.

That’s one window.

I see four equal parts.

I’m not sure how we could represent that as a fraction.

Is each partition a whole?

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Equivalent Fractions Explore 3 – Whole Numbers as Fractions e. I wonder how we can make a fraction. f. 15.

Ask students to draw a model of this window with a blank fraction next to it and a number line underneath.

16.

Explain that yes, this can be represented as a fraction. Guide students to the 4 realization that this whole window is represented by the fraction __4 using the following guiding questions, and have them discuss with their teams:

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.

20.

21.

FACILITATION TIP Relate the importance of understanding the size of the whole with other real-world 1 examples. For example, the size of __2 of a candy bar depends on whether the candy bar is snack size, fun size, regular size, or king size. 360

How is this whole window partitioned? Ask them to think about what number represents the number of parts in this whole.

DOK-1 How many parts are in the whole window? There are 4 equal pieces making up the whole window.

DOK-1 Where could we show that in the fraction next to our model? How do you know? The denominator tells us how many pieces there are, so we could put a 4 under the fraction bar.

DOK-1 What if we washed the whole window? How many pieces would we wash? If we washed the whole window, we would also be washing 4 pieces.

19.

Consider completing this Student Journal together as a whole group. Students may need step-by-step support for these window models.

e. Ask students to shade in the fraction and draw and label the “jumps” on the number line for the amount of window that is washed.

17. 18.

FACILITATION TIP

Is the denominator still one?

22. 23. 24.

DOK-1 Where could we show that in the fraction next to our model? How do you know? If the numerator tells us the number of pieces that are highlighted, then we would also put a 4 at the top.

Now, show three of the same window on the board or screen. Repeat the same line of questioning and models until students can understand 12 that they would be washing ___ or three whole windows. 4

Explain that some windows are partitioned into equal pieces. The total number of parts is represented at the bottom of a fraction. The number of individual parts they wash is represented at the top. These would still represent the entire whole. Congratulate the employees for graduating orientation. Explain that they will now go out into their ﬁrst day of window washing. Warn them that some windows are partitioned and others are not, so they have to be extra careful about how they log them so they are paid for all their work. Explain that there are window models (fraction manipulatives) placed at each station. They can pick the model that best ﬁts the kind of window they are washing. Give a Student Journal to each student. Assign each group a station to begin at. Give groups time to read, build a model, and record their thinking for each station on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

How many parts are in the whole window? How can you model that? Answers will vary. There are 4 parts in this window. I can use a fraction circle to model it.

Where could we show that in the fraction next to our model? How do you know? Answers will vary. I will write the 4 in the denominator because there are 4 parts in a whole window.

c. What if we washed the whole window? How many pieces would we wash? Answers will vary. We would wash 4 parts. d.

Ask students to shade in the fraction and draw a “jump” on the number line for the amount of window that is washed. Answers will vary.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

e. Where could we show that in the fraction next to our model? How do you know? Answers will vary. We write the number of pieces we washed on the top of the fraction bar (as the numerator), so if we washed one whole window, then we would write a 4 on top. 25. 26.

After completing the Window Job Cards, give students time to 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.

EQUIVALENT FRACTIONS

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FACILITATION TIP

Math Chat

Use the Print Files to project these questions DOK-2 Does representing a whole number as a fraction change the amount of and record the answers as you guide the the number? Why or why not? Whole numbers can be represented as a fraction discussion. without changing the amount. The only thing that changes is how the number looks, but the quantity and the amount remain the same. When we put a whole number into a fraction, we just specify how it is partitioned and how many of those partitions are being “highlighted.” STEMscopes Tip • DOK-3 Can all whole numbers be made into fractions? How do you know? Yes, all The Evaluate section, found along the whole numbers can be made into fractions. The kind of fraction depends on if the scope menu, contains assessment whole is partitioned and into how many parts. tools designed to help teachers gather • DOK-3 What is the role of the numerator and denominator in these jobs? Explain. the data they need to determine The roles of the numerator and denominator stay the same. The denominator still whether intervention or acceleration indicates the total number of pieces in a whole. Sometimes a whole is partitioned is warranted. From standards-based into smaller pieces; other times it is not. The numerator tells how many of those assessments to an open-ended parts are being highlighted or signaled in the scenario. reasoning prompt, there is an evaluation for every student’s learning Post-Explore style. 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. 4. Return to the Hook and instruct students to use their newly acquired skills to successfully complete the activity. •

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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 Visual 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 with Number Lines 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

Whole Numbers as Fractions 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

Mateo Makes Lunches

Michael Phelps

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

Bodies of Water

Equivalent Fraction Models – Denominators 2, 3, 4, 6, 8

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

Interactive Practice

Quilts for a Cause

Aztec Treasure

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

EQUIVALENT FRACTIONS

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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 visual models to explore equivalent fractions.

I can recognize and generate equivalent fractions.

I can explain why fractions are equivalent.

I can locate two equivalent fractions at the same point on a number line.

I can express whole numbers as fractions.

I can recognize fractions that are equivalent to whole numbers.

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SCOPE 1

Time Scope Introduction SCOPE SUMMARY

Student Expectations

3.MDR.5.2 Tell and write time to the nearest minute and estimate time to the nearest ﬁfteen minutes (quarter hour) from the analysis of an analog clock. 3.MDR.5.3 Solve meaningful 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. only.

Third-grade students tell and write time to the nearest minute. This builds on previous understanding of the concept of time in hours, half hours, and intervals of ﬁve minutes. Instruction with both analog and digital clocks is used to ensure that students have opportunities to develop their concept of telling time with both ways it is represented in their daily lives. Students are also expected to use number lines to solve elapsed time problems involving the operations of addition and subtraction of 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. only. The skills of understanding and applying strategies to solve for elapsed time situations are important in creating a deep understanding of how clocks are used as a tool to measure the passing of time.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Students begin their understanding of intervals of time in first grade. First graders are introduced to time for the first time when they start to use digital and analog clocks to tell and write time to the nearest hour and half hour. They also measure elapsed time to the hour on the hour using a scaled number line. Second-grade students extend their knowledge of time by distinguishing between a.m. and p.m. and by telling and writing time to the nearest five minutes using an analog and digital clock. They also use a number line to estimate and measure elapsed time to the hour or half hour on the hour or half hour.

In fourth grade, students solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. With regard to the concept of time, representations would involve hours > minutes > seconds. Students will be able to express the measurement in a larger unit in terms of a smaller unit (for example, 5 minutes = 300 seconds, etc.). Students in fourth grade will also continue building on the concept of elapsed time by using all four operations (addition, subtraction, multiplication, and division) to solve more complex problems.

Before beginning the lesson, the students’ prior knowledge is assessed to address any student needs and skills needed for content mastery. Students are assessed to determine if they can: •

tell and write time on analog and digital clocks to the nearest ﬁve minutes and with using a.m. or p.m.

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 time to determine what time they need to begin packing to leave for a vacation.

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. 366

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Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Time on an Analog Clock In this exploration, students will use analog clocks to tell time to the nearest minute by counting the minutes and estimate time to the nearest 15 minutes using only the hour hand. Students will: •

determine what the analog clock will look like for each part of our day.

•

ﬁnish a schedule by estimating the activity times to the nearest 15 minutes.

Explore 2

Explore 1

EXPLORE ACTIVITIES Problem Solve with Time on a Number Line For the ﬁnal exploration, students collaborate together using Scenario Time Interval Cards to determine where the card should be on the number line. Students will: •

solve problems involving addition and subtraction of time intervals in minutes using number lines or tools.

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 an Exit Ticket for assessment.

367

TIME

Time Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

368

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students tell and write time to the nearest 5 minutes using an analog clock and a digital clock. This activity is intended to assess mastery of the following standard(s): 2.MDR.6.1 Tell and write time from analog and digital clocks to the nearest ﬁve minutes, and estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour.

Materials Printed •

Reusable

1 Student Handout (per student, per group, or per class)

• •

1 Dry-erase board (per student or per group, optional) 1 Dry-erase marker (per student or per group, optional)

Preparation •

Print a Student Handout for each student or group, or prepare to project the Student Handout for the class.

•

If grouping students, put them into groups of two or three.

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

Distribute a Student Handout (and optional dry-erase board and marker) to each student or group, or project the Student Handout for the class. Read the scenario to the class. Ask students to determine the time on each analog clock to the nearest 5 minutes and write the correct time on the corresponding digital clock. Facilitate a class discussion about time. 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. a.

I remember that, with time, the short hand is the hour hand, and the long hand is the minute hand.

When I count by minutes, I know that each of the numbers on the clock represents 5 minutes.

When I start at 12, it shows me 0 minutes, and when I end at 12, it represents 60 minutes or 1 whole hour.

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

FACILITATION TIP Challenge students to circle either a.m. or p.m. on each digital clock. Discuss that p.m. signiﬁes the time period from noon to midnight and a.m. signiﬁes the time from midnight to noon. 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.

369

TIME

Time Hook – Packing for Vacation ACTIVITY PREPARATION Students add and subtract time to determine what time they need to begin packing to leave for a vacation.

