STEMscopes Georgia Math Teacher Guide Grade 5 by acceleratelearning

5 Georgia Math Teacher Guide

Grade 5 Teacher Guide

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

ISBN: 979-8-88826-664-9

5 GEORGIA

MATH G5

GEORGIA

Teacher Guide: Grade 5 ISBN: 979-8-88826-664-9 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

Read and Write Decimals .................................................................................... 46

SCOPE 3

Compare and Order Decimals .............................................................................. 66

SCOPE 4

Round Decimals.................................................................................................. 84

SCOPE 5

Add and Subtract Decimals ................................................................................. 98

SCOPE 6

Multiply Multi-Digit Whole Numbers .................................................................. 116

SCOPE 7

Divide Multi-Digit Whole Numbers ..................................................................... 132

SCOPE 8

Numerical Expressions ..................................................................................... 160

SCOPE 9

Compare and Order Fractions and Mixed Numbers ............................................. 186

TABLE OF CONTENTS

Table of Contents

SCOPE 10 Add and Subtract Fractions ............................................................................... 210 SCOPE 11 Multiply Fractions ............................................................................................. 230 SCOPE 12 Fractions as Division ......................................................................................... 254 SCOPE 13 Divide Fractions ................................................................................................ 274 SCOPE 14 Classify Two-Dimensional Figures..................................................................... 298 SCOPE 15 Unit Conversions .............................................................................................. 322 SCOPE 16 Volume ............................................................................................................ 346 SCOPE 17 Graph in the First Quadrant ............................................................................... 368 SCOPE 18 Generate and Graph Numerical Patterns ............................................................ 388 SCOPE 19 Represent and Interpret Data............................................................................. 406

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 • 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 through 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 • Give students the opportunity to see how math is used in a real-world situation • Is revisited and the problem is solved after students complete the Explore activities from the next section Ideas for using this element: • Explain the real-world situation while showing the video. • Facilitate a discussion about how the scope’s math concepts are used in the situation. • Return to the Post-Explore section to solve the problem after completing the Explore activities. • Students typically complete and discuss the Post-Explore activities in pairs or small groups.

USING STEMSCOPES

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

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

USING STEMSCOPES

Home

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

USING STEMSCOPES

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

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

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

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

USING STEMSCOPES

Home

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

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

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

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

• A general description of the activity

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

• Materials and preparation needed to complete the activity

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

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

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

INTERACTIVE NOTEBOOK • A general description of the Interactive Notebook

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

• Materials and preparation needed to complete the activity

and/or process the information presented in class.

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

Ideas for using this element:

• A printable Student Handout

• Provides students with the opportunity to solidify their learning

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

USING STEMSCOPES

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

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

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

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

• A real-world story students can relate to

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

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

• Offers questions covering both math concepts and reading comprehension

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

USING STEMSCOPES

Home

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

USING STEMSCOPES

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

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

USING STEMSCOPES

Home

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

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

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

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

USING STEMSCOPES

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

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

USING STEMSCOPES

Home

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

STANDARDS-BASED ASSESSMENT Use the 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 misunderstandings 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

Student Expectations

5.NR.1.1 E Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the 1 place to its right and ___ of what it 10 represents in the place to its left. 5.NR.1.2 Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 10³.

Students reason about the magnitude of numbers by recognizing that a digit in one 1 place represents 10 times as much as it represents in the place to its right and ___ of 10 what it represents in the place to its left. Place value work extends in ﬁfth grade by including decimals to the thousandths place. Students use concrete and representational manipulatives, such as base ten blocks, place value disks, place value charts, drawings, and interactive digital tools to investigate place value relationships. Also new to students in ﬁfth grade is the use of whole-number exponents to represent powers of ten. Students learn what an exponent is and express powers of 10 using exponents. They investigate how multiplying or dividing by a power of ten changes the place value; they observe and explain patterns in the placement of the decimal point and in the number of zeros at the end of a product.

VERTICAL ALIGNMENT Background Knowledge Fourth-grade students generalize the process of rounding numbers, and they round to digits other than the leading digit. In third and fourth grades, students begin to see that rounding is valuable when estimating, predicting, and justifying the reasonableness of an answer.

Future Expectations Sixth-grade students extend their knowledge of the base-ten system to include negative numbers. Students learn to use numerical reasoning to explain that positive and negative numbers are used together to describe quantities having opposite directions or values. Fluency with rounding enables students to apply it regularly as an important estimation tool.

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

explain the relationship between the same digit in two different places.

•

compare descriptions and match to explanations of the relationship of place value.

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: •

recognize that a digit in one place represents ten times what it represents in the place to its right.

•

1 ___ of what it represents in the place 10

to its left.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 20

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Place Value Relationships In this exploration, students will analyze the relationships between the digits both to the right and left of each number. Students will: •

manipulate objects such as place value disks, base ten blocks, and clues to build numbers.

•

participating in class discussions.

•

relationships between the digits both to the right and left of each number.

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, students will be tasked with solving a scenario where they pretend that they have been hired to help a business either ﬁgure out its earnings, pay its employees, or assist its customers. Students will: •

explore patterns of numbers as they multiply and divide by multiple factors of ten.

•

explain the patterns they notice as they multiply and divide by factors of 10.

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

Powers of Ten

PLACE VALUE RELATIONSHIPS

Home

Exponents In this exploration, groups of students will be faced with a real-world scenario about bacterial growth that they are tasked with solving. Students will: •

create models.

•

write the word form, powers of ten expression, expression and exponent forms for different values.

•

analyzing different samples for growth or reduction, then writing the powers of ten expressions, exponent forms and ﬁnally solving.

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

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 explain the relationship between the same digit in two different places. Students will choose the best description and explanation of the relationship of a place value and the place value directly to its right. This activity is intended to assess mastery of the following standard(s): 4.NR.1.2 Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division.

Materials

Preparation

Printed • • •

PLACE VALUE RELATIONSHIPS

Home

1 Slideshow (per class) 1 Set of Statement Cards (per group) 1 Set of Explanation Cards (per group)

• • • •

Plan to have students work in groups of 3 or 4 to complete this activity. Prepare to project the Slideshow for the class, or print one Slideshow for each group. Print a set of the Statement Cards on card stock for durability for each group of students. Cut the cards apart, and place them in a resealable bag. Print a set of the Explanation Cards on card stock for durability for each group of students. Cut the cards apart, and place them into a resealable bag.

Reusable • •

1 Projector or document camera (per class) 2 Resealable bags (per group)

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

Project the Slideshow for the class. Read the problem together as a class. Give a set of Explanation Cards and a set of Statement Cards to each group. Ask students to set out the four Statement Cards so that each group member can see all of the cards. Tell the groups to read each statement card and discuss and decide as a group which statement completes each of Samantha’s sentences. Ask student groups to read their sentences aloud using the statement that they chose to complete it. Explain that there is only one correct statement for each of the two sentence stems. Two cards cannot be used. a.

The digit 5 in 459 is like the digit 5 in 596 because the 5 in 459 and the 5 in 596 are the same digit. A digit is a number 0–9 in any place value.

The digit 5 in 459 is unlike the digit 5 in 596 because the 5 in 596 is 10 times as much as the 5 in 459. The value of the 5 changes when it is in a different place value. The 5 in the hundreds place has a larger value than the 5 in the tens place.

Ask the students to set out the four Explanation Cards so that each group member can see them. Tell students to choose the cards that describe the relationship between the digit 5 in the given numbers. More than one card may be correct.

FACILITATION TIP The students should include a written justiﬁcation for each of their choices. FACILITATION TIP The students should discuss within their groups and as a whole group why the other two choices are not correct and should provide an example of a possible correct answer for each. FACILITATION TIP The students may need you to demonstrate the ﬁrst relationship. Move around the room, facilitating and providing prompts as needed. 23

PLACE VALUE RELATIONSHIPS

Place Value Relationships Lesson Calendar and Accessing Prior Knowledge 8.

FACILITATION TIP Provide each group with an opportunity to share their answer choices with another group before sharing them with the class. Encourage students to use their justiﬁcations when sharing their answers.

Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

50 × 10 = 500 describes the relationship because the 5 in 459 is in the tens place, and 50 times 10 is 500, like in 596.

500 ÷ 10 = 50 describes the relationship because the 5 in 569 is in the hundreds place, and 500 divided by 10 is 50, like in 459.

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

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PLACE VALUE RELATIONSHIPS

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

PLACE VALUE RELATIONSHIPS

Place Value Relationships Hook – Check Out Their Checkouts ACTIVITY PREPARATION Students recognize that a digit in one place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

Materials

Preparation

Printed •

•

1 Check Out Their Checkouts (per pair)

Part I

Reusable • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Resealable bag (per pair)

Be prepared to project the ﬁrst page of Check Out Their Checkouts.

Part II • •

Consumable •

Plan to show the Phenomena Video.

1 Piece of scratch paper (per pair) •

Plan to have students work in pairs to complete this activity. Print a Check Out Their Checkouts per pair. Do NOT cut the first page. Each pair will need the first page to refer to and mark on the numbers. Cut out the true and false cards, along with the 20 statements on the 2nd page. Shuffle the statement cards before putting them in the bag. Use the second page of Check Out Their Checkouts before it is cut as your answer key.

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

Write their questions and ideas on the board or a large piece of paper to refer back to following completion of the Explore activities.

FACILITATION TIP Although not directly relevant, this would provide a teachable moment in which to explain proﬁt, including how it is determined and what role it plays in the success of a business.

5. 26

DOK-1 What do we need to determine in this problem? We need to look at the statements Savings Mart made when looking at their proﬁts and determine whether they are true or false.

DOK-1 What will you need to look at to determine whether the statements are true or false? I would look at the proﬁts for each month.

DOK-2 How does the place that each digit is in affect the value of that digit? The value of a digit changes a lot depending on where it is in the number. The digit 7 could have a value of 700,000 if it is in the hundred thousands place or 0.007 if it is in the thousandths place.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4. 5. 6.

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

DOK-1 What do we need to determine in this problem? We need to look at the statements Savings Mart made when looking at their proﬁts and determine whether they are true or false.

DOK-1 What will you need to look at to determine whether the statements are true or false? I would look at the proﬁts for each month.

Give each pair of students the ﬁrst page of Check Out Their Checkouts and the cards in a resealable bag. Review the problem, and allow students to solve it. Have students sort all cards into true statements and false statements with their partners. Discuss the following questions: a.

DOK-3 How did you determine whether the statements were true or false? We used our pencil to underline the digits the statements were talking about. We then wrote the value of each digit mentioned in the statement to see if the statement was true or false.

DOK-3 Share re your proof for a statement that was true. The digit 8 in 1

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

PLACE VALUE RELATIONSHIPS

Home

FACILITATION TIP Once the groups have completed their card sorts, allow them to move around the room reviewing how other groups sorted their cards. Provide sticky notes that students can use to provide constructive feedback as they review the card sorts.

of the value of the 8 in the tenths place in August. The 8 in May is ___ 10 May has a value of 0.008 and the 8 in August has a value of 0.08; 1

of the other 8, so 0.008 ÷ 10 = 0.08. That meant that the value is ___ 10 1

of what it is to it is true. We also knew that a digit in one place is ___ 10 the place on the left.

DOK-3 What was your proof when you knew a statement was false? We underlined the digits on the proﬁt chart. We also wrote the value of each digit. The digit 8 in February is 10 times the value of the 8 in January. In February the 8’s value is 8, while in January the 8 has a value of 80. 80 × 10 = 800, not 8. This statement is actually backward. 1 It should say ___ , not 10 ×. 10

FACILITATION TIP As an extension, ask the students to rewrite the false statements as true statements.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 1 – Place Value Relationships ACTIVITY PREPARATION Students use place value disks, base ten blocks, and clues to build numbers. They will analyze the relationships between the digits both to the right and left of each number.

Standards for Mathematical Practice • • •

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

Materials Printed • • • • • •

1 Student Journal (per student) 1 Set of Clue Cards (per group) 1 Set of Treasure Cards (per group) 1 Place Value Chart (per group) 1 Set of Additional Place Value Disks (per group, optional) 1 Exit Ticket (per student)

Reusable Part I: Whole Numbers • • • •

1 Dry-erase marker (per group) 2 Sheet protectors (per group) 1 Set of place value disks (per group) 1 Resealable bag (per group)

Part II: Decimals • • • • •

1 Dry-erase marker (per group) 2 Sheet protectors (per group) 1 Set of place value disks (per group) 1 Set of base ten blocks (per group) 1 Resealable bag (per group)

Consumable •

Preparation • • •

Part I: Whole Numbers •

• •

Print a set of Clue Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag. Gather a set of place value disks and a dry-erase marker for each group of students. Print the ﬁrst 2 pages of the Place Value Chart, on card stock for durability, for each group of students. Place these pages inside separate sheet protectors, and tape them together, with the Thousands Period coming ﬁrst, followed by the Ones Period.