Materials

Preparation

Reusable • • • • •

1 Phenomena Video (per class) 1 Projector or document camera (per class) 1–2 Suitcases or backpacks (per group) Several items to pack (per group) 1 Analog clock (per class)

• Arrange four chairs in an open area in your classroom. This will represent the car. • Bring suitcases or backpacks for students to pack. If none are available, have students use their own backpacks. • Provide students with items to pack. It can be anything from a pile of old clothes to a stack of towels to the students’ notebooks or boxes of tissues.

Consumable •

Plan to show the Phenomena Video. After Explore activities are completed, complete the following tasks:

• •

1 Large piece of paper (per group)

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

FACILITATION TIP Engage students by asking about travel. Ask if and when their families travel out of town. Consider your own students’ experiences. The ability to calculate being somewhere on time so you don’t miss out is always important.

DOK-1 What information do we know? We have to be at the train station by 3:00. It takes 30 minutes to drive. It takes 30 minutes to pack.

FACILITATION TIP

DOK-1 How many minutes are in 1 hour? There are 60 minutes in 1 hour.

Project this question before the Hook and follow up with posting the answer on an anchor chart or word wall during the Explore activities.

DOK-2 How can we ﬁgure out how much time we will need in all (packing and driving)? We can add the time it takes to do each thing: 30 minutes + 30 minutes.

DOK-2 Now that we know how much time we need, how can we ﬁgure out what time we need to start getting ready? We can subtract that amount of time from the time we need to be there.

e. DOK-1 What operations will we need to use? We will need to use addition and subtraction.

FACILITATION TIP Take time to review with the model analog clock. Provide several examples and have students respond chorally in whole group, small groups, in partners and individually. Use these responses to quickly assess prior knowledge.

DOK-1 How many minutes past the hour is it when the minute hand is on the 3? It is 15 minutes past the hour. On the 6? It is 30 minutes past the hour. On the 9? It is 45 minutes past the hour. On the 12? It is 0 minutes past the hour.

Move on to complete the Explore activities.

FACILITATION TIP If needed, use Show What You Know Part 1 to assess students’ analog clock skills. 370

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4.

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

DOK-1 What information do we know? We have to be at the train station by 3:00. It takes 30 minutes to drive. It takes 30 minutes to pack.

DOK-1 How many minutes are in 1 hour? There are 60 minutes in 1 hour.

DOK-2 How can we ﬁgure out how much time we will need in all (packing and driving)? We can add the time it takes to do each thing: 30 minutes + 30 minutes.

DOK-2 Now that we know how much time we need, how can we ﬁgure out what time we need to start getting ready? We can subtract that amount of time from the time we need to be there.

FACILITATION TIP

Review with students how to count up and count back using their fists and fingers. e. DOK-1 What operations will we need to use? We will need to use Pound a closed fist into a palm and then addition and subtraction. use fingers to count forward or backward to f. DOK-1 How many minutes past the hour is it when the minute hand is on calculate the time. the 3? It is 15 minutes past the hour. On the 6? It is 30 minutes past the hour. On the 9? It is 45 minutes past the hour. On the 12? It is 0 minutes past the hour. STEMscopes Tip Review the problem, and put students in groups of three or four. Assign each group an amount of time to pack. It will be easiest to use increments of 15 minutes, with 2 hours maximum. Group 1: 45 minutes to pack Group 2: 30 minutes to pack Group 3: 1 hour 15 minutes to pack Group 4: 15 minutes to pack Group 5: 1 hour 45 minutes to pack Group 6: 1 hour to pack Tell each group to discuss and figure out what time they need to start packing if it takes them 30 minutes of travel time. a.

Provide an analog clock where everyone can see so students can use it to help them add and subtract time.

Provide large paper so students can construct a number line to show their work, or provide the work mat from the Skill Basics.

Once each group has determined their start time, they will get one or two suitcases and a bunch of items to pack. Have students act out the scenario to help determine what time they need to start packing. (Ex. Group 1: Students will say it is 1:45 and then they will start packing items into suitcases. When they are ﬁnished packing, the time that elapsed was 45 minutes so now it is 2:30. Students will get into the car and then travel for 30 minutes. Then, they will say they arrived at the train station and it is 3:00.) Outlined below is an example of one group’s solution. a.

Group 1 is assigned 45 minutes to pack.

Group 1 might use a number line to solve the problem.

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.

FACILITATION TIP If time and space is limited, save this suitcase activity for later. As an alternative, use the “Fluency Builder Problem Solving With Time” in Elaborate.

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TIME

Time Hook – Packing for Vacation

Notice that this example shows the students jumping back 30 and 15 minutes to show 45 minutes and then uses increments of 15 minutes to count back the travel time.

Ask other groups to share their number lines with the class.

Discuss the following questions with the class: a.

DOK-1 How did you ﬁgure out what time you needed to leave? We used a clock or a number line to help us count.

DOK-1 What operations are you using to ﬁnd how much time you need? We are using addition (counting forward) and subtraction (counting backward).

DOK-1 Which numbers on the clock show 0, 15, 30, and 45 minutes past the hour? The numbers 12, 3, 6, and 9 show them. Notes

372

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

373

TIME

Time Explore 1 – Time on an Analog Clock ACTIVITY PREPARATION Students use analog clocks to tell time to the nearest minute by counting the minutes and estimate time to the nearest 15 minutes using only the hour hand.

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 Station Cards (per class) 1 Exit Ticket (per student)

Preparation • • • •

• • • •

Reusable • •

1 Geared analog clock* (per station) *Important Note – Do not use paper clocks; the lack of gears on a paper plate makes the pace of minutes vs. hours inaccurate.

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Station Cards, and place them around the room. Place one geared analog clock at each station.

• •

Start of Our Day Science Lab Math Lunch

• • • •

Recess Special Areas Reading and Writing Dismissal

For students who need more support in recalling information, please see our Analog Clock 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. (Clock)

PROCEDURE AND FACILITATION POINTS Part I: Telling Time to the Nearest Minute 1. 2. FACILITATION TIP Explain that most analog clocks run on batteries, so a power outage would not affect their ability to tell time. FACILITATION TIP As students read the cards, have them underline or circle the time. Then, have students discuss whether the activity is an a.m. (morning) or p.m. (afternoon) activity. FACILITATION TIP Project the Virtual Manipulative Clock for students, and have them create clocks for different times. 374

3. 4.

5. 6. 7. 8.

Hand students the geared clocks. Invite the students to turn and talk to their shoulder partners about what they notice about the geared clocks. DOK-1 Ask students to share. We can only move the minute hand, but moving the minute hand also moves the hour hand, just at a slower pace. Read the following scenario to the class: Last night there was a storm, and all of our digital clocks went out, and they are all blinking a big, red 12:00! In order to stay on schedule, we must determine what the analog clock will look like for each part of our day. Place students into groups of three. Explain that they will rotate through the stations with their clocks. Let students know that at each station is a description of the scheduled activity and the time the class usually does it. Explain that they will use the analog clocks provided to determine what the clock should look like as well as write down the corresponding digital time on their Student Journals.

TIME

Home

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-2 Where do you think the hour hand is going to be?

DOK-1 How will you count the number of minutes described?

DOK-1 Which direction should we move the hands?

Part II: Estimating Time to the Nearest 15 Minutes 1.

3. 4. 5.

Read the following scenario to the class: After having to reset all the clocks, I decided that if each activity starts on or near an hour, a half hour, or a quarter hour, our schedule would be a lot easier to remember! I quickly wrote out a new schedule by drawing just the hour hands on clocks, but that’s as far as I got. Would you please help me ﬁnish the schedule by estimating the activity times to the nearest 15 minutes? Discuss the following questions: a.

DOK-1 How can you tell the time is on or near the hour using only the hour hand? The hour hand points at or near a number.

DOK-1 How can you tell the time is on or near the half hour using only the hour hand? The hour hand points at or near the middle between two numbers.

DOK-1 How can you tell the time is on or near the quarter hour using only the hour hand? The hour hand points between two numbers, but it is closer to one number than the other number.

Place students in groups of three or four. Explain that they will look at each clock and estimate the new time each activity will begin to the nearest ﬁfteen minutes. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP Students can use their arms and hands to show the hands of a clock. To approximate the different lengths, hour hand has pointing ﬁnger and minute hand is closed ﬁst.

FACILITATION TIP Consider doing page 4 of the Student Journal together. Students may need support calculating and drawing the minute hands on the clocks.

a. DOK-2 How did you determine the estimated time showing on this clock?

DOK-2 Why is this an estimated time and not the actual time?

DOK-1 Which direction does the hour hand move?

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 the position of the hands as the time moved forward? When we moved the minute hand, the hour hand moved, too! It did not stay on the number of the hour it represented. DOK-2 How did the hour hand move in comparison to the minute hand? The hour hand moved much more slowly. It took an entire minute hand a revolution of the hour hand to move numbers completely. DOK-2 How did you determine where the minute hand would be based on the time? Each number on the clock represents 5 minutes. To ﬁnd the exact minute, we counted by ﬁves to the nearest number on the clock, then from there every tick mark represents one minute. DOK-2 How do you determine the hour if the hand is not directly on the number? To determine the hour, we have to see which number it has already passed on the clock before it reaches the next one. The closer we are to the next hour, the later in the hour it is.

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. This Exit Ticket can be used as both a preand post-assessment for this Explore activity. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

375

TIME

Time Explore 2 – Problem Solve with Time on a Number Line ACTIVITY PREPARATION Students determine the solutions to problems involving addition and subtraction of time intervals in minutes using number lines.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. 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 Set of Time Interval Cards (per group) 1 Exit Ticket (per student)

•

Reusable • • • •

•

1 Pair of scissors (per student) 1 Geared analog clock (per group) 4 Resealable bags (per group) 1 Permanent marker (per group)

• • •

Consumable •

1 Roll of masking tape or painter’s tape (per class)

•

Plan to have students work in groups of 4 to complete the 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. If desired, laminate them for future use. Print a set of Time Interval Cards for each group. Cut the cards apart. If desired, laminate them for future use. Place each set of Time Interval Cards in a resealable bag with a Scenario Card. Label the bag with the scenario number. A large area is needed for the ﬂoor timelines. Arrange to use a long hallway or other open area. Use masking tape or painter’s tape to make an approximately 6-foot timeline on the ﬂoor for each group. 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 Find a location in which all groups will have enough space to solve the problems.

376

1. 2. 3.

Students should number themselves one through four. Give each group the four bags with the Time Interval Cards and a set of Scenario Cards. Give each group a geared analog clock. Explain to students how to complete the following activity: a.

Students will place the Scenario 1 Time Interval Cards in the correct positions on the ﬂoor number line.

FACILITATION TIP

This activity has speciﬁc roles for each member. Choose groups with the activity in mind, and display the roles on the board.

Student 1 will start as the number line time walker. Student 2 will read the ﬁrst sentence of the Scenario 1 card. The number line time walker will stand at the starting time on the ﬂoor number line.

Student 3 will read the next sentence, and the group will decide whether the time interval should be added to or subtracted from the starting time. The number line time walker will walk backward or forward to move to the new location. © Accelerate Learning Inc. - All Rights Reserved

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Student 4 will read the last sentence, and the group will decide whether the time interval should be added or subtracted. The number line time walker will walk backward or forward to move to the new location.

e. As the walker walks on the number line, teammates mirror his or her moves on the analog clock. They can also use the clock to determine which direction to move. f.

The number line time walker will state the answer to the question on the Scenario Card.

Students will check with you to see if their answer is correct. If the answer is incorrect, groups should repeat the scenario. If the answer is correct, students will move on to the next scenario.

h. After Scenario 1 is complete, the students will switch jobs so that when all 4 scenarios are complete, each student will have done each job.

FACILITATION TIP Create a signal for groups to indicate when they are ﬁnished, such as all group members sitting or a group placing a colored paper on their number line.

i. Scenario answers: i. Scenario 1: 4:45 p.m. ii. Scenario 2: 1:00 p.m. iii. Scenario 3: 45 minutes iv. 4. 5.

Scenario 4: 8:30 p.m.

Once students have acted out the ﬁrst four scenarios, have them work together to complete scenarios 5 and 6 without building the number line. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP After checking each group for scenarios 1–4, release them to complete scenarios 5 and 6 without the number line. FACILITATION TIP

Math Chat DOK-2 How do you know whether to add or subtract time intervals? If something happens after a particular time, I know I need to add the time interval to the time. If something happens before a particular time, I know I need to subtract the time interval from the time. • DOK-3 How is thinking about time as a number line helpful to you? It makes it easier to add or subtract time because I can move forward or backward on the number line. I can skip count the time intervals. • DOK-3 When thinking about adding and subtracting time, how does the number line help you? I know that if I am subtracting time, I need to move backward on the timeline, and if I am adding time, I need to move forward on the timeline. It makes it easier to add and subtract time. •

Use the Print Files to project the Math Chat questions as you guide the discussion. Consider recording student responses. Reassure students that using a number line as a thinking tool is a powerful skill. They will continue to need it throughout their later math standards and life.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. On this Exit Ticket, provide read-aloud support to students as needed. 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.

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TIME

Time 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

Time on an Analog Clock 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 with Time on a Number Line 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

378

TIME

Home

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 Hiking Club

Preschool Teacher

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

To Surf or Not to Surf

Problem Solving with Time

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

Fluency Builder

We’re Going to the Zoo

Time 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

379

TIME

Time 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

380

 Interactive Practice

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

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

What prompts will be used?

What does mastery look like?

I can tell and write time to the nearest minute.

I can estimate time to the nearest quarter hour.

I can solve problems involving elapsed time, including intervals of time to the hour, half hour, and quarter hour.

I can use clock diagrams and number lines to solve problems involving adding and subtracting intervals of time.

381

SCOPE 1

Measurement Scope Introduction SCOPE SUMMARY Students select and use appropriate tools to measure the length and weight of an object and the volume of a liquid by using customary units. They use a ruler to measure to the nearest half, fourth, or whole inch. Students also use containers of various sizes to measure liquid volumes, and they use a platform scale to measure weight. They apply what they know about measurement to model and solve real-world problems involving any of the four operations with whole-number lengths, weights, or liquid volumes. Student Expectations

3.MDR.5.4 Use rulers to measure lengths in halves and fourths (quarters) of an inch and a whole inch. 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.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students construct simple measuring instruments using unit models and then compare their unit models to a ruler. Students estimate the length of an object and then identify appropriate measurement tools and units for obtaining a precise measurement to the nearest whole unit. Second-grade students measure the lengths of two objects by using the same unit, and they determine how much longer or shorter one object is than another. They also solve real-world problems involving addition and subtraction of lengths given in the same unit using a number line.

In fourth grade, students select and use appropriate tools to measure attributes of objects by using metric measurements, including length, mass, liquid volume, and time. 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 and 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.

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

estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.

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: •

reason about which measuring tools to use to measure various parts of a roller coaster, and they solve real-world problems involving length, weight, and liquid volume.

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. 382

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Select Tools to Measure In this exploration, students will select and use appropriate tools to measure the length and weight of an object and the volume of liquid in a cup. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

select and use the correct measurement tool to measure the attribute described using standard units.

Mass and Weight In this exploration, students will solve word problems pertaining to weight using addition, subtraction, multiplication, and division. Students will: •

Length In this exploration, students will solve real-world problems involving length by using addition, subtraction, multiplication, or division. Students will: •

analyze the length of samples of plants.

•

model and solve problems about length.

•

labeling the units for each problem.

After students have solved the scenario, the teacher guides students sharing and discussing ﬁndings. Then, the activity ends with a discussion over their learning and an Exit Ticket.

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.

MEASUREMENT

Home

ﬁgure out certain weights while riding rides, playing games, and eating food at a theme park.

Once students have solved the scenario, they discuss their learning with the class and conclude with an Exit Ticket.

Liquid Volume In this exploration, students will solve for liquid volume in word problems using addition, subtraction, multiplication, and division. Students will: •

determine the liquid volume for different problems.

•

draw a model and write the equation they used to solve each problem.

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

383

MEASUREMENT

Measurement Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

384

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE

MEASUREMENT

Home

Students evaluate measuring tools and choose the best tool for various tasks. Students then use a visual model of a ruler to measure an object in inches. This activity is intended to assess mastery of the following standard(s): 2.MDR.5.2 Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.

Materials Printed • •

Reusable

1 Student Handout (per student) 1 Measurement (per class)

• • • •

1 Ruler, with inches (per pair) 1 Yardstick (per class) 1 Tape measure (per class) 1 Measuring tape (per class)

Preparation • • • •

Place students in pairs. Print a Student Handout for each student. Gather the measuring tools with which students will be analyzing and working. Prepare to project Measurement to the class.

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

5. 6. 7. 8. 9.

Project Measurement to the class. Discuss the different tools, including similarities, differences, and possible uses. Have the class read the questions and discuss their thoughts with their partners. Facilitate a class discussion about the thoughts students shared with their partners about the different tools. 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. Distribute a Student Handout to each student. Have students work with their partners to complete their Student Handouts. Monitor pairs by walking around to ensure students are on task. Engage students as they work by facilitating small group discussions. If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Suggest that students take each measurement twice. If the measured lengths vary, have students check a third time. If a student is struggling, ask another student to demonstrate how they measured, pausing to clarify misconceptions. Emphasize the importance of starting at zero and placing the ruler straight along the edge of the item being measured.

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Measurement Hook – Roller Coaster ACTIVITY PREPARATION Students reason about which measuring tools to use to measure various parts of a roller coaster, and they solve real-world problems involving length, weight, and liquid volume.

Materials

Preparation

Printed •

• •

1 Student Handout (per pair)

Plan to show the Phenomena Video. For Part II, print a Student Handout for each pair of students.

Reusable • •

1 Phenomena Video (per class) 1 Projector or document camera (per class)

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

FACILITATION TIP Studying units of measurement could be a cross-curriculum unit with science.