Part II: Decimals •

• •

1 Roll of tape (per class) •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. If place value disks are not available, print a set of Additional Place Value Disks for each group. Cut them out in advance, if desired. Consider printing each place value on different-colored card stock so students can easily differentiate between them.

Print a set of Treasure Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag. Gather a set of place value disks, a set of base ten blocks, and a dry-erase marker for each group of students. Print the second and third pages of the Place Value Chart, on card stock for durability, for each group of students. Place these pages inside separate sheet protectors, and tape them together, with the Ones Period coming ﬁrst, followed by the Decimals Period. 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. (Place Value Disks and Base Ten Blocks)

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PROCEDURE AND FACILITATION POINTS Part I: Whole Numbers 1.

2. 3. 4. 5. 6.

Read the following scenario to the class: A pirate captain has just discovered a cave of ancient treasures. Inside this cave were 4 treasure chests. The pirate also found 4 clues on how to open each treasure chest but is having a hard time determining what the clues mean. The pirate has come to your shop and has hired your team of locksmiths to help solve the clues and has agreed to give you and your team two of the treasure chests if you are able to open all the treasure chests. Give a Student Journal to each student. Explain to students that they will be working with their group to solve each clue using their place value knowledge, place value disks, and a Place Value Chart. Give a set of place value disks, a Place Value Chart, a set of Clue Cards, and a dry-erase marker to each group. Explain to students that they must read each treasure chest clue together and represent each clue using their place value disks on their Place Value Charts. Instruct the students to use their Place Value Charts to find the value of each number in their lock code by multiplying and dividing clues based on the given information and to record their lock code, expression, and values on their Student Journals for each treasure chest. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 What did you notice about the Clue Cards you received? The cards gave us multiple clues. Some of the clues have given numbers of which place that number should be in, while some clues said they were onetenth or 10 times the value of another place value. b. DOK-2 What patterns do you notice among the place value periods on your Place Value Chart? There are three place values in each period. The smallest place value in a period is on the right. The left of that place value is a group of 10, and a group of 100 is to the left of the group of 10. c. DOK-1 How can you represent the value of the given number in clue _? Answers may vary. Since my given number of 2 is in the ones place, I can write 2 × 1 to find that the value is 2. Or since my given number of 5 is in the hundred thousands place, I can write 5 × 100,000 to find that the value is 500,000. d. DOK-2 How do you know whether to multiply or divide in order to find the missing place value digit? I know to multiply when my value is times another value. I know to divide when my value is a fraction of another value. e. DOK-2 How can you represent the value of a missing place value that is (10 times/100 times/1,000 times) the value of another place as an equation? I can multiply the value of the given number by (10/100/1,000) to find the missing place value. For example, 2 × 10 = 20. f. DOK-1 How can you represent the value of each clue using the place value disks? Answers may vary. When a clue states the given number for a certain value, I can place the given number of place value disks in the correct place on the Place Value Chart. When a clue states that a value is (10 times/100 times/1,000 times) a given value, then I know that my place value will be larger and move (1, 2, 3) spaces left on my Place Value Chart, and I will place the given number of disks in that spot. When a clue states that a value is (one-tenth/one-hundredth/one-thousandth) of a given value, then I know that my place value will be smaller and move (1, 2, 3) spaces right on my Place Value Chart, and I will place the given number of disks in that spot.

PLACE VALUE RELATIONSHIPS

Home

FACILITATION TIP Demonstrate how to use the Place Value Disk and the Place Value Chart to represent each numerical clue. FACILITATION TIP Students may need you to review and demonstrate how to determine when to multiply and divide to ﬁnd the numerical value for their clues. FACILITATION TIP Create a “I Have Mastered Place Value” reference card using the provided guiding questions. Laminate and distribute one to each group. Instruct the students to use these questions during collaborations within their groups and for self-assessment. FACILITATION TIP Ask the students to point out examples of each type of clue and explain whether they would multiply or divide to determine the value of a particular clue. FACILITATION TIP Ask the students to point out examples of each type of clue and explain whether they would multiply or divide to determine the value of a particular clue. FACILITATION TIP Provide examples of non-mathematical patterns, such as a checkerboard, to help students understand and recognize patterns.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 1 – Place Value Relationships g.

h. DOK-2 How can you represent the value of a missing place value that is (one-tenth/one-hundredth/one-thousandth) the value of another place as an equation? I can divide the value of the given number by (10/100/1,000) in order to ﬁnd the missing place value. For example, 500,000 ÷ 100 = 5,000. i. DOK-2 What do you notice when you divide a number by (10/100/1,000)? Answers may vary. I notice that my original number becomes smaller, it becomes one-tenth/one-hundredth/one-thousandth the value of the original number. The value is (1, 2, 3) places to the right of the original place value. FACILITATION TIP Identify individuals or groups who understand the activity and are willing to assist others who might be struggling. Instruct them to use the guiding questions when helping another group or individual. You may need to demonstrate how this would look. FACILITATION TIP Allow each student group the opportunity to discuss and compare their clues with another group. Demonstrate how to resolve differences through questioning instead of simply providing the correct answer. FACILITATION TIP To provide context, contact a local coin collector about borrowing a mill and silver dollar to share with your students. FACILITATION TIP Give students the opportunity to review and discuss other groups’ matches. Have them ask guiding questions during the review process. 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.

DOK-2 What do you notice when you multiply a number by (10/100/1,000)? Answers may vary. I notice that my original number becomes larger. The new value is (1, 2, 3) places to the left of the original place value.

8. 9. 10. 11.

If students are struggling with how to show their work, guide students in recording the expanded form of their number in order to ﬁnd the value. Check each student’s work after solving each Clue Card. Guide and correct students through any misunderstandings. Allow enough time for students to complete the lock codes for each treasure chest. After students have completed all their Clue Cards, discuss their ﬁndings of place value and the lock codes as a class.

Part II: Decimals 1.

2. 3. 4.

5. 6.

Read the following scenario to the class: In the 1700s, there was a unit of currency known as the mill. This currency was worth one-thousandth of a US dollar. Also in the 1700s, a one-dollar coin was invented known as the silver dollar. It just so happens that inside the pirate’s treasure chests were silver dollars, dimes, pennies, and mill coins. Distribute base ten blocks and place value disks to each group. Review with students what they know about decimals. Explain to students that now we are going to change the whole. The thousand cube is now going to have the value of 1, and the place value disks each group received represent the different coins inside the treasure chest. Instruct the students to work with their groups to match the value of their place value disks to the cube, ﬂat, rod, and unit base ten blocks. Have the students work together to discuss and solve the following questions. Allow the groups time to work together to discuss their answers before sharing with the class. a. DOK-1 Which place value disk represents the value of the thousand cube? 1 b. DOK-1 What unit of currency represents the 1 whole or thousands cube? The silver dollar 1

c. DOK-1 What place value disk represents the value of the ﬂat? 0.1 or ___ 10 1

d. DOK-1 What unit of currency represents 0.10 or ___ of a dollar? A dime 10

e. DOK-1 What place value disk represents the value of the rod? 0.01 or ____ 100

f. DOK-1 What unit of currency represents 0.01 or 1/100 of a dollar? A penny 1

g. DOK-1 What place value disk represents the value of the unit? 0.001 or _____ 1000 1

h. DOK-1 What unit of currency represents 0.001 or _____ of a dollar? A mill 1000

i. DOK-1 What are the number names that we give these fractional/decimal values? The number names are one-tenth, one-hundredth, and onethousandth.

7. 8. 9.

10.

11. 12.

13.

Engage

Explore

Explain

Elaborate

Evaluate

j. DOK-2 How did you figure out the value of each model? It takes ten flats to make a cube, so one flat is worth one tenth of the cube. There are 1 100 rods in a cube, so one rod would equal ____ . There are 1,000 units in 100 1 _____ a cube, so one unit would equal 1000.

Discuss their ﬁndings with the class. Have the students record their work on their Student Journals. Give a set of Treasure Cards and a Place Value Chart to each group of students. Read the following scenario to the class: The pirate is ready to pay up what he owes you and your team of locksmiths for opening the treasure chests. The amount of money in the treasure chests has been counted, and the pirate is giving you and your team of locksmiths the two treasure chests with the most money. If students are commenting that they aren’t getting a lot of money for their work, it is important to note the inﬂation of $1 from the 1700s to now. $1 in the 1700s is worth about $63 in current value. Explain to students that they will be using their place value disks or base ten blocks to represent the amount of money they earned for opening the treasure chests. Instruct the students to read each Treasure Card and to represent the money they earned on their Place Value Charts. Students will then record their work on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

Intervention

Acceleration

FACILITATION TIP Assign each pair or group one of the above questions. Explain that they are responsible for sharing and justifying the answer to their assigned question with the class.

PLACE VALUE RELATIONSHIPS

Home

FACILITATION TIP Point out that students will follow the same process they used in Part I to determine the clue values but that this time the values might include decimals.

a. DOK-2 What do you notice is different about your Place Value Chart in this part? I notice that now we have the decimals period. b. DOK-1 What do we know about decimals? Answers may vary. I know that decimals are part of a whole. c. DOK-1 How many dimes does it take to make a dollar? 10 d. DOK-1 What decimal name represents the dime? Tenths e. DOK-1 How many pennies does it take to make a dollar? 100 f. DOK-1 What decimal place represents the penny? Hundredths

FACILITATION TIP Where possible, provide actual coins for students to use when determining how many coins of a certain value make a dollar.

g. DOK-1 How many mills does it take to make a dollar? 1,000 h. DOK-1 What decimal place represents the mill? Thousandths i. DOK-2 How can you represent the value of a missing place value that is (10 times/100 times/1,000 times) the value of another place as an equation? I can multiply the value of the given number by (10/100/1,000) in order to ﬁnd the missing place value. For example, 0.004 × 10 = 0.04. j. DOK-1 What do you notice when you multiply a number by (10/100/1,000)? FACILITATION TIP Answers may vary. I notice that my original number becomes larger. The Take time to ensure that students new value is (1, 2, 3) places to the left of the original place value. recognize patterns associated with k. DOK-2 How can you represent the value of a missing place value that is multiplying and dividing with whole and (one-tenth/one-hundredth/one-thousandth) the value of another place as decimal numbers. an equation? I can divide the value of the given number by (10/100/1,000) to ﬁnd the missing place value. For example, 7 ÷ 10 = 0.7. l. DOK-1 What do you notice when you divide a number by (10/100/1,000)? Answers may vary. I notice that my original number becomes smaller. The value is (1, 2, 3) places to the right of the original place value.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 1 – Place Value Relationships m.

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.

14. 15.

16.

•

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.

If students are struggling with how to show their work, guide students in recording the expanded form of their number in order to ﬁnd the value. Ensure that each group has had an opportunity to represent each Treasure Card and answer their reﬂection questions. Check each student’s work, and correct any misunderstandings. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat

•

STEMscopes Tip

DOK-1 How can you represent the value of each clue using the place value disks? Answers may vary. When a clue states the given number for a certain value, I can place the given number of place value disks in the correct place on the Place Value Chart. When a clue states that a value is (10 times/100 times/1,000 times) a given value, then I know my place value will be larger and move (1, 2, 3) spaces left on my Place Value Chart, and I will place the given number of disks in that spot. When a clue states that a value is (one-tenth/one-hundredth/onethousandth) of a given value, then I know my place value will be smaller and move (1, 2, 3) spaces right on my Place Value Chart, and I will place the given number of disks in that spot.

•

DOK-3 Why can each digit in a number be represented with a multiplication expression? Each digit in a number has a certain value. If you have a 2 in the ten thousands place, you have two groups of 10,000. When you are trying to ﬁnd the total of equal groups, it can be shown using multiplication. DOK-2 How does the value of a number change as it moves to the left on the Place Value Chart? Each place you move a digit to the left increases its value times 10. DOK-2 How does the value of a number change as it moves to the right on the Place Value Chart? Each place you move a digit to the right decreases its value 1 by ___ . 10

DOK-2 How do you determine the change in value of a digit that is more than one place to the left or right? The value of a digit one place to the left or right is ten 1 1 times bigger or ___ smaller. Every space after that is another ten times or ___ . So if 10 10 you go 2 spaces to the right, that number is 1/100 smaller. If you go three places to the left, that number is 1,000 times bigger.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PLACE VALUE RELATIONSHIPS

Home

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 2 – Powers of Ten ACTIVITY PREPARATION Students explore patterns of numbers as they multiply and divide by multiple factors of ten. Students explain the patterns they notice as they multiply and divide by factors of ten.