FACILITATION TIP

Bring in different tools to measure liquid volume, length, mass, and temperature.

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.

5. 386

DOK-2 What type of measurement will help the family decide if they are tall enough to ride the roller coaster, and what type of measuring tool could they use to ﬁnd out? Length is used to measure a person’s height. They could use a measuring tape or a yardstick.

DOK-2 What type of measurement will help the family decide how large of a drink to buy, and what type of measuring tool could they use to ﬁnd out? Drinks are liquid so they can be measured in ounces or cups. We can use a measuring cup to ﬁgure out how large of a drink we want.

DOK-2 What type of measurement will help the family decide if they drink enough water so that they can stay hydrated throughout the day, and what type of measuring tool could they use to ﬁnd out? Liquid volume measures the amount of water. Some water bottles have markings that show how much water is inside. The family could also measure the water ahead of time using measuring cups.

DOK-2 Each roller-coaster cart has a weight limit. What type of measurement will help the family decide if they can all ride at once, and what type of measuring tool could they use to ﬁnd out? Weight is used to determine if they fall within the limit, and a scale measures weight.

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 situation. Discuss the following questions with the class: a.

3. 4.

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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.

Provide each pair of students with a Student Handout. Explain that all questions relate to measuring at an amusement park. Instruct each pair of students to work together on both parts of the activity. Make sure that students show their work and are prepared to share their thinking with the class. Discuss the following questions with the class: a.

DOK-2 How did you decide which types of measurement and which FACILITATION TIP types of measuring tools to use? We have learned that a scale measures Provide images with names of tools for weight, a yardstick provides a length in inches, and measuring cups or students to use as a reference. beakers measure liquid volume.

DOK-2 Which types of measuring tools might actually be available at FACILITATION TIP the park? The roller coaster carts probably have digital scales built in Playing videos of amusement parks may them. Sometimes a height chart or ruler is drawn on a wall and a worker help facilitate student discussion. checks to see if you meet the requirement before getting onto the ride. A water bottle is usually marked with liquid volume units that it contains.

DOK-3 What models did you choose to solve the problems and why? We drew a diagram to show how much lemonade was in each bottle or part that made up the whole amount drank by the family.

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Measurement Explore 1 – Select Tools to Measure ACTIVITY PREPARATION Students select and use appropriate tools to measure the length and weight of an object and the volume of liquid in a cup.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of Tea Party Cards (per class) 1 Exit Ticket (per student)

• •

Reusable • • • • • •

1 Platform scale (per station) 1 Measuring cup (per station) 1 Ruler (per station) 1 Teapot or pitcher (per class) 1 Teacup (per class) 1 Set of plates and silverware (fork and spoon) (per class)

Consumable • •

1 Bottle of tea (per class) 1 Roll of tape (per class)

•

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 Tea Party Cards, on card stock for durability, for the class. Cut the cards apart, and tape the cards up around the room in order to create 5 stations. Place a ruler with inches (if ruler also has centimeters, instruct students to use only inches), a measuring cup with ounces and cups, and a platform scale at each station. Prepare the following stations as described below: • Teapot/pitcher station–Fill the teapot with 2 cups of water. • Teacup station–Fill the teacup with 6 ounces of water. • Plates and silverware station–Place one plate, fork, and spoon at the station.

PROCEDURE AND FACILITATION POINTS 1.

2. 3.

FACILITATION TIP Discuss the ways in which the rulers, graduated cylinders, and thermometers are similar to number lines. Model for students how to accurately determine measurement with the tools. 388

Read the following scenario to the class: Your birthday is coming up, and you are having a tea party to celebrate. It is important to serve food and drinks at your tea party so the guests can enjoy the party with some food in their stomachs. You want to make sure all the food is the same size so everyone’s treats are equal. It is also important to measure the volume of the drinks so everyone gets the same amount. Help measure the food and drinks at the tea party to make sure all the measurements are the same and you’re ready to treat your guests to a great tea party. Give a Student Journal to each student, and place a group at each station around the room. Explain to students that at each station, they have several tools, and they must determine which tool would work best to measure the attribute described on each Tea Party Card. Discuss the following question: a.

DOK-1 What measurement tools do you notice at each station? I notice a scale, measuring cup, and ruler.

7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Note: Instruct students that the drinks are tools for the Explore activity and they are not for drinking.

b. Optional: If uncertain about the class pouring the drinks into a measuring cup to ﬁnd volume, you can have groups raise their hands when it comes to the volume portion, and the teacher can help pour the liquid.

10.

Acceleration

Explain to the students that they should look for the measurements on the scale that represent pounds and ounces. (There may be grams on the scale, but students will only use customary units.) Instruct students to record their responses for the name of each tool and what they are used for on the ﬁrst page of their Student Journals. Challenge each group to now read the Tea Party Card at their station and estimate the measurement described on their cards. Then, they will select and use the correct measurement tool to measure the attribute described on their card. a.

Intervention

Students record their estimations, measurements, and responses in the correct table on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Which attribute of measurement is being described by your Tea Party Card? Answers will vary. Length, volume, or weight

DOK-1 What is your estimate for this measurement? Answers will vary.

Ask the following length questions:

MEASUREMENT

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FACILITATION TIP Another option is to have students use bins to catch any spills while they are measuring liquid volume.

FACILITATION TIP Students can circle the units of measurement for each tool on their Student Journals.

i. DOK-1 Which tool measures length? The ruler ii. DOK-2 What do you notice about the number line used for measuring on a ruler? Answers may vary. I notice that the ruler measures inches. I notice that each number line shows a whole number, and then there are lines between each whole number that represent fractional amounts. iii. DOK-2 How can we use a ruler to measure length? We can place the ruler at one end of an object, starting at 0, and ﬁnd where the end of the object lands on the ruler. That number will tell me the length. iv. DOK-2 How can we represent the length if the item falls between two whole numbers on the ruler? We can represent the length with a 3 1 1 whole number and a fraction. Some fractions we can use are __4, __2, or __4 v.

DOK-1 How can we represent the length of an object using a unit of measurement? We write length using in. (inches).

FACILITATION TIP Make the connection with students that rulers are number lines and that the measurement is a mixed fraction.

Ask the following weight questions: i. DOK-1 Which tool measures the weight of an object? The scale ii. DOK-2 How do we use the scale to ﬁnd the weight? We place the object on the scale and look where the arrow is pointing. We look to see which numbers represent pounds or the lines in between that represent ounces. iii. DOK-1 How do we represent the weight using a unit of measurement? We write the weight using lb. (pounds) or oz. (ounces). iv. DOK-3 How do I know if I should measure in pounds or ounces? If the object is heavy, we will use pounds. If it is light, we will use ounces.

e. Ask the following volume questions: i. DOK-1 Which tool measures the volume of an object? The measuring cup ii. DOK-1 What unit of measurement is used on a measuring cup when representing volume? Volume is represented with cups or ounces on a measuring cup. © Accelerate Learning Inc. - All Rights Reserved

FACILITATION TIP Brieﬂy introduce the word “mass” as an alternative vocabulary term for weight.

MEASUREMENT

Measurement Explore 1 – Select Tools to Measure iii. DOK-2 How do we use the measuring cup to ﬁnd the volume of the liquid? We pour the liquid into the measuring cup and then view the height of the liquid in the measuring cup with our eyes directly level with the liquid. The liquid may look like it’s curving upward. We always read the measurement at the bottom of the curve.

11. 12. 13. FACILITATION TIP Be prepared with some relevant, engaging real-world applications for accurate measurement. Consider recipes, home improvement projects, and travel distances as sources for examples.

•

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.

•

DOK-1 How do we represent the volume using a unit of measurement? The measuring cup represents cups and ounces. I know this because the top line reads 2 cups, and the smaller lines say oz., which stands for ounces. We write the volume using cups or oz.

Make sure each station is cleaned up and any liquids are returned to their original containers before students rotate to the next station. Facilitate group rotations through each station, and ensure that students record their measurement data on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-2 How did you estimate the measurement of your objects without actually measuring them? I compared the object to something I thought was about an inch (pound, cup) and estimated how many of each unit it would take to measure the object. DOK-2 How did the number line represented on the ruler help you find an accurate measurement? The number line on a ruler counts by one, with fractional amounts in between each whole number. I could place a ruler next to an object, starting at zero, and find where the end of that object landed on the ruler in order to find an accurate length. DOK-2 How did the number line represented on the measuring cup help you find an accurate measurement? The number line on a measuring cup is vertical. I know the numbers are labeled for either cups or ounces. DOK-3 What would happen if we used the incorrect tool to measure an attribute of an object? The result of the measurement will be inaccurate and may be hard for others reading the measurement to understand. DOK-3 Why is it important to correctly label the unit of measurement for an object? It is important to correctly label the unit of measurement for an object because there are many units of measurement within the customary system, and this will allow people to easily understand the size of an object. DOK-3 Why is it important to accurately measure the attributes of an object? It is important to accurately measure the attributes of an object so people understand how large or small an object is. Also, if someone wanted to recreate the object but didn’t have accurate measurements, this would be difficult to accomplish.

Post-Explore 1. 2. 3.

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DOK-2 How can we use the number line represented on the measuring cup to help ﬁnd an accurate measurement? The number line on a measuring cup is vertical. I know the numbers are labeled for either cups or ounces.

Math Chat

•

STEMscopes Tip

iv.

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 __________________________________________________________________________________________________________________________________________________

MEASUREMENT

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Measurement Explore 2 – Length ACTIVITY PREPARATION Students solve real-world problems involving length by using addition, subtraction, multiplication, or division.

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 Nature Cards (per class) 1 Exit Ticket (per student)

•

Reusable •

•

1 Timer (per class)

• •

Plan to divide the class into 9 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Nature Cards, on card stock for durability, for the class. Laminate the cards, if desired, for long-term use. Cut the cards apart on the dotted lines, and place the cards around the room for students to rotate through as stations. Set up a displayed class timer with a set amount of time allowed for students to complete each station. For students who need more support in recalling information, please see our 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. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS 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.

2. 3. 4.

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Read the following scenario to the class: Exploring nature is a great way to get to know the area you live in and the plants and animals that cover Earth. There are many wildlife conservation groups in the United States whose mission is to protect plant and animal species and their habitats. In their effort to protect them, they also collect nature samples to measure and collect data in order to better understand the wildlife around them. A local wildlife group called Protect the Planet has collected various plant and animal samples and needs your help analyzing the length of these samples. Use your knowledge about length to help the wildlife conservation group analyze their nature samples! Give a Student Journal to each student. Instruct students to apply their knowledge about length and rulers to determine answers regarding the nature samples discovered by the wildlife conservation group. Discuss the following questions: a.

DOK-1 What units of measurement can we ﬁnd on a ruler? We can ﬁnd inches on a ruler.

FACILITATION TIP

Challenge students to think of the best way to measure the length of the classroom, a pencil, a desk, their bed, and a car.

DOK-2 Are those the only units of measurement used to measure length? Explain. No, we can also measure length with feet and yards.

DOK-3 Why do you think it is important to label the units of measurement when labeling the size of an item? It is important to label our units of measurement because each unit of length is a different size. The label helps people determine the exact size of an item. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

Explain to students that there are various Nature Card stations around the room. They collaborate with their groups to read each card and determine what operation is needed in order to solve the problem. Challenge students to continue working together to come up with a plan to prove their answers by drawing a model and writing the equation or equations they can use to solve each problem on their Student Journals. Explain to students that you are setting a timer for the given amount of time they have at each station. At the end of that time, they should have their work completed for that station and recorded on their Student Journals and should be prepared to rotate. a.

8. 9.

Engage

FACILITATION TIP While reading the problem, use a literacy strategy such as circling the measurements and underlining the problem that needs to be solved.

Note that the teacher determines the amount of time for each station.

DOK-1 What is the problem asking you to ﬁnd? Answers will vary. How many feet long was the second palm frond that was found?

DOK-1 What information is given? Answers will vary. The ﬁrst palm frond found was 6 feet long, and the second palm frond was 3 feet shorter than the ﬁrst palm frond.

DOK-1 What are the four operations used to solve a word problem? Addition, subtraction, multiplication, and division

DOK-2 Which operation is needed to solve this problem? Explain. Answers will vary. I will need to use subtraction to solve this problem because I know the second palm frond is smaller or shorter than the ﬁrst palm frond, so I will need to subtract in order to ﬁnd the length.

11.

Acceleration

Students should be given enough time to complete all of the stations. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

e. DOK-1 How did you model this problem? Answers will vary. I drew 2 different palm fronds, and one is bigger than the other. I labeled the bigger palm frond “6 feet long.” I labeled the distance between the end of the shorter palm frond to the end of the larger palm frond with “3 feet: to show that the smaller one was 3 feet less than the big one.

10.

Intervention

MEASUREMENT

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FACILITATION TIP While arriving at a correct answer is essential, learning the process of problem solving may be more important for some students at this point.

DOK-2 How did the model help you solve the problem? Answers will vary. I could easily see that I needed to subtract 3 feet from 6 feet to ﬁnd the shorter palm frond since the smaller palm frond was 3 feet shorter than the big palm frond.

FACILITATION TIP DOK-1 What unit of measurement is used to label your answer? Answers will vary. I will use feet to measure my answer since the problem is Have students include their units of talking about the palm fronds being measured in feet. measurement in their answers.

Once students have answered all of their Nature Cards, allow them enough time to answer 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.

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Measurement Explore 2 – Length Math Chat DOK-3 How did you determine what operation to use for each problem? I used the model to help me determine what operation to use. I used the information and vocabulary given in the word problem to help me determine what operation to use. We knew if we are looking for the total, we would need to multiply or add. If we are looking for a part, we would need to subtract or divide. • DOK-3 When might you use addition or subtraction to solve a measurement problem? I might use addition when I know the length of an item, but I need to know the length of 3 of those items, so I will add the length of the item 3 times. I might also add when I know the length of an item but something is longer than it, so I will add the two lengths to find the total. I might subtract when I’m finding the difference between the two sizes of an object or when something is shorter than another item and I need to subtract from the original item to find the size of the other item. • DOK-3 When might you use multiplication or division to solve a measurement problem? I might use multiplication when I have a repeated length of an item and I’m trying to find the total length of those items combined. I might use division when I have a total length and the length of each item that makes up that total and each item is the same size. I can divide the total by the equal parts to find the size of a single item or how many items make up the total. • DOK-2 How can a model help you solve a word problem? A model can be helpful when solving a word problem because it can create a visual image to represent what the words in a problem are explaining. I can then use that model to help me determine an operation needed to solve the problem. • 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 Reassure students that models also provide excellent visualization practice. Using models supports their ability to eﬃciently solve problems mentally as they become more proﬁcient in math.

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.

394

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

MEASUREMENT

Home

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Measurement Explore 3 – Mass and Weight ACTIVITY PREPARATION Students will solve word problems pertaining to weight using addition, subtraction, multiplication, and division.

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 Station Cards (per class) 1 Set of Scenario Cards (per group) 1 Exit Ticket (per student)

Reusable • •

1 Resealable bag (per group) Sample objects such as the following: • • • •

•

• •

Book Canned food Rock Stuffed animal

•

Manipulatives:

Plan to divide the class into 4 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Station Cards on card stock. Place Station Cards around the room to prepare each station. Prepare manipulatives in a central location for students to use as needed. Gather 2 objects for each group such as a book, canned food, rock, or stuffed animal. Make sure each object has a noticeably different mass. Print the Scenario Cards on card stock for each group. Cut them apart, and place each set in a resealable bag. For students who need more support in recalling information, please see our 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. (Base Ten Blocks, Two-Color Counters, and Color Tiles)

• Base ten blocks • Counters • Tiles

PROCEDURE AND FACILITATION POINTS Part I: Packing Genevieve 1.

FACILITATION TIP Have students give examples of objects that have less mass or weight versus more mass or weight that they interact within the classroom. 396

4. 5.

Give each group of students 2 objects to compare the mass. Invite students to hold two objects, one in each hand. Make sure each object has a noticeably different mass. Invite students to share observations about the feel of the two objects with their elbow partners. After a few seconds, invite students to share observations with the class. Observations may vary. The two objects are two different sizes, their texture is different, they have different weight. Explain that all things around us, big and small, are made up of different amounts of matter, which give them different mass, and means their weight feels different. Point out two examples and the differences in mass. Explain that weight is a measurement of how heavy something is. Mass is a measurement of how much matter is in an object. We use various tools like scales to measure weight. Explain that for the purposes of this Explore activity, students will only be measuring weight. In future grades, they will learn to also measure mass. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Discuss the following questions:

Intervention

Acceleration

FACILITATION TIP

Weight includes the the force of gravity DOK-1 What are some different units of weight? Student answers should acting on the object. Mass is the amount of include ounces and pounds. “stuff,” or matter, in an object. b. DOK-2 Are all units of weight the same? No. Some units are very small, and some are large. a.

8. 9. 10. 11. 12.

Read the following scenario to the class: Genevieve is going on a trip with her family to the happiest theme park in the country! She needs to pack and wants to make sure everything is packed properly. Will you help her? Give a Student Journal to each student. Explain that students travel around “her room” as they help her pack everything she needs. If classes are large, consider running two sets of cards. Encourage students to collaborate and discuss with their groups to determine what Genevieve must do to overcome her packing challenges. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 Why did you use that operation to solve the problem? Answers will vary. I needed to add all the objects together because I am trying to reach 50 ounces.

DOK-2 What strategies did you use? Answers will vary. I estimated the total by rounding the numbers ﬁrst.

DOK-2 How did the manipulatives/model help you solve this problem? Answers will vary. Since each outﬁt has a weight of 6 pounds, I used 6 counters for each outﬁt. Then, I added the counters together and got 18 pounds, which is less than 22 pounds.

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FACILITATION TIP Have groups discuss the manipulative and its value prior to solving the problem.

Part II: Scenarios 1.

3. 4.