Standards for Mathematical Practice • • •

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

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Business Cards (per group) 1 Set of Coin Cards (per class) 1 Exit Ticket (per student)

•

Reusable • • • • •

• •

1 Set of place value disks (per group) 1 Set of pennies, at the corresponding station (per class) 1 Set of dimes, at the corresponding station (per class) 1 Set of nickels, at the corresponding station (per class) 1 Set of quarters, at the corresponding station (per class)

•

Plan to divide the class into 4 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Business Cards for each group, and cut the cards apart. If possible, print them on card stock for durability. Print a set of Coin Cards on card stock, and laminate them for durability. Cut the cards apart, and place each card at a station around the room. Place a set of coins at the corresponding stations. For students who need more support in recalling information, please see our Decimal Place Value Mat 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 Part I 1. FACILITATION TIP

Allow students the opportunity to review how other groups organized their place value disks.

Give a Student Journal to each student and a set of Business Cards and place value disks to each group. Have students organize the place value disks based on place value and order from greatest place value to least place value. Ask students the following questions about what they notice with the place value disks, and have them turn and talk with their groups about their observations: a.

How many disks are needed before you get to the next place value? 10

DOK-1 What relationship do the place value disks represent between each place value? The relationship the place value disks represent is that the place to the left is ten times more than the place to the right, 1 and the place to the right is ___ the value of the place to the left. 10

FACILITATION TIP If the students are struggling to identify this relationship, demonstrate it by performing the mathematical calculation using an example number. 34

DOK-1 How do we determine which place value is greater than another place value? We can determine which place value is greater by looking at its location. The value of each place increases as you move to the left, so values on the left will be greater than values on the right. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Read the following scenario to the class: There are many businesses in the city where you live and around the world. A business must earn money to stay open, but it also must pay employees and help customers. Each business has different needs, and some have hired you and your group to help it ﬁgure out its earnings, how to pay employees, or how to help its customers. Explain to students that they will be reading each Business Card scenario with their groups and working together to represent each scenario as a model with their place value disks, as an expression, and then with a value. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How can you tell when we need to multiply to ﬁnd our answer? I know I need to multiply when I am combining equal groups to ﬁnd a total.

DOK-1 How can you tell when we need to divide to ﬁnd our answer? I know I need to divide when I’m given a total and it is being split or separated into parts.

DOK-2 What pattern do you notice happening over and over again? I notice that I continue to either multiply by 10 or divide by 10.

DOK-2 What do you notice about the whole numbers when you either multiply by 10 or divide by 10? I notice that my whole number is either gaining a zero or losing a zero.

Groups will record their work and observations on their Student Journals as they complete each Business Card.

Intervention

Acceleration

FACILITATION TIP To ensure that the groups understand how to model each scenario, ask them to create their model for the ﬁrst scenario and then wait for you to check their work before they move forward with the activity.

PLACE VALUE RELATIONSHIPS

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Part II 1.

Explain to students that they will continue to work with multiplying and dividing by 10 in Part II of the Explore activity; however, now they will be working with decimal numbers. Brieﬂy review with students the following questions: a.

DOK-2 What pattern did you notice when you would multiply a whole number by 10 or multiple 10s? I noticed that my product would gain a zero or some zeros on the end.

DOK-2 What pattern did you notice when you you would divide a whole number by 10 or multiple 10s? I noticed that my quotient would lose a zero or multiple zeros.

DOK-2 Do you think when I multiply or divide a decimal by a 10 or multiple 10s that it will have the same outcome? Answers may vary. Some may say yes, and some may say no. Wait until after the Explore activity to see what the students discover about this question.

Read the following scenario to the class: Banks deal with all kinds of different coins, and they must place them in rolls so they are easier to organize. Banks must also undo these rolls and distribute these coins to bank customers. The bank needs your help organizing and distributing these coins. Explain to students that there are Coin Cards with the appropriate coins at each station around the room. Their group’s job is to read each Coin Card and model that scenario using their coins. They will then write an expression and a value for each part of their scenario on their Student Journals. Place a group at each station, and encourage them to work together to solve.

FACILITATION TIP If the students struggle to see this pattern, model this concept on the board without explaining what you are modeling. Start with an example number, and continue to multiply or divide by 10 until they begin to notice the pattern. You may need to prompt them to notice whether any new digits are being added to or removed from the product or quotient.

FACILITATION TIP Review how to write proper mathematical expressions with the students prior to beginning the activity.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 2 – Powers of Ten 6.

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

FACILITATION TIP

Following the activity, present these questions to the students. Give them an opportunity to discuss the questions within their groups or between groups before discussing them as a whole class.

DOK-1 How can you tell when we need to multiply to ﬁnd our answer? I know I need to multiply when I am combining equal groups to ﬁnd a total.

DOK-1 How can you tell when we need to divide to ﬁnd our answer? I know when I need to divide because I’m given a total, and it is being split or separated into parts.

DOK-1 How can I use the coins to help me represent the scenario? I can use the coins to act out what is happening in the scenario and to understand the value of each step in the scenario.

DOK-2 What pattern do you notice when we are multiplying a decimal by 10? Can I simply add a zero to the end of my product? No, when I multiply a decimal by 10, my decimal shifts to the right because my value is becoming 10 times larger.

e. DOK-2 What pattern do you notice when we are dividing a decimal by 10? Can I simply take a zero away from the end of my quotient? No, when I divide by 10, my decimal shifts to the left because my value is one-tenth smaller than its original value. FACILITATION TIP

Each student group should have an opportunity to discuss their outcomes and responses with another group. Encourage them to update their responses if necessary.

Allow enough time for each group to solve their scenarios and record their work. Rotate the groups from station to station until each group has had an opportunity to solve each scenario and answer their reﬂection questions. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • 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.

•

FACILITATION TIP On this Exit Ticket, provide struggling readers with support. Some students may have limited experience with the quantity and style of text on this Exit Ticket.

DOK-1 What happened to your whole numbers or decimals every time you multiplied by 10? Every time I multiplied a number by ten, the place value became 10 times greater than its original value. DOK-2 Did multiplying a decimal number by 10 have the same outcome as multiplying a whole number by 10? Yes, but I had to show it in different ways. Each time I multiplied a number by 10, all the digits in the number shifted one place to the left. Sometimes I had to ﬁll in the ones place with a zero, and sometimes I just had to move the decimal to show my new value. DOK-1 What happens if I just add a zero to the end of my decimal number? If I just add a zero to the end of a decimal, it doesn’t change the value. My value remains the same. DOK-3 Is it possible to multiply a number by 10 and get a number less than 1? If so, give an example. Yes. I can multiply any number in the hundredths or thousandths place by ten and get a number less than one: 0.06 × 10 = 0.6. DOK-1 What happens to your whole numbers or decimals every time you divide by 10? Every time I divide a number by ten, the place value is one-tenth its original value. DOK-2 Did dividing a decimal number by 10 have the same outcome as dividing a whole number by 10? Yes, but I had to show it in different ways. Each time I divided a number by 10, all the digits in the number shifted one place to the right. Sometimes I had to remove the zero from the ones place, and sometimes I just had to move the decimal to show my new value.

Post-Explore 1. 2. 3.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PLACE VALUE RELATIONSHIPS

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PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 3 – Exponents ACTIVITY PREPARATION Students relate the notation of exponents to the powers of ten. Students extend this knowledge of exponents to multiply and divide a number by powers of ten in multiple ways.The numbers used in this lesson are for example use only and should not be portrayed as actual data collected.

Standards for Mathematical Practice • • •

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

Materials

Preparation

Printed • • • • •

• •

1 Student Journal (per student) 1 Bacteria Growth Sort (per group) 1 Bacteria Reduction Sort (per group) 1 Set of Bacteria Scenario Cards (per class) 1 Exit Ticket (per student)

Part I: Bacteria Growth and Bacteria Reduction • • •

Reusable • • • •

Plan to divide the class into six groups to complete this activity. Print a Student Journal and an Exit Ticket for each student.

1 Set of place value disks (per group) 2 Clear resealable bags (per group) 2 Dry-erase markers (per station) 1 Sheet protector (per station)

Print the Bacteria Growth Sort and Bacteria Reduction Sort pages on card stock for durability for each group. If possible, print these pages on different-colored card stock: green for growth and red for reduction. Cut out the individual cards for the Bacteria Growth Sort and Bacteria Reduction Sort pages, and place each set in a separate resealable bag for each group.

Part II: Bacteria Scenario Cards • • • • •

•

Print a set of Bacteria Scenario Cards per class. Place each Bacteria Scenario Card in a sheet protector so it can easily be written on and erased. Place each Bacteria Scenario Card at a station around the room. Provide 2 dry-erase markers at each station. For students who need more support in recalling information, please see our Decimal Place Value Mat 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. (Place Value Disks)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP You can print each card sort on different colored paper. If the bacteria colony is growing, the number of cells are increasing and multiplication is used. Division is used when the bacteria colony is dying. 38

Part I: Bacteria Growth and Bacteria Reduction 1. 2.

Give a Student Journal to each student and a Bacteria Growth Sort, a Bacteria Reduction Sort, and place value disks to each group. Explain to students that today they will be discovering exponents and their relationship to powers of ten that they learned about in Explore 2. © Accelerate Learning Inc. - All Rights Reserved

10.

Explain

Elaborate

Evaluate

DOK-1 What do you think it means? We are multiplying 10 by itself three times.

Explain that just like multiplication represents repeated addition, exponents are a way to represent repeated multiplication. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

Acceleration

FACILITATION TIP You should model for students how to complete chart with the values of 10 and 100. Demonstrate how the information is from the pictorial model from the bacterial growth sort. FACILITATION TIP Be sure students are writing the exponent in the correct location that is above the number 10.

DOK-1 How can we use the place value disks to model the bacteria growth? I can use the disks to show the original value and how many times bigger it gets each time.

DOK-2 How can we use the power of ten expression to help ﬁnd the other matching expression? The power of ten expression can be multiplied to ﬁnd the other expression. For example, 10 × 10 = 100, so I know that 1 × 100 is equal to 10 × 10.

FACILITATION TIP DOK-2 How can we use the power of ten expression to ﬁnd the matching exponent? I noticed that I can match the multiples of ten that are given Discuss with students how 10 × 3 = 30 is with the value of the exponent. different than 10 × 10 × 10 = 100. Model For example, if I am multiplying 10 × 10 × 10, then my exponent will be a with manipulatives to demonstrate the 3 because I multiplied by 3 tens. difference. DOK-2 How can I use the exponent to ﬁnd the correct word form? The exponent tells me by what power my ten is being represented. For example, if the exponent is 2, then the ten is being represented to its second power.

Allow students enough time to complete both sorts and to record work on their Student Journals. Review their matches, and discuss their ﬁndings on what they think an exponent represents.

Part II: Bacteria Scenario Cards 1.

Intervention

Explore

Read the following scenario to the class: Scientists have discovered a growing bacteria in your digestive tract that can help break down food and keep you healthy. They are examining the growth of this bacteria to see how they can use it to help others who lack this bacteria in their digestive tracts. They are also examining food bacteria and how it is being broken down. They need junior scientists like you to model and record this growth and breakdown in multiple numerical forms. Explain to students that they will be working with their groups to complete the models and their sorts. They will ﬁrst need to build a model for the original bacteria and then continue to represent its growth using the place value disks. Explain that after they create their models, they will match the word form, power of ten expression, another expression, and the exponent that goes with that model. They will record their work on their Student Journals. Exponents help you write large numbers in a much more compact way. To show 10 × 10 × 10, we would just write 103. a.

Engage

Review that exponents represent repeated multiplication and multiples of ten. Students will be using what they learned from Part I to help them with their stations in Part II. Read the following scenario to the class: Scientists are collecting bacteria samples from common household objects. These bacteria samples have a starting value of the number of living cells in the sample. Scientists are then testing the growth and reduction of these bacteria samples to see how the bacteria changes over time. They need your help documenting these bacteria changes.

PLACE VALUE RELATIONSHIPS

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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.

PLACE VALUE RELATIONSHIPS

Place Value Relationships Explore 3 – Exponents 3.

FACILITATION TIP

To help students with the math literacy, they can circle the variables from each scenario and what is happening to the bacteria colony (reducing or growing) after they read the card.

5. 6.

Explain to students that they will be working with their groups at each station around the room to represent each scenario as a power of ten expression, another expression, and as an exponent. They will then create a growth or reduction model and find their answer. Encourage students to pay close attention to how their original bacteria sample changes depending on if they are multiplying or dividing to find the growth or reduction. Allow students enough time to complete their work at each station, record their observations, 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 • 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.

• •

•

DOK-2 What relationship do you notice between an exponent and the multiples of 10 in a powers of ten expression? I notice that the exponents represent the number of tens that are being multiplied. DOK-2 How can an exponent represent multiples of ten? The exponent represents how many multiples of ten will be used to solve. DOK-2 What relationship do you notice between the exponent and how many places the decimal moved during division? I notice that the decimal moves to the left as many places as the exponent represents because the place value is changing. DOK-2 What does the exponent represent when it is being used to multiply by a power of ten? The exponent represents how many times larger the number is becoming and how many places my decimal will move to the right. DOK-2 What does the exponent represent when it is being used to divide by a power of ten? The exponent represents how many times smaller the number is becoming and how many places my decimal will move to the left.

Post-Explore FACILITATION TIP

When previewing this Exit Ticket with students, take time to support careful reading. This Exit ticket includes slightly more text than students may have experienced on past grade-level Exit Tickets.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PLACE VALUE RELATIONSHIPS

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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

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

Anchor Chart

Show What You Know, Part 2

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

Powers of Ten 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

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Vacation at the Beach

Thomas M. Whitney

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

Number One!

Powers of Ten

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

PLACE VALUE RELATIONSHIPS

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Problem-Based Task Video Game Victory 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 make sense of place value within multi-digit numbers, including decimal numbers to the thousandths place.

What prompts will be used?

What does mastery look like?

PLACE VALUE RELATIONSHIPS

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I can reason that a digit in one place represents 10 times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

I can reason about where to place the decimal point when a decimal is multiplied or divided by a power of 10.

I can reason about the relationship between an exponent and the number of places the decimal point moves when multiplying and dividing by powers of 10.

SCOPE 1

Read and Write Decimals Scope Introduction SCOPE SUMMARY Students apply place value knowledge and reasoning to read and write decimals to the thousandths. This is done with base-ten numerals, number names, expanded form, and expanded notation. Concrete models and place value charts help to support student understanding.

Student Expectations

5.NR.4.1 Read and write decimal numbers to the thousandths place using baseten numerals written in standard form and expanded form.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Fourth grade extends the fractional concept of fraction equivalence, and it introduces operations with fractions and mixed numbers. As decimals are introduced, students learn decimal notation for fractions with denominators of 10 or 100. Students work with decimals and fractions interchangeably, such as locating them on a number line. Fifth grade builds on this, and students are expected to read and write decimals to the thousandths place by using different methods.

In sixth grade, students begin to work with negative numbers. Sixth graders learn to identify and compare integers, positive and negative numbers including zero, to explain the meaning of zero based on multiple authentic situations.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

•

evaluate a given expanded notation as correct, partially correct or incorrect.

• •

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

demonstrate an understanding of place value.

use their knowledge of place value and expanded form.

•

read and write decimals to the thousandths place.

support reasonings with a class discussion.

•

order digits into correct place values.

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

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

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Read and Write Decimals In this exploration, students will work in groups, participate in discussing and manipulate objects to learn about reading and writing decimals. Students will:

Explore 2

Explore 1

EXPLORE ACTIVITIES Decimals in Expanded Form In the last exploration, students will solve a scenario where they analyze players’ batting averages. Students will:

•

practice reading and writing decimals.

•

represent and model decimals using base ten blocks and word form.

deepen their understanding of hundredths and thousandths.

•

convert decimals into standard form.

provide a visual from which to derive the expanded notation of decimal numbers to the thousandths place.

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

READ AND WRITE DECIMALS

Home

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

READ AND WRITE DECIMALS

Read and Write Decimals Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students decide whether a given expanded form is correct, partially correct, or incorrect. This activity is intended to assess mastery of the following standard(s): 4.NR.1.1 Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form.

Materials

Preparation

Printed • •

1 Slideshow (per class) 1 Set of Opinion Signs (per class)

• •

READ AND WRITE DECIMALS

Home

Prepare to project the Slideshow for the class. Print one set of the Opinion Signs, and hang each sign in a different location around the classroom.

Reusable •

1 Projector or document camera (per class)

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

Project the Slideshow for the class. Instruct students to read the information independently. Have students decide whether they agree, partially agree, or disagree with Ramie’s answer. Have students choose one of the three choices and stand under their choice. Tell students that they should be ready to justify their choices. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

I agree with Ramie. He has written the expanded form with the correct number and disk value. When you combine the numbers, you get 411.6.

I partially agree with Ramie. He wrote the expanded form correctly, but when he wrote the number using base-ten numerals, he needed to regroup the ones. Since 10 ones equals 1 ten, he should have 5 tens and 1 one. His number should be 51.6.

I disagree with Ramie. He should have regrouped before he wrote the expanded form. The expanded form should have been written as 50 + 1 + 0.6 = 51.

FACILITATION TIP Provide place value chips for the students who need a visual or tactile representation. FACILITATION TIP Allow time for the students to share their justifications with the group of others who made the same choice. Instruct them to choose or create a justification that represents the thought of the group. Then, have each group share their justifications with the class. After the justifications are given, allow the students to change which group they stand with. Those who decide to move to a different group should explain why they changed their minds.

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

READ AND WRITE DECIMALS

Read and Write Decimals Hook – The Decimal Is Right (Contest) ACTIVITY PREPARATION Students participate in a schoolwide contest to demonstrate an understanding of place value and how to read and write decimals to the thousandths place. They will work in small groups to order digits into the correct place value and will then write and read their decimal answers in an attempt to have the whole class win a signing bonus based on its decimal prowess.

Materials

Preparation

Printed • •

• • • •

1 Student Handout (per group) 1 Place Value Cards (per group)

Reusable • • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Resealable bag (per group) •

Consumable •

1 Piece of black construction paper (per class)

Plan to show the Phenomena Video. Plan to divide the class into groups of 3 to complete this activity. Print a Student Handout for each group. Print the Place Value Cards on three different colors of paper. Each set of pages is enough for 12 students (4 small groups of 3 students each). Print them on card stock, and laminate them if you want to reuse the same set for multiple classes. Cut out one row from each colored page. Then, cut each row apart into 6 cards. Put all cards (6 of each of 3 colors, 18 total) into a resealable bag. Cut out one small black circle per group from the black construction paper (as a decimal point), and put one in each resealable bag.

Part II •

Plan to have students work in groups of three to complete this activity.

PROCEDURE AND FACILITATION POINTS

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

FACILITATION TIP Provide each group with these questions, and allow them to discuss the answers within their group before discussing them as a whole class.

Part I: Pre-Explore 1.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Your school is holding a contest to see which class should be the treasurers of the student fundraising committee. In order to see which class is the best qualiﬁed to work with money, you are being screened to evaluate your understanding of decimals to the thousandths place. In order to secure your place as treasurers, each small group must be able to read, write, and understand decimals. You will unscramble and correctly place digits, write decimal numbers, and read them correctly. Each decimal you identify correctly will earn you a letter. If all the small groups earn the letters W-I-N, your class will be treasurers, which involves a fun signing bonus. Can each group work together to unscramble, read, and write the correct decimals? Show students the Student Handout and a resealable bag with a decimal point and the different colored squares with place values on them. Discuss the following questions: a.

DOK-2 Why do you think the values in the bags are different colors? The different colors represent digits that go together to form a complete decimal number.

DOK-1 What is the order of place values from greatest to least for the numbers we are forming? Hundreds, tens, ones, tenths, hundredths, thousandths

FACILITATION TIP Write 762.149 on the board. Ask volunteers to come forward and label the place values for the number. Students should also write this information on sheets of paper that they can use while completing the activities. 50

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What form of reading and writing decimals would allow you to understand the value of each digit and where it belongs? Expanded form or expanded notation because the number in the place value is multiplied by the value of its place DOK-1 Write on the board (or butcher paper or an overhead): 762.149 How do we read this decimal number out loud? Seven hundred sixty-two and one hundred forty-nine thousandths i. DOK-1 When we read that number out loud, how can you tell where the decimal point is? The decimal point is represented by the word and.

Move on to complete the Explore activities.

Intervention

Acceleration

FACILITATION TIP Refer again to the number 762.149 written on the board. Ask volunteers to rewrite the number in expanded form and word form. The students should add this information to their note pages. FACILITATION TIP Address the common practice of saying “and” between “seven hundred” and “sixtytwo” when reading 762.

READ AND WRITE DECIMALS

Home

Part II: Post-Explore 1. 2.

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

DOK-2 Why do you think the values in the bags are different colors? The different colors represent digits that go together to form a complete decimal number.

DOK-1 What is the order of place values from greatest to least for the numbers we are forming? Hundreds, tens, ones, tenths, hundredths, thousandths

DOK-1 Write on the board (or butcher paper or an overhead): 762.149 How do we read this decimal number out loud? Seven hundred sixty-two and one hundred forty-nine thousandths ii. DOK-1 When we read that number out loud, how can you tell where the decimal point is? The decimal point is represented by the word and.

3. 4. 5.

Divide the class into small groups of 3. Give each group the Student Handout, a resealable bag with 3 different colors of place value cards, and a decimal point. Review the problem, and allow students to solve it. Tell students they should utilize their knowledge of decimals to order the digits into decimal numbers. They should accomplish this by separating the digits into three piles of different colors. Starting with one color, each student should take 2 squares. Observing the expanded form, students should work together to arrange all 6 digits in the correct order. 237.859, 463.271, 974.563 Next, a student should write the decimal number on the Student Handout in one of the rectangles (W, I, or N). (Teachers can specify a certain color with a certain letter.) Students should take turns writing the 3 different decimal numbers so each student gets a chance. After each number is written, all students should practice reading the decimal number correctly out loud.

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.

READ AND WRITE DECIMALS

Read and Write Decimals Hook – The Decimal Is Right (Contest) 7.

FACILITATION TIP After each group has ordered their numbers, allow them to observe how other groups ordered their digits. Encourage them to discuss any differences they observe through the use of guiding questions.

Give students about 5–10 minutes to work with their groups to put the digits in the right order, to ﬁnd all three decimal numbers, to write them on their Student Handout, and to practice reading the decimal numbers aloud. Walk around during this time and observe groups. Offer assistance and ask guiding questions to help groups that might be struggling. Have 3 different groups each present the decimal number answer for one of the colors. Use a show of hands to determine if other groups also got the same answers. (Teachers can use their discretion to offer a signing bonus of their choice if all groups correctly write the decimal numbers.) Gather students in a whole group, and discuss the following questions: a.

DOK-2 How did you ﬁgure out where each digit belonged in the decimal numbers? We used the expanded form on the cards to see the place value of each number and order the cards. Once the cards were ordered, we could see the whole decimal number, write it, and read it aloud.

DOK-2 What was the most difficult aspect of the project for you? Answers will vary because it may be more difficult for some students to figure out the numbers; others may struggle with writing decimals; still others may become confused reading decimals. Accept all answers.

DOK-1 When you move to the left one place, what happens to the value of the digit? The value of the digit increases by 10 times.

FACILITATION TIP

Provide visual mathematical examples for students that are struggling to identify this pattern.

DOK-1 When you move to the right one place, what happens to the value of the digit? The value of the digit decreases by 10 times.

e. DOK-2 If you were to move past the thousandths place one more place value to the right, what place would that be? The ten thousandths place f.

DOK-2 Why might you need to know how to read and write decimals to the thousandths place even if you are working with money, which only goes to the hundredths place? Sometimes values might need to be rounded to the nearest cent (hundredths place) from the thousandths place.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

READ AND WRITE DECIMALS

Home

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READ AND WRITE DECIMALS

Read and Write Decimals Explore 1 – Read and Write Decimals ACTIVITY PREPARATION Students practice reading decimals and representing them as a model using base ten blocks and with a number name. Students also practice reading a decimal number name and converting it into a decimal.

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 Meal Cards (per class) 1 Place Value Mat (per station) 1 Exit Ticket (per student)

•

Reusable •

• • • • • • •

•

1 Set of base ten blocks (per station) 1 Thousand cube 10 Base-ten ﬂats 10 Base-ten rods 10 Base-ten units

•

1 Plastic container (per station) 1 Sheet protector (per station) 2 Dry-erase markers (per station)

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and Exit Ticket for each student. Print a set of Meal Cards; cut them out; and laminate them, if desired; and tape them around the room to designate the 5 stations. Print a Place Value Mat for each station, and place each in a clear sheet protector for reuse. Put a Place Value Mat along with 2 dry-erase markers at each station. Place a thousand cube, 10 base-ten ﬂats, 10 base-ten rods, and 10 base-ten units in a plastic container. Prepare enough plastic containers for 5 stations. 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 Review with the students the procedures and expectations when rotating through stations. Describe the materials that they will work with at each station. 54

Read the following scenario to the class: Today, you are working for Wally World grocery store and helping it prepare meal kits for customers. Each meal kit needs to be a speciﬁc weight and have a label placed on the container so customers know the food inside and its weight. Help the grocery store place the correct weight inside each container using base ten blocks, and write the correct weight on the label using the numeral form and number name. Explain to students that around the room are 5 stations of meal kits that need to be prepared to the proper weight. Some of the weights are written as a numeral, and some are written with a number name. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Explain that when writing a number name, we will write the word and to represent the decimal, just like when we say and to represent a decimal in money. We must also include the name of the place value spot of the last digit in our numeral. a.