Read the following scenario to the class: Genevieve and her family have arrived at the happiest theme park in the country! Genevieve has to help ﬁgure out certain weights while riding rides, playing games, and eating food. Help Genevieve out so she can have a fun day at the park. Give a set of Scenario Cards to each group. Instruct students to solve some problems Genevieve encountered involving pounds and ounces while at the theme park. Encourage students to collaborate and discuss with their groups to determine what Genevieve must do to be able to experience everything in the park. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

FACILITATION TIP

Have students put a square around the units in the Scenario Cards. Ensure that DOK-2 How did you know what operation to use to solve the problem? students use the same units on their Student Answers will vary. We needed to add the family’s weights together so we Journals. could ﬁnd out if the total was greater or less than 500 pounds. DOK-2 How did the manipulatives/model help you solve this problem? Answers will vary. We took 48 counters and divided them into 4 groups. Then, we counted the number of counters in each group to ﬁnd out how many ounces of slushie each person got.

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

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Measurement Explore 3 – Mass and Weight Math Chat •

FACILITATION TIP Remind students that proﬁciency with models leads to stronger problem-solving skills and ﬂuency with mental math. FACILITATION TIP This Exit Ticket provides a good opportunity to model math literacy skills. Support struggling students by underlining, circling, or highlighting key values and words in the scenarios.

•

DOK-3 How did you determine which operation to use for each word problem? If we needed to ﬁnd the total weight, we added. Other times, we had to ﬁnd the difference in weight, so we subtracted. There were also times when we had to determine the weight of several objects with the same weight; in that case, we multiplied or divided. DOK-2 How did models or drawings help you determine a solution? Models helped me understand what was happening to the numbers. I was able to break numbers apart, make equal groups, and combine weight amounts.

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

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399

MEASUREMENT

Measurement Explore 4 – Liquid Volume ACTIVITY PREPARATION Students solve for liquid volume in word problems using addition, subtraction, multiplication, and division.

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 Station Cards (per class) 1 Exit Ticket (per student)

Preparation • • • • • •

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 the Station Cards. Laminate them, if desired, for long-term use. Put Station Cards around the room for students to rotate through. For students who need more support in recalling information, please see our 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. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Project visuals of various bottles of liquid. Have students identify the units on the bottles’ labels.

2. 3. 4. 5. 6.

FACILITATION TIP

Students are solving real-world problems by creating models. The models are a focus in this Explore activity.

Read the following scenario to the class: Derek’s Cleaning Company is a new business. It is growing, and every day it has new customers. Since the employees dedicate themselves to making spaces spotless, they need to make sure they have enough of their materials. Can you help Derek’s company keep track of the supplies it needs? Give a Student Journal to each student. Instruct students to apply their knowledge about liquid volume to determine answers to the questions Derek has. Encourage students to think about what is happening to the supplies and what operation would need to be applied to answer the question. Tell students that each cleaning station around the room describes how much cleaner is used or needed for each type of cleaning. Challenge students to collaborate in their groups to determine solutions and record them on their Student Journals. Ask students to prove their answers by drawing a model and writing the equation they used to solve each problem. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 Why did you use that operation to solve the problem? Answers will vary. There were 12 groups of 3 pints, and I needed to ﬁnd the total number of pints used, so I multiplied.

b. DOK-2 Is there another way you could have solved the problem? Answers will vary. I could have added 3 twelve times or added 12 three times. c. 400

d. 9.

Engage

Explore

Explain

Elaborate

DOK-2 How did the model help you solve the problem? Answers will vary. I could easily see how much cleaner was used.

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

Evaluate

Intervention

Acceleration

FACILITATION TIP Allow groups to share with the class how they solved one of the Station Cards.

MEASUREMENT

Home

Math Chat DOK-3 How did you determine what operation to use for each problem? We had to determine what was happening to the supplies. We knew if we are looking for the total, we would need to multiply or add. If we are looking for a part, we would need to subtract or divide. • DOK-2 Why might you want to use quarts instead of cups? If you are using a large amount of liquid, it doesn’t make sense to use such a small unit. It would take a longer time to measure, and the measurement would be a larger number that may be diﬃcult to work with. • DOK-2 Why would you want to use pints instead of gallons? If you are using a small amount of liquid, it doesn’t make sense to use large units like gallons. Since the amount of liquid would be small, the measurements would not be accurate. FACILITATION TIP • DOK-2 How did the models help you solve the problem? The models showed how much of that cleaner was used Continue to encourage students to use the models to help them solve the problems. Post-Explore They will need these tools as they progress 1. Have students complete the Exit Ticket to formatively assess their understanding through more complex math standards in later grades. of the concept. 2. Complete the Anchor Chart as a class. FACILITATION TIP 3. Have each student complete their Interactive Notebook. Use this Exit Ticket to model math literacy 4. Return to the Hook and instruct students to use their newly acquired skills to skills. Underline, circle, or highlight key successfully complete the activity. values and words in the scenarios. •

401

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

Select Tools to Measure 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

Length 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

Mass and Weight

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

Liquid Volume

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

402

Engage

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

Art Night Fundraiser

Civil Engineer

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

Setting Up an Aquarium

Problem Solving with Measurement – Metric and Customary

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

Fluency Builder

Feeding Time

Measurement Estimation – Metric and Customary

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

403

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

404

 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER

MEASUREMENT

Home

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 rulers to measure lengths in halves and fourths of an inch and in whole inches.

I can select and use appropriate tools to measure liquid volume, length, and weight.

I can solve real-world problems involving the estimation and measurement of liquid volumes, lengths, or weights.

405

SCOPE 1

Represent and Interpret Data Scope Introduction SCOPE SUMMARY Students become familiar with analyzing, interpreting, representing, and using data to solve problems. They analyze data and represent it in a variety of ways, including the use of frequency tables, line plots, pictographs, and bar graphs with scaled intervals. In addition, students use data that has been represented on such graphical displays and solve one- or two-step problems. Student Expectations

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.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students collect, organize, and represent data by using tables, pictographs, and bar graphs. They interpret and use the data to solve addition and subtraction problems.

In fourth grade, students collect data by accurately measuring objects to an eighth of an inch. Students represent the measured data by creating a line plot. They 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.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

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.

summarize a set of data with multiple categories, using a graph with scaled intervals, and solve one-and two-step problems based on that data.

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

406

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Frequency Tables and Line Plots In this exploration, students will explore how to organize data into frequency tables and line plots and analyze the data to solve problems. Students will: •

create a frequency table to keep track of how many students are a certain height.

•

use the line to create a graph that shows the data.

Explore 2

Explore 1

EXPLORE ACTIVITIES Pictographs and Bar Graphs In this exploration, students will work through a set of stations where they gather data and represent it using a pictograph or a bar graph. Students will: •

create either a bar graph or a pictograph with the data about animal populations.

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 an Exit Ticket for assessment.

REPRESENT AND INTERPRET DATA

Home

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

408

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE In this activity, students will read a pictograph and a bar graph and identify the information that each represents. This activity is intended to assess mastery of the following standard(s): 2.MDR.5.4 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Preparation

Materials Printed •

•

1 Represent and Interpret Data (per class)

•

Print and cut apart both pages of Represent and Interpret Data for the class. Hang the pictograph and bar graph separately on the board. Hang the hand showing a B in sign language beside the bar graph and the hand showing a P in sign language beside the pictograph.

REPRESENT AND INTERPRET DATA

Home

Procedure and Facilitation Points 1.

Explain to students that two third-grade classes were asked about their favorite foods. One class’s results are organized in the pictograph, and the other class’s results are organized in the bar graph. Tell students you will read a statement and they will respond with the sign language for P if the statement relates to the pictograph or B if the statement relates to the bar graph. Demonstrate and have students practice making a P and a B in sign language. Read the following statements to the class: a.

This graph uses pictures to represent data. Students make a P.

This graph uses bars to represent data. Students make a B.

This graph shows that the favorite food for two students is hamburgers. Students make a P.

This graph shows that the favorite food for three students is chicken tenders. Students make a P.

FACILITATION TIP Take time to ensure that students clearly understand which graph is the pictograph and which one is the bar graph. Struggling students may need to point to the appropriate graph rather than use sign language. FACILITATION TIP Project each question in print as you read them to the class.

e. This graph shows that the favorite food for most students asked is chicken tenders. Students make a B. f.

This graph shows that there are three more students who like pizza more than tacos. Students make a B.

This graph shows that the least-liked food is tacos. Students make a B.

h. This graph shows that ﬁve students like tacos. Students make a B. Note: Additional questions can be added to help determine students’ abilities to read and interpret bar graphs and pictographs. 4.

Facilitate a class discussion about their responses. 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. If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Hook – Favorite Popcorn Flavors ACTIVITY PREPARATION Students summarize a set of data with multiple categories, using a graph with scaled intervals, and solve one-and two-step problems based on that data.

Materials

Preparation

Printed • •

1 Favorite Popcorn Flavors (per class) 1 Student Handout (per group)

Reusable • • • • •

Plan to show the Phenomena Video. Print Favorite Popcorn Flavors, and prepare to project it for the class. If you have more than one class, you will want a separate copy for each class so you can come back to the same data when you revisit this topic. Print enough copies of the Student Handout for each student to have one type of graph. Each Student Handout document contains a pictograph, a bar graph, and a line plot. You will want more than one graph type so students can compare how the same data is displayed on more than one graph and with different scaled intervals. Prepare to project the Student Handout.