DOK-1 What would be the number name if my decimal went one place after the decimal? Tenths

DOK-1 What would be the number name if my decimal went two places after the decimal? Hundredths

DOK-1 What would be the number name if my decimal went three places after the decimal? Thousandths

Explain that the students’ job is to represent each weight using the least number of base ten blocks on their Place Value Mats. The Place Value Mat is provided for students to practice drawing, with the dry-erase markers, the models of the base ten blocks with their groups before drawing them on their Student Journals. It also provides a place to work as a group to decide on the correct numerals and number names. Once the group agrees on the model, numeral, and number name, they will record their work on their Student Journals.

Intervention

Acceleration

FACILITATION TIP Write a couple of examples on the board, and allow the students an opportunity to practice reading aloud and writing the decimal.

READ AND WRITE DECIMALS

Home

FACILITATION TIP Complete a practice example for the students using the blocks and the Place Value Mat. Explain what the instruction “using the least number of base ten blocks” is asking them to do in this activity.

FACILITATION TIP Note: Students may want to accurately draw each base ten block. Encourage them to represent the base ten blocks by drawing boxes for The students should create a legend to ones, squares for tenths, lines or sticks for hundredths, and dots for explain which shapes represent which base thousandths. This will allow students to draw their models more quickly. ten blocks. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What does the cube represent? 1

DOK-1 What does the ﬂat represent? One-tenth

DOK-1 What does the rod represent? One-hundredth

DOK-1 What does the unit represent? One-thousandth

e. DOK-1 What word do we use to represent the decimal in a number name? We use the word and to represent the decimal. f.

DOK-2 How do we know whether to put tenths, hundredths, or thousandths at the end of the number name? It depends on how many digits are after the decimal.

DOK-2 How can we use the numeral to help us represent a model? Answers may vary. The numbers before the word and tell me how many wholes I will need. The numbers after the word and tell me how many total units I will need. The tenths will be represented with the ﬂats, the hundredths will be represented with the rods, and the thousandths will be represented with the units.

h. DOK-2 How can we use the number name to help us represent a model? Answers may vary. The words before the word and tell me how many wholes I will need. The words after the word and tell me how many total units I will need. The tenths will be represented with the ﬂats, the hundredths will be represented with the rods, and the thousandths will be represented with the units. 7.

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

Math Chat •

DOK-2 How can I use the numeral to represent my model? The numbers before the word and tell me how many wholes I will need. The numbers after the word and tell me how many total units I will need. The tenths will be represented with the ﬂats, the hundredths will be represented with the rods, and the thousandths will be represented with the units.

FACILITATION TIP The students could indicate which place value each represents by writing its name below the correct place value title on their Student Journals. FACILITATION TIP For students who are still struggling, consider using money as a relatable example. 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.

READ AND WRITE DECIMALS

Read and Write Decimals Explore 1 – Read and Write Decimals DOK-2 How can I use my numeral to help me turn my decimal into a number name? I can name the number before the decimal and then write the word and to represent the decimal point. I can then write the number names for the digits after the decimal and include the place value name for the last digit to the right of the decimal point. • DOK-2 How can I use my number name to help me turn it into a numeral? The number name before the word and tells me the whole number to write. I will make a decimal to represent the word and. Finally, I will represent the digits and their correct place value for the number names that come after the word and. The words tenths, hundredths, or thousandths will tell me where my last digit should be placed. •

Post-Explore FACILITATION TIP This Exit Ticket could also be used as a simple pre-assessment before the scope.

1. 2. 3.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

READ AND WRITE DECIMALS

Home

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READ AND WRITE DECIMALS

Read and Write Decimals Explore 2 – Decimals in Expanded Form ACTIVITY PREPARATION Students use base ten blocks to deepen their understanding of the meaning of hundredths and thousandths. The concrete manipulatives will provide a visual from which to derive the expanded notation of decimal numbers to the thousandths place.

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) 2 Place Value Mats (per group) 1 Set of Baseball Cards (per group) 1 Set of Additional Place Value Disks (per group, optional) 1 Exit Ticket (per student)

• • •

Reusable •

• • • •



1 Set of base ten blocks (per group) • • • •

Plan to have students work in groups of 3 or 4 to complete this activity. Print two Place Value Mats for each group, and place them in separate clear sheet protectors for reuse. Print a set of Baseball Cards for each group, cut them apart, and place each set in a quart-size resealable bag. Gather enough base ten blocks for each group to have at least one thousand cube, ten ﬂats, ten rods, and ten units.

1 Thousand cube 10 Base-ten ﬂats 10 Base-ten rods 10 Base-ten units

•

1 Set of place value disks (per group, optional) 2 Clear sheet protectors (per group) 2 Dry-erase markers (per group) 1 Quart-size resealable bag (per group)

•

Optionally, if place value disks are not available, print a set of Additional Place Value Disks for each group. Cut them out in advance, if desired. Consider printing each place value on different-colored card stock so students can easily differentiate between them.

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

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Provide some practice time for students to say the values of decimals aloud. Be sure they are pronouncing tenths, hundredths, and thousandths precisely.

Part I 1. 2.

Distribute a set of base ten blocks, Place Value Mats, and dry-erase markers to each group. Instruct students to place 6 ﬂats in the tenths column on their Place Value Mats. Have students discuss the following questions:

FACILITATION TIP

DOK-1 What is the value of each ﬂat? The value of each ﬂat is 0.1.

Take time to pause and have students chorally respond by holding up a ﬂat when you say, “Show me 0.1.” Also ask, “Say the value of this ﬂat aloud.”

DOK-2 How does having 6 ﬂats change the value in the tenths place? The value changes from 0.1 to 0.6.

DOK-2 How do I express this ﬂat being repeatedly used 6 times? I would express this situation as (6 × 0.1) since each ﬂat has a value of 0.1 and I have 6 of them. © Accelerate Learning Inc. - All Rights Reserved

3. 4.

5. 6.

Explore

Explain

Elaborate

Evaluate

3. 4.

Acceleration

DOK-1 What is the value of each rod? The value of each rod is 0.01.

FACILITATION TIP

DOK-2 How does having 4 rods change the value in the hundredths place? The value changes from 0.01 to 0.04.

DOK-2 How do I express this rod being repeatedly used 4 times? I would express this situation as (4 × 0.01) since each rod has a value of 0.01 and I have 4 of them.

Take time to pause and have students chorally respond by holding up a rod when you say, “Show me 0.01.” Also ask, “Say the value of this rod aloud.”

After this brief discussion, have students write their values and expressions in the hundredths place to match the given rods. Finally, instruct students to place 5 units in the thousandths place on their Place Value Mats, and discuss the following questions: a.

DOK-1 What is the value of each unit? The value of each unit is 0.001.

DOK-2 How does having 5 units change the value in the thousandths place? The value changes from 0.001 to 0.005.

FACILITATION TIP

Take time to pause and have students chorally respond by holding up a unit when DOK-2 How do I express this unit being repeatedly used 5 times? I would you say, “Show me 0.001.” Also ask, “Say express this situation as (5 × 0.001) since each unit has a value of 0.001 the value of this unit aloud.” and I have 5 of them.

After this brief discussion, have the students write their values and expressions in the thousandths place to match the given units. Explain to students that this way of expressing numbers is known as expanded form or expanded notation. Expanded form or notation is a way of writing numbers to show the value of each digit. It is shown as a sum of each digit multiplied by its value. For example, the expanded form for the expressions we just wrote would be (6 × 0.1) + (4 × 0.01) + (5 × 0.001). Write the expanded form for the decimal number given on the board or an anchor chart to display as a reminder for students for Part II of the Explore activity.

Part II 1. 2.

Intervention

After this brief discussion, have students write their values and expressions in the tenths place to match the given ﬂats. Now, instruct students to place 4 rods in the hundredths place on their Place Value Mats and discuss the following questions:

Engage

READ AND WRITE DECIMALS

Home

Give a Student Journal to each student. Explain to students that they are going to use their understanding of expanded form to help them with the following scenario. Give a set of Baseball Cards and a set of place value disks to each group. Read the following scenario to the class: A brand-new coed baseball team is ﬁnishing its ﬁrst season. The Sunny City Cyclones are made up of men and women of all ages. Your task is to analyze some of the players’ batting averages. Explain to students that they will be using decimal numbers with varying digits in each place and that they will work with their groups to represent this decimal in various forms, including expanded form. Explain that students will be looking at each player’s Baseball Card. They will focus on the player’s batting average. They will write this decimal in numerals on their Student Journals. Then, they will use base ten blocks and place value disks to model each decimal.

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.

FACILITATION TIP Consider re-creating the Student Journal pages from Part II as large posters and posting them with their corresponding Baseball Cards around the room. Assign each group to a poster as a starting point. Have each group write the standard form of the batting average on their assigned poster. Then, have each group rotate to the next poster, check the previous group’s work, and complete the next step. Continue this until all posters are completed.

READ AND WRITE DECIMALS

Read and Write Decimals Explore 2 – Decimals in Expanded Form 7.

The Place Value Mats are provided for students to practice drawing their models of the base ten blocks and place value disks with their partners before drawing them on their Student Journals. a.

FACILITATION TIP Once all the posters are completed, have each group return to their original poster and present the information. Have the rest of the class copy the information on their Student Journals.

10.

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.

11.

Note: Encourage students who may want to accurately draw each base ten block that their drawings don’t have to be perfect. Encourage them to represent the base ten blocks by drawing boxes for ones, dots for thousandths, lines or sticks for hundredths, and squares for tenths. This will allow students to draw their models more quickly.

Two Place Value Mats and dry-erase markers are given to each group in case some students are more comfortable using one manipulative over the other. Students within the group can work on different Place Value Mats and explain their work to each other. Once students have completed their work on their Place Value Mats and discussed their ﬁndings, they will then write an expression to show the value of each digit in the decimal and use these values to write the number in expanded form. Ensure each group has had an opportunity to represent each Baseball Card and answer the reﬂection questions. Check each student’s work, and correct any misunderstandings. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-2 How can a model or picture help us write a number in expanded form? The model or picture can help us see how many there are of each place value. We can use those pictures to develop expressions that can be combined to write the expanded notation. DOK-2 What do you notice in your expanded form about the difference in the value of each place as you go from left to right? The place on the left is ten times the place on the right. DOK-2 What do you notice in your expanded form about the difference in the value of each place as you go from right to left? The place on the right is onetenth the place on the left. DOK-2 How does knowing that one place is 10 times larger or smaller than another help us with expanded notation? The pattern helps us determine the place name, which helps us determine the value of a digit. DOK-1 How do we know that both fraction and decimal notation show the same value? We are simply writing equivalent values in different forms.

Post-Explore FACILITATION TIP This Exit Ticket provides a great opportunity to help with sifting through extraneous information on math assessments. Errors can occur when students don’t successfully locate the necessary values or numerals. Take time to support careful reading and allow questions before students complete the Exit Ticket.

1. 2. 3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

READ AND WRITE DECIMALS

Home

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READ AND WRITE DECIMALS

Read and Write Decimals Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

Read and Write Decimals 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

Decimals in Expanded Form 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

The Perfect Book

America and Penelope Lopez

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 Biggest Is Not Always in Texas

Decimal Models to the Thousandths Place

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

Creepy Crawly Things

Represent Decimals to the Thousandths Place – Models and Expanded Form

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

READ AND WRITE DECIMALS

Home

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

Students who are still acquiring the concept and need remediation

READ AND WRITE DECIMALS

Read and Write Decimals

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

 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?

READ AND WRITE DECIMALS

Home

I can read and write decimals using base-ten numerals.

I can read and write decimals using standard form.

I can read and write decimals using expanded form.

SCOPE 1

Compare and Order Decimals Scope Introduction SCOPE SUMMARY Students build on their prior knowledge and understanding of place value, comparing and ordering numbers’ decimals to the hundredths place, to now compare and order decimals to the thousandths place. They use comparative language (greater than, less than, or equal to) and symbols (>, <, or =) to make comparisons while using place value charts, place value disks, and scaled number lines to help them model the values of decimals. Student Expectations

5.NR.4.2 Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

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

In sixth grade, students extend previous understanding of numbers to deﬁne, plot, order, and compare rational numbers. Students are able to add, subtract, multiply,

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

compare decimal numbers from a real-world situation and use visual models to justify their comparisons.

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

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

compare and order decimals to the thousandths and represent comparisons 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.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Compare Decimals In this exploration, students will use place value and a scaled number line to plot and compare decimals. Students represent comparisons with decimals to the thousandths, using the symbols >, <, and =. Students will: •

show the value of each horse’s race with their place value disks on their Place Value Charts.

•

compare the times it took champion horses from different years to run the track at the Kentucky Derby.

Explore 2

Explore 1

EXPLORE ACTIVITIES Order Decimals In this exploration, students will use a place value chart and a scaled number line to plot and order a series of decimals. Students will: •

order decimals to the thousandths from least to greatest and from greatest to least, using the symbols >, <, and =.

COMPARE AND ORDER DECIMALS

Home

After completion of the activity, students will 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.

COMPARE AND ORDER DECIMALS

Compare and Order Decimals 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 compare decimal numbers from a real-world situation and use visual models to justify their comparisons. This activity is intended to assess mastery of the following standard(s): 4.NR.5.3 Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

Materials

Preparation

Printed •

1 Student Handout (per student)

Reusable •

• •

Print the Student Handout for each student. If you choose to use colored pencils for shading, gather enough colored pencils for each student to have one.

1 Colored pencil (optional, per student)

Procedure and Facilitation Points 1. 2.

COMPARE AND ORDER DECIMALS

Home

STEMscopes Tip

Give a Student Handout and a colored pencil to each student. Read the following scenario to the class: Emmanuel and Samantha each ﬁnd gold at the bottom of a riverbed. Emmanuel claims he has found more gold because he has found 0.36 of a gram, but Samantha disagrees. She believes she has found more gold because she has found 0.4 of a gram. Allow time for students to use the hundredths model to compare the two amounts of gold that were found. Students may use the colored pencil to shade each amount and plot them on the number line. Ask students to explain how 0.4 is shown on a hundredths model. a.

1 tenth is the same as a rod in base ten blocks, so we can shade 4 rods or columns.

10 hundredths equals 1 tenth, so to show 4 tenths, we need to shade 40 hundredths.

After shading the amounts in the models and plotting them on the number line, students complete the comparison by using the >, <, or = symbols and labeling the models. Facilitate a class discussion about the students’ work and how the symbols would be different if the models were in a different order, like if Samantha’s model was on the left and Emmanual’s model was on the right. 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 this gap in prior knowledge before moving on to other parts of the scope.

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.

FACILITATION TIP Write the numbers 0.4 and 0.40 on the board, and ask students if they are equal in value. Ask students if adding any number of zeros to the end of a decimal number will change its value, and discuss their reasoning. FACILITATION TIP At this point, prompt students to represent the comparison on the provided open number line template. If students are not sure how to begin, ask them what range of values should be included (0.30 to 0.40). Ask what the value of each increment represents (0.01). Have them locate 0.36 and 0.40 and describe the relationship between these values. Point out that 0.40 is farther to the right and therefore greater in value.

COMPARE AND ORDER DECIMALS

Compare and Order Decimals Hook – World Cycling Tour ACTIVITY PREPARATION Students compare and order decimals to the thousandths and represent comparisons using the symbols >, <, and =.

Materials

Preparation

Printed • •

• •

1 World Cycling Tour Race Results (per group, optional) 1 Student Handout (per group)

Part II

Reusable • •

Plan to show the Phenomena Video. Print World Cycling Tour Race Results for each group. Alternatively, plan to project World Cycling Tour Race Results for the class.

• •

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

Print the Student Handout for each group. Plan to have students work in groups of 2–4 to complete this activity.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore FACILITATION TIP

Record and post the Pre-Explore discussions for the students to refer to during and following the Explore activities.

4. 5.

FACILITATION TIP Allow the students to place the times in order from least to greatest. Encourage them to use their knowledge of place value to help them order the times. Remind them that this is a Pre-Explore activity and that it is okay if their order is not accurate at this time.

6. 7.

Explain that students need to be able to compare numbers even when they are very close together. 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 scenario. Discuss the following question: a. DOK-1 What do you notice about the times? They almost look the same. They include decimals.

3. 4. 5.

Distribute the World Cycling Tour Race Results to each group, or project it for the class. Distribute the Student Handout to each group. Allow students to work together with a partner or small group to order the times from least to greatest. Discuss the following questions: a. DOK-3 Why do you think we are ordering the times from least to greatest? The person who ﬁnished the race in the least amount of time is the one who won. b.

DOK-2 How did you order the numbers from least to greatest? We put the values of the seconds in a place value chart and started comparing with the biggest place value. Each time there was a difference between digits in a certain place value, we could determine which was greater or less. We didn’t need to look at the numbers of hours or minutes, because they were all the same.

COMPARE AND ORDER DECIMALS

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FACILITATION TIP Ask students for other examples of when they might need to compare and order decimal numbers, such as grades, money, and so on. FACILITATION TIP Allow the students time to compare their ﬁnal order with their Pre-Explore order and discuss any changes and reasons for those changes.

COMPARE AND ORDER DECIMALS

Compare and Order Decimals Explore 1 – Compare Decimals ACTIVITY PREPARATION Students use place value and a scaled number line to plot and compare decimals. Students represent comparisons with decimals to the thousandths, using the symbols >, <, and =.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

• • • •

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

Reusable • • • •

• • •

1 Set of place value disks (per group) 1 Clear sheet protector (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 an Exit Ticket for each student. Print a Champion Chart for each group of students. Print a Place Value Chart for each group, and place it in a sheet protector so students can write on it using the dry-erase marker. Optionally, laminate the Place Value Chart. Gather a set of place value disks for each group. Gather a dry-erase marker and sheet of blank paper for each group. For students who need more support in recalling information, please see our Base Tens 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 Use an online search engine to locate a video of a recent Kentucky Derby to show to the students. To add authenticity, locate the winning races for the horses mentioned in this activity. FACILITATION TIP Students might have the misconception that the winner is the horse with the greatest time. Address this misconception before beginning the activity.

1. 2.

4. 5.

FACILITATION TIP Allow the students to evaluate one another’s work before proceeding with the activity. 72

Ask students if they have ever seen a horse race. Allow them to share their experiences. Read the following scenario to the class: There is a famous horse race called the Kentucky Derby that is run every year on a track called Churchill Downs in Louisville, Kentucky. The length of the track is 1.25 miles. Thoroughbred horses race for the ﬁnish line so they can be called the champion of the Kentucky Derby. Tell students they will be comparing the times it took champion horses from different years to run the track at the Kentucky Derby. If those two horses raced, the one with the faster time would be the champion. Give a Student Journal to each student. Give each group a Champion Chart. Encourage students to work together to show the value of each horse’s race with their place value disks on their Place Value Charts. Be sure to check that students are correctly using the place value disks to build the number. Have them draw a representation of the place value disks and record the correct digit in each place value on their Student Journals. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 When comparing numbers, what do you have to make sure you are doing? You have to make sure you are comparing the same place values. For example, you have to compare the hundredths with the hundredths because they are the same values. You can’t compare the hundredths with the tenths because they have different values. The tenths is 10 times more than the hundredths.

Intervention

DOK-1 Look at the thousandths place. What digits do you see? I see a 2 and a 6.

DOK-1 Which is greater? The 6 is greater.

DOK-1 Does that mean the number is greater? No, we have to look at the digits in the highest place values to see which number is greater.

FACILITATION TIP As you move among the groups, stop and ask them to explain their process for comparing the numbers. Address any misunderstandings at this time. FACILITATION TIP Take the time needed to ensure that the students have a good understanding of this concept. Use money to help demonstrate this concept if they are still struggling.

COMPARE AND ORDER DECIMALS

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Have students use the extra sheet to cover the tenths place and all the digits to the right of it. Discuss the following questions: a. DOK-2 Which number is greater? Can you tell? Explain. They are both equal.

10. 11.

DOK-2 What process could you follow to compare numbers? 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. If they are the same, we have to look at the next-highest place value and use those digits to compare.

DOK-1 How could we record this comparison using symbols? We could write 2.042 > 2.036.

DOK-1 Is there another way we could write it? Yes, we could write 2.036 < 2.042 because it means the same thing.

Students will build each number using their place value disks and Place Value Charts and then check their work by using the number lines on their Student Journals to plot and label their decimals in order to compare. Then, students will record their comparison statements on their Student Journals. Instruct students to now look at the number line. Explain that we can also use number lines in order to compare numbers. Discuss the following questions: a. DOK-1 What do you notice about the number line? The number line starts at 2.030 and counts to 2.042. The number line is counting by one thousandth. b.

DOK-1 How can we plot Justify’s time on the number line? Well, I know that Justify’s time was 2.042, so since the number line is counting by one thousandth, then I will ﬁnd 2.042 and put a point on that line and label it “Justify.” i. Instruct students to plot and label this point on the number line.

DOK-1 How can we plot Always Dreaming’s time on the number line? I know that Always Dreaming’s time was 2.036, so I will ﬁnd this decimal on the number line, place a point on that line, and label it “Always Dreaming.” ii. Instruct students to plot and label this point on the number line.

d. DOK-2 How can I use the number line and plotted points in order to compare? I can see that the decimals start small and work to bigger numbers, so the number line is going from least to greatest. Since Always Dreaming’s point comes ﬁrst, I know that Always Dreaming’s time is less than Justify’s time. © Accelerate Learning Inc. - All Rights Reserved

FACILITATION TIP Point out that the open mouth of the symbol is always in the direction of the largest number. Write examples on the board, and practice reading them aloud to ensure that the students understand when to say “less than” and “greater than.” You could also have them use hand motions to indicate the appropriate symbol. FACILITATION TIP If students are struggling to understand how decimals fall on a number line, create a number line from 0 to 3. Divide each section into tenths to demonstrate that you have a whole and part of a whole. This will help with fractions in the future. 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.

COMPARE AND ORDER DECIMALS

Compare and Order Decimals Explore 1 – Compare Decimals e. DOK-2 Does this comparison match my comparison when we used place value disks? Explain. Yes, my comparisons match. In both strategies, 2.036 is less than 2.042. 12. 13.

Have students record the number comparisons using the appropriate symbols on their Student Journals. After the Explore, invite the class to a Math Chat to share their observations and learning. a.

DOK-2 How did you know which number was greater or less? We looked at the digits in the largest place value. If they were the same, we had to move on to look at the digit in the next-highest place value. The greater digit in the highest place value told us which number was greater. The smaller digit in the highest place value told us which number was less.

DOK-2 What tools or strategies could help you compare decimals? We could build a number using place value disks. We could record the number on a Place Value Chart and compare the numbers one place value at a time. We can use a number line to compare decimals.

DOK-2 How can a number line help us compare decimals? A number line is helpful when comparing decimals because I can see that a number to the left of the other number is less than the number to its right.

DOK-2 Why can each comparison be shown using two statements? The two statements are saying the same thing. We are just changing the number order. When we do that, the symbol changes.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE AND ORDER DECIMALS

Home

COMPARE AND ORDER DECIMALS

Compare and Order Decimals Explore 2 – Order Decimals ACTIVITY PREPARATION Students use a place value chart and a scaled number line to plot and order a series of decimals. Students order decimals to the thousandths from least to greatest and from greatest to least, using the symbols >, <, and =.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Place Value Chart (per station) 1 Set of Field Day Results Cards (per class)

•

1 Exit Ticket (per student)

• • • •

Reusable • • • • • • •

1 Set of place value disks (per group, optional) 1 Clear sheet protector (per station) 1 Dry-erase marker (per station) 5 Resealable bags (per class) 1 Sheet of construction paper (per station) 1 Yard of yarn (per station) 6 Paper clips (per station)

•

1 Roll of tape (per class)

•



•

Consumable •

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Place Value Chart, on card stock for durability, for each station, and place each inside a sheet protector. Print a set of Field Day Results Cards on card stock. Cut them apart, and laminate them for future use. Place each group of cards in its own resealable bag. Label each bag by its page title: Boys’ 100 m Dash, Girls’ 100 m Dash, Boys’ 400 m Dash, Girls’ 400 m Dash, and Boys’ and Girls’ Long Jump. Set up stations around the room by cutting one yard of yarn for each station. Tape this piece of yarn to a desk, and place 6 paper clips, evenly spaced, on the piece of yarn. Place a bag of Field Day Results Cards at each station, along with a Place Value Chart and a dry-erase marker.

10 Sheets of white card stock (per class) •

Optionally, have place value disks available for students who need extra support.

For students who need more support in recalling information, please see our Base Tens 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 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. 76

2. 3. 4.

Explain to students that the cards in each bag come from the competition results of a ﬁeld day fundraiser at the local high school. Winners of each event got to select the charity of their choice to receive funds. Boys competed against each other in a 100 m dash and a 400 m dash, and girls competed against each other in a 100 m dash and a 400 m dash. Both boys and girls competed against each other in the long jump. Give a Student Journal to each student. Assign each group to a station. Instruct students to take out all six cards from the plastic bag and ﬁll in each number on their Place Value Charts using dry-erase markers. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

10. 11.