• •

•

1 Set of colored pencils, markers, or crayons (per student or table) 1 Glue stick (per group) 1 Set of dot markers (per class) *optional 1 Phenomena Video (per class) 1 Projector or document camera (per class)

•

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

FACILITATION TIP Before reading this scenario, display some engaging real-world graphs for students. Consider using graphs that are in their science or social studies books, recent school newsletter, or on a high interest website. FACILITATION TIP Prepare students by requesting that they pick a ﬂavor even if it is not the one they like best. Some students may not like popcorn or ﬂavored popcorn at all; don’t let those preferences affect the process.

4. 5. 6. 7. 8.

9. 410

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? Where can you see math in this scenario? Allow students to share all ideas. Read the following scenario to the class: I am taking a survey on favorite popcorn flavors. I want to know which flavor is the favorite and which is the least favorite in this class. I want to know how many more people like the favorite than the second favorite. I want to know how much it would cost to buy everyone a bag of popcorn if the bags cost $2 each. Display Favorite Popcorn Flavors using the projector or document camera. Ask the students to look at the four flavors listed—butter, cheese, caramel, and kettle corn—and think about which of those four flavors they like best. Ask everyone who likes butter the best to raise their hand. Put a tally mark for each of those students in the appropriate box on Favorite Popcorn Flavors. Repeat this process for cheese, caramel, and kettle corn. Discuss the following questions with the class: a.

DOK-1 What information do we know? We know how many people like each ﬂavor of popcorn.

DOK-2 What information would we need to know to determine how many more people like the favorite flavor than the second favorite? We need to know how many people like the favorite flavor and how many people like the second favorite flavor.

Engage

Explore

Explain

Elaborate

Evaluate

Part II: Post-Explore 1. 2.

3. 4.

Intervention

Acceleration

STEMscopes Tip

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

DOK-1 What information do we know? We know how many people like each ﬂavor of popcorn.

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.

Show students the Favorite Popcorn Flavors frequency table from their class. Hand out the three different types of graphs. You can do this randomly, assign them, or have students select which they want.

REPRESENT AND INTERPRET DATA

Home

FACILITATION TIP The bar graph has a scaled interval of ﬁve, the pictograph is two, and the line plot is one. Take time to review the importance of intervals. Clarify the labeled values and Tell the students to create a graph from the data in the Favorite Popcorn Flavors the possible values in between for each frequency table. They will need to see which type of graph they were given and speciﬁc graph. look at the scaled interval. a.

For the pictograph, students can cut out the popcorn shapes at the bottom and glue them onto their graph. Note that some of the popcorn shapes are half a popcorn shape. These may be needed if an odd number of students like any of the ﬂavors. The scaled interval is two for the pictograph.

For the bar graph, students may color the bars any color they would like. Note that the scaled interval is ﬁve, so they may need to draw some of their bars up to a point between the given lines.

For the line plot, students may use dot markers, if they are available. Otherwise, they can just draw or color dots. Each dot will represent one student.

FACILITATION TIP Consider cutting the popcorn shapes ahead of time or allow students to draw the shapes on the graph rather than glue. FACILITATION TIP Consider having students use regular pencil before coloring. Fixing mistakes in color is more complicated than erasing light pencil marks.

As the students are making their graphs, encourage them to discuss among each other some of the differences in their graphs. Are they noticing any challenges with their particular graph that someone with a different graph (or scaled interval) may not be having? Is there one graph that seems to display the data more clearly than another graph?

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Hook – Favorite Popcorn Flavors 7.

Discuss the following questions with the class: a.

DOK-1 Look at your graph. Which ﬂavor is the favorite in the class? Answers will vary.

DOK-1 Look at your graph. Which ﬂavor is the least favorite in the class? Answers will vary.

DOK-1 How many more people like the favorite than the second favorite? Answers will vary. Subtract the number of students who like the second favorite from the number of students who like the favorite.

DOK-1 How much would it cost to buy everyone a bag of popcorn if popcorn costs $2 per bag? Answers will vary. Add the number of students who liked each ﬂavor, and then multiply that total by two.

e. DOK-2 What was challenging about making the line plot for this set of data? There were a lot of dots, and some of the columns could be really tall. f.

DOK-2 What was challenging about making the bar graph for this set of data? Each line was ﬁve apart, so if one of the bars had to go between the lines, you had to guess where it should be.

DOK-3 How could changing the scaled interval help you when you’re making a bar graph? If you have a lot of data with high numbers, you can make your scaled interval bigger, like 5, 10, or even 100. If your data doesn’t have a lot of high numbers, you can do a smaller scaled interval, such as 2.

h. DOK-2 What was challenging about making the pictograph for this set of data? I had to cut out a lot of pictures. Each time I wanted to know the total for one ﬂavor, I had to skip count. i. DOK-3 How could changing the scaled interval help you when you’re making a pictograph? If your numbers are really big, each picture could represent a lot more. If your numbers are really small, each picture could represent one or two. If your scaled interval is too much, it is hard to show numbers that are in between. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

412

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT AND INTERPRET DATA

Home

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413

REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 1 – Frequency Tables and Line Plots ACTIVITY PREPARATION Students will explore how to organize data into frequency tables and line plots and analyze the data to solve problems.

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.6 Attend to precision.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Station Cards (per class, print two sets for larger classes) 1 Set of Line Plot Circles (per group) 1 Exit Ticket (per student)

•

Reusable • • • • •

•

1 Yardstick (per group) 1 Ruler (per student) 1 Die (per class) 1 Pencil (per class) 1 Paper clip (per class)

•

• Station 1: 1 die and the Station Card • Station 2: 1 pencil and 1 paper clip, along with the Station Card • Station 3: Station Card only

Consumable • • •

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 Line Plot Circles for each group on colored card stock. Hang the strip of butcher paper horizontally on a wall where all students can clearly see it. Draw a straight line near the bottom of the page. Print and cut out a set of Station Cards. For larger classes, plan to have two sets of stations running at the same time. Prepare the following materials at each station:

•

1 5’ strip of butcher paper (per class) 2 Sheets of colored card stock 1 Roll of clear tape (per class)

For students who need more support in recalling information, please see our Number Cube and Open Number Line Supplemental Aids elements in the Intervention section.

PROCEDURE AND FACILITATION POINTS Part I: How Tall Are We? 1. FACILITATION TIP

To facilitate eﬃcient measurements, consider having an adult help each small group measure heights ahead of time.

414

Place students in groups of four or ﬁve and give a yardstick to each group and a colored circle and Student Journal to each student. Students should help measure the height of their group members to the nearest inch using the yardstick and record their heights on their Student Journals. Bring the class together. Discuss the various heights of the students in the room. Note that if height is a sensitive topic for the students in your classroom, feel free to change the topic to something else such as hand width, foot length, etc.

Ask students things they could not easily answer yet, such as the following questions: a.

DOK-1 How tall are most of the students in the class?

DOK-1 How tall are the shortest and tallest students?

5. 6.

9. 10.

12.

14.

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 Why do you think drawing tallies this way could be helpful? It’s really easy to skip count by fives. If we mark the tallies this way, we can easily skip count groups of five to find the total number of tallies.

Students should be keeping track of the tallies in their Student Journals as well. Give groups a few moments to ﬁll in the frequency column on their own. Help students see how the frequency chart helped you organize your data. a.

13.

Explore

Allow students to struggle with these questions to help them see the need to somehow organize their data before they can answer questions like this. Introduce that there are many ways we can organize data so it’s easier to use. We FACILITATION TIP can start by creating what’s called a frequency table. Draw a three-column table Project the three column table from the on the board with the column titles Height Height, Tally Tally,, and Frequency. Student Journal under the document Explain to students that the frequency table can be used to keep track of how camera. many students are a certain height. Ask the following question: FACILITATION TIP a. DOK 2 What do you think we need to do to start keeping track of the Consider doing some simple frequency heights? We need to list the possible heights in the first column, and tables with the class in the weeks before then we can tally how many students are each height. this activity. Take some quick surveys about Use a process of elimination to figure out the heights of the shortest and tallest lunches, recess, field trips, or favorite toys. students. List all of the whole numbers in between the two heights in the Height Model the tallying on a frequency table. column. FACILITATION TIP Call on students one at a time to share their heights. They can then come up to If adults help students measure and record the board and add tally marks next to their heights if they want. heights, this data collection in Step 9 will go Introduce what to do if you need to add a fifth tally mark to a certain height by much more quickly. allowing the fifth mark to be a slash through the first four marks. If this situation comes up, discuss the following questions: a.

11.

Engage

REPRESENT AND INTERPRET DATA

Home

DOK-2 What are some other ways you know for organizing data? We have used pictographs and bar graphs before. We’ve used other kinds of tables before.