Engage

Explore

Explain

Elaborate

Evaluate

Remind students that in order to compare numbers, the decimals need to be lined up so the place values line up. Tell students they can use the construction paper as needed to cover up and ignore certain place values as they are comparing. Give students some time to figure out the best method to compare and order the numbers. Tell them they should recall looking at the highest place values to compare from Explore 1. When students see digits in a place value that are not equal, have them stop and make note of the digit that is the least. Have them label this number with a 1 on the left-hand side of their chart. Have them continue moving to the right and label the following numbers with a 2, 3, 4, etc. to signify the order from least to greatest. Explain to students that the piece of yarn on the desk in front of them represents a number line. As they are deciding on the order of decimals, they will place the cards on the paper clips on their yarn number lines from least to greatest. As students complete their work on their Place Value Charts and yarn number lines, tell them to find their field day event on their Student Journals to determine whether they are to list the order of numbers from greatest to least or least to greatest. Have students record the numbers in the correct order and plot and label their decimals on the number line on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

Intervention

Acceleration

FACILITATION TIP This is an important concept for the students to understand and master, as it prepares them for the addition and subtraction of decimals. Move among the groups, ensuring that they have correctly written the numbers. FACILITATION TIP Demonstrate this method for any students or groups who are struggling. Also, consider having groups assist each other as peer tutors.

COMPARE AND ORDER DECIMALS

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FACILITATION TIP Students should get your approval after the completion of their ﬁrst station before moving forward with this activity.

a. DOK-2 What do you notice about the number line on your Student Journal? Answers will vary. I notice that my number line starts with _____ and ends with _____ and is counting by _____. b.

12.

14. 15.

DOK-2 How can we use our number line to help us order decimals? Once my decimals are all plotted on the number line, when I read the number line from left to right, those points are represented from least to greatest. If I read my number line from right to left, then my plotted points will be represented from greatest to least.

Once students have plotted and labeled their decimals on the number lines, as well as listed their decimals in the correct order, have them answer the questions that follow. a.

13.

DOK-2 How can you ﬁgure out where to plot your decimal on your number line? Answers may vary. My decimal is exactly on a line represented on my number line. I know that my decimal comes between _____ and _____ and is closer to _____ or the middle of these two decimals.

Optionally, students who need extra support can use the place value disks along with their Place Value Charts in order to visualize the value of each digit.

When ﬁnished, have students mix up their cards, place them back into the resealable bag, and rotate to the next set of competition results. Have students repeat the same process for each set of results. 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 how to order each set of competition results? We used a Place Value Chart. We looked at the digits in each place value, starting with the highest place value ﬁrst. We also used a number line to order our decimals, which placed my decimals in order from least to greatest when reading from left to right and greatest to least when reading from right to left.

FACILITATION TIP Point out that although students are unable to plot their times in the exact positions on the number line, plotting them in the right area is important so that the decimals can be compared correctly, especially when the numbers are very close to each other. Students should use their knowledge of place value to estimate the correct location on the number line. You may need to demonstrate this concept.

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.

COMPARE AND ORDER DECIMALS

Compare and Order Decimals Explore 2 – Order Decimals •

• • • • FACILITATION TIP Remind students to read every comparison scenario carefully. A common error is to place a whole set of values carefully in order and then realize that it’s reversed. “Least to Greatest” and “Greatest to Least” are powerful phrases in math scenarios and on assessments. FACILITATION TIP When you preview this Exit Ticket with students, consider allowing them to abbreviate the team names or draw arrows to their points on the number line.

•

DOK-1 Which place did you start with on the Place Value Chart when you were comparing the results? We started with the place at the left of the entire number, the highest place value. Sometimes that was the tens place, while at other times it was the ones place. DOK-1 What do we do if the digits are the same? We move to the next-highest place value. DOK-1 What do we do if the digits are different? We compare them to see which is greater and which is less. DOK-1 Which direction did you move as you were comparing the digits in each number on the Place Value Chart? We moved to the right. DOK-2 Could you compare the results just by looking at the thousandths place in each number? Explain. No. If you only look at the thousandths place, you cannot tell which number is greater. A number may have a 3 in the thousandths place, but another number with a 2 in the thousandths place may still be greater because it has a greater digit in a higher place value. DOK-1 Did you have to start over comparing the numbers from least to greatest if you already knew their order from greatest to least? No. We just reversed the order.

Post-Explore 1. 2. 3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE AND ORDER DECIMALS

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COMPARE AND ORDER DECIMALS

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

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

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

Anchor Chart

Show What You Know, Part 2

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

Order Decimals 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 New Start For Franco

Athletic Coach

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 Track Meet

Compare Decimals to the Thousandths Place

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

COMPARE AND ORDER DECIMALS

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

Students who are still acquiring the concept and need remediation

COMPARE AND ORDER DECIMALS

Compare and Order Decimals

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can represent decimal numbers to the thousandths place using a variety of tools.

What prompts will be used?

What does mastery look like?

COMPARE AND ORDER DECIMALS

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I can use concrete materials, drawings, number lines, and other visual representations to compare and order decimal numbers to the thousandths place.

I can represent comparisons with the symbols >, =, and <.

SCOPE 1

Round Decimals Scope Introduction SCOPE SUMMARY

Student Expectations

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

5.NR.4.3 Use place value understanding to round decimal numbers to the hundredths place.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Fourth-grade students generalize the process of rounding numbers, round larger numbers, and round to digits other than the leading digit. In third and fourth grades, students begin to see that rounding is valuable when estimating, predicting, and justifying the reasonableness of an answer.

In sixth grade, students can eﬃciently round multidigit whole numbers to any place. Fluency with rounding enables students to apply it regularly as an important estimation tool.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

•

choose a method created by two different students that will estimate the solution to an addition problem.

•

use that method to complete an estimation.

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: •

use place value understanding to round decimals to any place.

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

Explore 1

EXPLORE ACTIVITIES

ROUND DECIMALS

Home

Round Decimals In this exploration, students will work with peers to solve real-world scenarios about the Olympics. Students will: •

use objects such as stopwatches & Olympic Event Cards.

•

use number lines to estimate completion of different tasks.

•

practice rounding numbers to the nearest hundredth, tenth, or whole number.

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

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

ROUND DECIMALS

Round Decimals 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 choose the method that most closely estimates the solution to an addition problem and use that method to complete the estimation. This activity is intended to assess mastery of the following standard(s):

ROUND DECIMALS

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

Materials

Preparation

Printed •

•

1 Slideshow (per class or group)

Reusable •

• •

Prepare to project the Slideshow for the class, or print a Slideshow for each group. Make two columns on the board. At the top of the columns, write Student 1 and Student 2. Plan to have students work in groups to complete this activity.

1 Projector or document camera (per class, optional)

Consumable •

1 Sticky note (per student)

Procedure and Facilitation Points 1. 2. 3. 4. 5. 6. 7. 8. 9.

Give each student a sticky note. Project the Slideshow for the class, or give a printed Slideshow to each group. Introduce the information in the table to the students. Ask students to read the responses from Student 1 and Student 2, and have them find which of the two student responses they more strongly agree with. Explain to students that they will now use the sticky note to find the best estimate for the scenario. Allow time for students to find their estimate, and then have them use a show of fingers to tell which of the two students they more strongly agree with. Invite students to show how Student 1 estimated and how Student 2 estimated on the columns on the board. Encourage students to help correct the student with whom they disagree. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

10.

I agree more strongly with Student 1 because if you use the thousands place to estimate, you can drop the place values to the right of the thousands place. Then, you add the number of thousands (18, 21, and 19) to ﬁnd the total. The estimated total would be approximately $58,000. I agree more strongly with Student 2 because if you round to the nearest thousand to estimate, you can use a number line to help you ﬁnd the nearest thousand. For example, $18,780 is between $18,000 and $19,000. The halfway point of these two numbers is $18,500, and $18,780 is larger than that, so it is closer to $19,000. Student 2 rounded correctly, so their estimate is better.

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

FACILITATION TIP Sticky notes may be too small for students to effectively show their work. Consider dividing the board in half and having students write directly in the spaces on the board. Alternatively, they could use full sheets of paper that you display with magnets or tape on the board.

FACILITATION TIP Draw an open number line to represent each scenario, and challenge students to justify their thinking in relation to the number line. 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. 87

ROUND DECIMALS

Round Decimals Hook – Reading Time ACTIVITY PREPARATION Students use place value understanding to round decimals to any place.

Materials

Preparation

Printed •

• •

1 Reading Log (per group, optional)

Reusable • • • •

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

Plan to show the Phenomena Video. Print the Reading Log for each group. Alternatively, plan to project the Reading Log for the class.

Part II • •

Plan to divide the class into 6 groups to complete this activity. Gather enough whiteboards or scratch paper and dry-erase markers for each student to have one of each.

Consumable •

6 Index cards (per class)

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

FACILITATION TIP Ask students for other examples of when they might need to record the time it takes them to complete an activity, such as doing chores, running, walking, swimming laps, and so on.

FACILITATION TIP Remind the students that the total is found by adding the numbers together. FACILITATION TIP Remember that the students have not learned how to perform calculations using decimals yet. As a preview to that lesson, consider asking them to predict how they might add using decimals and what role the decimal point would play. FACILITATION TIP

4. 5.

DOK-1 What problem does Michelle have? She knows the total minutes read each week. She isn’t sure about the best way to round the time.

DOK-1 How does Michelle want to round each number? She wants to round each time to the nearest hundredth, tenth, and whole number.

Move on to complete the Explore activities.

Give the students a brief time to decide how they would round each number. Have them get into groups with other students who would round to the same place value. Each group should discuss the justiﬁcation for their choice and share it with the whole group. Write these justiﬁcations on the board for future reference.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

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

As an alternative, create a poster for each week with columns for tenths, hundredths, and thousandths, and hang the posters b. DOK-1 How does Michelle want to round each number? She wants to around the room. Ask each group to round round each time to the nearest hundredth, tenth, and whole number. all 6 numbers to the tenths, hundredths, Give each student a whiteboard or scratch paper and a dry-erase marker. Split the and thousandths and to write each answer on a small separate sheet of paper or class into 6 groups. Give a Reading Log to each group, or project it for the class. note card. Have them post their answer, Review the problem, and allow students to solve it. As students are working in with the blank side facing outward, in the groups, walk around and check for understanding. appropriate location on each poster. Assign Discuss the following questions: each group to evaluate a poster and provide feedback for the whole class. a. DOK-2 How did you round your time to the nearest hundredth? We had week 4, and 73.896 minutes were spent reading that week. We FACILITATION TIP underlined the hundredths place. We then looked at the digit in the When they share the information from their thousandths place to determine if we should round up or keep the assigned poster, have each group describe digit underlined the same. The digit in the thousandths place told us the process they used. we needed to round up the hundredths place. We then knew we had to regroup the 10 hundredths to make another tenth. Here is our work: a.

FACILITATION TIP

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DOK-1 What problem does Michelle have? She knows the total minutes read each week. She isn’t sure about the best way to round the time.

STEMscopes Tip

DOK-2 How did you round to the nearest tenth? We had week 5, and 155.432 minutes were spent reading. We looked at the digit in the hundredths place. The digit is a 3. So, we knew we would not need to round up. 155.43 rounded to the nearest tenth is 155.4.

DOK-2 How did you round to the nearest whole number? We have week 1, and 120.867 minutes were spent reading. We looked at the digit in the tenths place. The digit is an 8. We rounded up to 121 since there was an 8 in the tenths place.

You can have each group share their answers for rounding to each place value. The rest of the students should give a thumbs up if they agree or a thumbs down if they disagree. Have students justify their thumbs up or down to the class.

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

FACILITATION TIP Refer to the Pre-Explore discussion regarding the best way to round the times. Ask whether any students would like to change their answers and why.

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Round Decimals Explore 1 – Round Decimals ACTIVITY PREPARATION Students use stopwatches to time themselves completing different tasks. They will then use number lines to practice rounding those numbers to the nearest hundredth, tenth, and whole number.

Standards for Mathematical Practice • •

MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically.

Materials

• •

Preparation

Printed • • • • •

1 Student Journal (per student) 1 Number Line (per student) 1 Set of Olympic Event Cards (per class) 1 Set of Hidden Items (per class) 1 Exit Ticket (per student)

Reusable • • • • • • •

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

1 Stopwatch or app that displays time to the thousandths (per group) 1 Sheet protector (per student) 1 Dry-erase marker (per student) 1 Container (per class) 1 Small puzzle (per class) 1 Set of pattern blocks (per class) 1 Shoe with shoelaces (per class, optional)

• • • • • • • • •

•

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 Number Line for each student, and place it in a sheet protector to create an erasable surface. Print a set of Olympic Event Cards, on card stock for durability, for the class. Cut the cards apart. Print a set of Hidden Items, on card stock for durability, for the class. Place the Olympic Event Cards and Hidden Items at stations around the room. Place the pattern blocks in the container. Place the container of pattern blocks, shoe, and small puzzle with the appropriate Olympic Events Cards. Prepare a device for each group with the timer ready for use. Spend a couple of minutes reviewing the functions of the timer. If a device for each group is not available, project one on the screen, and direct students to hit the “split” or “lap” button to separate the time for each group without stopping the timer. For students who need more support in recalling information, please see our Decimal Place Value Mat and Assorted Number Lines Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Number Lines and Pattern Blocks)

PROCEDURE AND FACILITATION POINTS

STEMscopes Tip

Part I

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.