Explain that a frequency table is a helpful tool for gathering and organizing data. We can then use the information in the frequency table to create another type of graph or represent our data in a different way. Direct students’ attention to the butcher paper with the line at the bottom. Tell students the goal is to use the line to create a graph that shows our data. a.

DOK-2 What does the line at the bottom remind you of? It looks like a number line.

DOK-2 How could we show our heights on a number line? We could make tick marks for each possible height on the number line and put points on the number line for our heights.

DOK-1 What tick marks would need to be on our number line? Answers will vary. We would need the numbers 42 through 51. (Answer should represent class data.)

DOK-2 What if more than one person needs to put their point in one spot on the number line? We could put them on top of each other.

FACILITATION TIP Gather some examples of dot plots or line plots to show to students before this discussion.

FACILITATION TIP Students will need support to determine the appropriate ranges for graphs and dot plots.

e. DOK-2 How can we let others know what a dot represents? We can add a key to show that one dot represents one student. 15.

16.

17.

Allow a few students at a time to come tape their colored circles above the tick marks that represent their height. Help students see how the dots can be stacked above each height. Introduce to students that what they created together is called a line plot. Students should record the class line plot on their Student Journals to practice completing all the necessary parts. Provide students with rulers that are marked at halves and fourths to create evenly spaced tick marks on the number line. After Part I, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP As students place their colored circles, be sure they are being spaced equally from the line and each other. FACILITATION TIP Struggling students may need the tick marks already noted on the number lines to create equal spacing. 415

REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 1 – Select Tools to Measure Math Chat • • • • •

DOK-2 What do you notice about the line plot? Some heights have more dots above them than others. DOK-1 How tall are most of the students in the class? Answers will depend on individual class data. DOK-1 How tall are the shortest and tallest students? Answers will depend on individual class data. DOK-1 How much taller is the tallest student than the shortest student? Answers will depend on individual class data. DOK-2 What is the relationship between the frequency table and the line plot? They both show the same data, just in different ways. It would be easy to create a line plot if you had the frequency table. Each dot on the line plot shows the same thing as a tally mark on the frequency table.

Part II: Line Plot Stations FACILITATION TIP

1. 2.

Consider having students independently record the data on the frequency tables. Bring the class together to create the line plots. Carefully model step by step how to make a neat and readable line plot.

Assign each group of students to a station. At each station, students should follow the instructions on the card to organize data into a frequency table and a line plot. As students are working, monitor their work and discuss their progress with them. Ask questions about the relationships and patterns they are noticing within the data. Keep the following considerations in mind as students explore each station: a.

Station 1: Students are rolling a die 40 times and recording the outcomes. i. Students may need guidance to realize a dot on a line plot can represent more than one piece of data. ii. If needed, students may need guidance in representing an odd number if their dots represent two pieces of data. For example, students may need help representing the number seven if each dot represents two rolls.

i. Students may need guidance to realize a line plot can represent categories as well as numerical data.

Station 2: Students are determining choices for a rainy-day activity, using a spinner.

Station 3: Students are organizing given weather data. i. Students may make the mistake of leaving out 90 in their frequency table or line plot because there are no data points associated with 90 degrees. Help students see how each whole number should be represented, even if the data states the value is zero.

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

Math Chat •

DOK-2 How is this way of representing data helpful? It is easy to see which category has more than the others. It helps you see the results of your data.

As time allows, display the data collected by one of the groups, and ask analysis questions about the data, such as the following: • • •

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DOK-1 Which ____ occurred the most? DOK-1 How many more _____ than _____? DOK-1 Which category was the least?

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. When you preview this Exit Ticket with students, show them how to lightly cross Complete the Anchor Chart as a class. out data as they record it on the table. For Have each student complete their Interactive Notebook. example, as they tally they should lightly cross out each name.

Notes __________________________________________________________________________________________________________________________________________________

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Represent and Interpret Data Explore 2 – Pictographs and Bar Graphs ACTIVITY PREPARATION Students work through a set of stations where they gather data and represent it using a pictograph or a bar graph.

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.6 Attend to precision.

Materials Printed • • •

1 Student Journal (per student) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

Preparation • • •

Reusable • • •

• Station 1: Bouncing putty and yardstick • Station 2: Small circular stickers • Station 3: Station Card only

1 Pack of bouncing putty (per class) 1 Yardstick (per class) 4 Types of food items (per class, optional)

•

Consumable • •

Plan to have students work in groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Station Cards. Place the Station Cards, along with the following materials, at each station. For larger classes, consider having two sets of stations running at the same time.

1 Set of small circular stickers (per class) 1 Small pack of gummy bears (per class)

If desired, real food items could be brought in, and students could develop their own tally chart.

• Station 4: Small pack of gummy bears

•

Consider altering the amount in the gummy bear pack so it is easily represented in a pictograph. For example, there may be so many bears that students need their symbol to represent a group of 5 bears, but there may be 13 green bears in a pack that is purchased. This means the bear symbol would have to be split into fractional parts that are smaller than one-half, which is not appropriate for third grade. Students should only be expected to use a whole or half of a symbol.

•

Ensure there are an even number of red and green gummy bears.

For students who need more support in recalling information, please see our Bar Graphs Supplemental Aids element in the Intervention section.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS 1. 2. 3.

Divide the class into four groups. If the class is larger, consider breaking the class up into eight groups and having two sets of stations. Assign each group of students to a station. At each station, students should follow the instructions on the Station Card to either gather and organize data or organize an existing data set. Students will create either a bar graph or a pictograph with the data (both of which they have seen before). As students are working, monitor their work, and discuss their progress with them. Ask questions about the relationships and patterns they are noticing within the data and between types of graphs. Keep the following considerations in mind as students explore each station: a.

FACILITATION TIP To support success at the stations, consider having an older student or adult help with collecting and recording data. Alternatively, you could do each station as a class and try to include every student as you collect the data.

REPRESENT AND INTERPRET DATA

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Station 1: Students are stretching bouncing putty and measuring how far they can stretch it with one pull. i. Students will likely stretch the bouncing putty over 12 in. Students may need guidance to realize the scale on a bar graph does not need to count by ones. Prompt them to think what the lines on their graph could count by in order to ﬁt all the data on the graph.

Station 2: Students are organizing data on animal populations into a pictograph. Students will use stickers as the symbols in their graph on their Student Journals. i. Students will likely want to make each dot equal to one or two animals. Encourage students to think about what each dot could represent so they have a reasonable number of dots in their graphs.

FACILITATION TIP If stickers are limited in supply, have students draw simple symbols in their graph on their Student Journals.

ii. Students may need guidance to see that a dot could be torn or cut in half if needed to show the proper number of animals. c.

Station 3: Students are either gathering data on food items brought to the classroom (optional) or organizing the given data set into a bar graph. i. Students may need guidance to create a horizontal bar graph. Tell them it’s the same process, except the bars go across instead of up and down. ii. Encourage students to think about what their lines need to count by so that all the data can be represented on the graph.

Station 4: Students are sorting gummy bears by color and representing the color distribution with a vertical pictograph. i. Students may need guidance to create a vertical pictograph. Tell them it’s the same process, except you can stack the symbols on top of each other instead of side by side. ii. Encourage students to think about what symbol they could use to represent the gummy bears as well as how many gummy bears each symbol should represent.

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

FACILITATION TIP Creating an appropriate range and interval for a graph is a complex skill. Provide guidance for this skill when you demonstrate how to create a horizontal bar graph in Step i. FACILITATION TIP Rather than real gummy bears, use colored bear counters. If you prefer to use packs of gummy bears, consider completing this station as a whole class, teacher-guided activity.

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Represent and Interpret Data Explore 2 – Pictographs and Bar Graphs Math Chat • FACILITATION TIP To support struggling students on this Exit Ticket, provide a pre-selected symbol and key.

DOK-2 How is this way of representing data helpful? It is easy to see which category has more than the others. It helps you see the results of your data. You can make the data look simpler than a list of numbers.

As time allows, display the data collected by one of the groups, and ask analysis questions about the data, such as the following: • • • •

DOK-1 Which ____ occurred the most? DOK-1 How many more _____ than _____? DOK-1 Which category was the least? DOK-1 What is the difference between the most and the least?

Post-Explore 1. 2. 3. 4.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT AND INTERPRET DATA

Home

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Represent and Interpret Data 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

Frequency Tables and Line Plots 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

Pictographs and Bar Graphs 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

Fixing up the Playground

Audiologist

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

Patch Collecting

Match Frequency Tables to Line Plots, Pictographs, or Bar Graphs

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

REPRESENT AND INTERPRET DATA

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

Problem-Based Task

Fluency Builder

Reading Goals

Problem Solving with Data

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 INTERPRET DATA

Represent and Interpret Data

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 create a statistical investigative question that can be answered using data.

What prompts will be used?

What does mastery look like?

REPRESENT AND INTERPRET DATA

Home

I can determine strategies for collecting and organizing numerical and categorical data.

I can create and use a pictograph to summarize data and solve problems about the data.

I can create and use a bar graph to summarize data and solve problems about the data.

I can create and use a line plot to summarize data and solve problems about the data.

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