2. 3.

Read the following scenario to the class: In track and field short events (including the 100 m, 200 m, and 400 m races), times are measured to the thousandth of a second, rounded, and reported to the hundredth. In 2009, Usain Bolt set the current World Record in the 100 m dash with a time of 9.576 seconds. Help the official timekeepers come up with the official time for Usain Bolt. Give a Student Journal to each student. Allow the students to complete Part I of their Student Journals with their groups. As they work, ask the following questions: a.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What are the two benchmark numbers on the number line? 9.570 and 9.580

DOK-2 How did you ﬁnd those two numbers? Bolt’s time of 9.576 has 7 hundredths. The next hundredth after that is 8 hundredths.

DOK-1 How does the number line help you when rounding? The number line makes it easy to ﬁnd the closest number to the number I’m rounding. As long as I know which two numbers I’m in between, I can just place my number on the number line and see which one I’m closer to.

Part II 1.

2. 3.

4. 5.

7. 8.

Read the following scenario to the class: Now, it’s time for our own Rounding Olympics! You must complete a series of tasks. Just like the track and ﬁeld times, we will record our times to the thousandths place but round them to the hundredths, tenths, and ones places. Give a Number Line and a dry-erase marker to each student and a device or stopwatch to each group. Explain that each group will rotate through different activity stations. Students will record the time for each person in the group. They will use their Student Journals to record all data. Students will collaborate to round their times to the closest hundredth, tenth, and one. Encourage students to use their Number Lines and dry-erase markers to help determine the closest benchmark numbers before recording their ﬁnal answers 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 benchmark numbers would you use to round this number? Answers will vary.

DOK-1 Where will your number be located on the number line? Answers will vary.

DOK-2 Which benchmark number is your time closest to? Answers will vary.

Once the groups have completed all the stations, they will work with their groups 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 What happened to the accuracy of your numbers as you rounded them to a greater place value versus a lower place value? Explain why that is. As I rounded to a higher place value, my number became less accurate. The higher the place value, the less places I actually used and the farther away from my original number I became. • DOK-2 How do you determine the benchmark numbers on a number line? I start with the number that is in the place that I’m rounding to. If I’m rounding to the tenths place, I write my number to the tenths place. That is my ﬁrst benchmark. My second benchmark is one unit past that. So if I’m in the tenths place, the next number is one-tenth more. • DOK-2 How would you determine which place value is the best to round to? It depends on the situation. The more accurate I need to be, the more places I would include in my rounding. •

Intervention

Acceleration

FACILITATION TIP The students may need you to explain the term benchmark numbers.

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FACILITATION TIP As you introduce the vocabulary word number line, point out that in the previous lessons you used a Place Value Mat to model the position of each digit within a number. Now, you will use a number line to model the position of a number as it compares to other numbers. FACILITATION TIP Allow several students to share their processes for using the number line to help them round. FACILITATION TIP Demonstrate the procedure and expectations for the students to follow as they move between and are working at each station.

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.

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Round Decimals Explore 1 – Round Decimals Post-Explore 1. FACILITATION TIP When you preview this Exit Ticket with students, consider providing some scaffolded supports by helping them ﬁll in the ﬁrst and last values on the number lines.

2. 3. 4.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

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ROUND DECIMALS

Round Decimals Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

Round Decimals 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

The Big Sale

Robotics Technician

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

Batting a Thousand

Round Decimals – Tenths Place and Hundredths Place

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

ROUND DECIMALS

Round Decimals 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?

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What does mastery look like?

I can use my understanding of place value to round decimals to the hundredths place.

I can use number lines and benchmark numbers to reason about rounding decimals.

I can explain how a decimal is rounded.

SCOPE 1

Add and Subtract Decimals Scope Introduction SCOPE SUMMARY Students add and subtract multi-digit numbers with decimals to the hundredths by using various strategies. They use base ten blocks, place value disks, partial sums, and the standard algorithm to help them solve.

VERTICAL ALIGNMENT

Student Expectations

5.NR.4.4 Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.

Background Knowledge

Future Expectations

Students explore decimals starting in fourth grade. Understanding decimal place value comes before adding and subtracting. Fourth-grade students represent and compare decimals to the hundredths place, and they use decimal notation to represent fractions and mixed numbers with denominators of 10 or 100. Fourth graders also represent decimals up to the hundredths place using base-ten models and number lines, and then they reason about the size of the given decimal values to compare and justify these comparisons, using comparison symbols.

By the end of sixth grade, students are able to ﬂuently add, subtract, multiply, and divide positive multi-digit numbers with decimals by using models and student-selected strategies.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

determine solutions to problems in which multi-digit numbers were added and subtracted using problem-solving strategies.

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.

add and subtract whole numbers and decimals to the hundredths place.

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

Add Decimals In this exploration, students will ﬂuently add decimals to the hundredths place by using various strategies. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES Subtract Decimals In this exploration, students will ﬂuently subtract decimals to the hundredths place. Students will: •

use base ten blocks, place value disks, partial sums, and the standard algorithm in order to help them solve.

make a diagram, write an equation, and show their work solving different problems.

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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ADD AND SUBTRACT DECIMALS

Add and Subtract Decimals Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

100

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students determine solutions to problems in which multi-digit numbers were added and subtracted using problem-solving strategies. This activity is intended to assess mastery of the following standard(s): 4.NR.2.1 Fluently add and subtract multi-digit numbers to solve practical, mathematical problems using place value understanding, properties of operations, and relationships between operations.

Materials

Preparation

Printed • •

•

1 Slideshow (per class) 1 Student Handout (per group)

•

Reusable •

•

Plan to have students work in groups of 2 or 3 to complete this activity. Prepare to project the Slideshow for students, or print a Slideshow for each group. Print the Student Handout for each group.

1 Projector or document camera (per class)

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

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Project the Slideshow for the class. Read the following scenario to the class: It’s the school’s annual fundraiser! Can you help a couple of students answer some questions? Give a Student Handout to each group or student. Have students use the strategies on the Student Handout to determine the answer to each slide. Facilitate a class discussion as students create their models. 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 this gap in prior knowledge before moving on to other parts of the scope.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 not be ﬂuent in all three strategies (partial differences, standard algorithm, and open number line) on the Student Handout. Consider allowing students to choose any successful method for each question. FACILITATION TIP Take a quick survey of students preferred strategies. Consider actively reviewing and modeling the most commonly used strategy before moving on to other parts of the scope.

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Add and Subtract Decimals Hook – Student Heights ACTIVITY PREPARATION Students add and subtract whole numbers and decimals to the hundredths place.

Materials

Preparation

Printed • •

• •

1 Recorded Heights (per group) 1 Decimal Frame (per group)

Part II

Reusable • • • •

Plan to show the Phenomena Video. Print the Recorded Heights for each group or prepare to project it for the class.

• • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Clear sheet protector (per group) 1 Dry-erase marker (per group)

Plan to have students work in groups of 3–4 to complete this activity. Print the Decimal Frame for each group. Place it in a clear sheet protector. Gather enough dry-erase markers for each group to have one.

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

FACILITATION TIP

Provide examples of the different types of tools a nurse might use to measure height. Allow the students to examine them before responding to the questions.

FACILITATION TIP Ask the students to share any experiences where their heights have been recorded: at doctors’ oﬃces, at home, for sports, and so on. FACILITATION TIP

4. 5. 6.

Use the Recorded Heights to review place values, comparing, and ordering before moving forward. This will help set the foundation for the upcoming activities. FACILITATION TIP Review or create a list of other words that would also indicate the need to use addition to solve the problem (all together, total, sum...).

7. 8.

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DOK-2 Which operation will the nurse use to determine the combined height of two different students? She will use addition.

DOK-2 What operation will the nurse use to determine how much taller one student is than another? She will use subtraction.

DOK-1 Look at these heights. The heights are not expressed as whole numbers. How do you know? They have decimals points.

DOK-1 Do any of these students have the same height? How do you know? No, all the heights have different values.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4. 5.

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

DOK-2 Which operation will the nurse use to determine the combined height of two different students? She will use addition.

DOK-2 What operation will the nurse use to determine how much taller one student is than another? She will use subtraction.

DOK-1 Look at these heights. The heights are not expressed as whole numbers. How do you know? They have decimals points.

DOK-1 Do any of these students have the same height? How do you know? No, all the heights have different values.

Divide the class into groups, and give a Recorded Heights, a Decimal Frame, and a dry-erase marker to each group. Instruct students to collaborate to help the school nurse answer questions about students’ growth by using the Decimal Frame as needed. Discuss the following questions:

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.

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FACILITATION TIP

Ask the students to cut the students’ names and heights into strips. Next, ask them to place the students in order from shortest to tallest, being sure to line up b. DOK-3 Which student was the tallest, which student was the shortest, the decimal points. Use this activity, along and what is the difference between their heights? The tallest student is with the guiding questions, to access Greg, the shortest student is Willow, and the difference in their heights is prior knowledge and provide feedback for 1.8 – 1.49 or 0.31 of a meter. any students who are still struggling with c. DOK-4 When adding and subtracting decimals, is it necessary to line up comparing and ordering decimals. the decimal points? Explain your reasoning. Yes, it is necessary to line up the decimal points because each place value position (hundredths, tenths, ones) needs to line up. a.

DOK-3 Which two students had the shortest height, and what is their combined height? Willow and Erika are the shortest. Their combined height is 1.49 + 1.52 or 3.01 meters.

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Add and Subtract Decimals Explore 1 – Add Decimals ACTIVITY PREPARATION Students focus on ﬂuently adding decimals to the hundredths place by using various strategies. Students use base ten blocks, place value disks, partial sums, and the standard algorithm in order to help them solve.

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 Scenario Cards (per group) 1 Grid Model Mat (per group) 1 Place Value Mat (per group) 1 Set of Place Value Disks (per group) 1 Exit Ticket (per student)

Reusable • • • • •

1 Set of base ten blocks (per group) 1 Set of colored pencils (per group) 3 Sheet protectors (per group) 2 Dry-erase markers, different colors (per group) 2 Resealable bags (per group)

Preparation • • •

Part I: The Games •

• • •

1 Roll of tape (per class)

Print a set of Scenario Cards, on card stock for durability, for each group of students. Cut the Scenario Cards apart, and place them in a resealable bag for each group. Gather enough base ten blocks for each group of students. Print a Grid Model Mat, on card stock for durability, for each group of students. Place the Grid Model Mat inside a sheet protector. Gather a set of colored pencils for each group.

Part II: The Food •

•

Consumable •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Gather 2 different-colored dry-erase markers for each group.

•

Print the Place Value Mat, on card stock for durability, for each group of students. Note that there are two separate pages. You will need to place the Place Value Mat into sheet protectors and then tape the two pages together. Print one set of Place Value Disks for each group of students. We recommend that each denomination be printed on different-colored card stock. Cut the Place Value Disks on the dotted lines, and place each set in a resealable bag. For students who need more support in recalling information, please see our Base Tens and Decimal Place Value Mat Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS Part I: The Games FACILITATION TIP Allow the students an opportunity to share their family reunion or gathering experiences.

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2. 3.

Read the following scenario to the class: It’s time for your family reunion! You are so excited to see all your cousins, aunts, uncles, and other relatives! You always enjoy getting together and playing games, eating, and having a really good time. Give a Grid Model Mat and a set of base ten blocks to each group. Explain to students that one whole is represented by a hundred grid. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Have the students work together to discuss and solve the following questions. Allow time for students to discuss and then share. a.

DOK-2 If the hundred grid has a value of 1, what is the value of one 1 ___

column? Explain. 0.1 or 10 because it takes 10 columns to make one

whole, so 1 column would be one-tenth of 1 b.

DOK-2 If the hundred grid has a value of 1 and a column has a value 1

FACILITATION TIP As you move among the groups, stop and ask them to explain their process for comparing the numbers. Address any misunderstandings at this time.

of 0.1 or ___ , what is the value of the unit? Explain. 0.01 or ____ because 10 100

it takes 100 units in order to make a whole, so 1 unit would be one-

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hundredth of 1 5.

Next, ask students to discuss and then share how they use place value when adding whole numbers. Listen and guide students as they talk within their groups before sharing. Students must have the following understanding: a.

Digits 0–9 have a different value depending on the position in a number.

Add whole numbers with like units, such as the digits in the ones place are added, the digits in the tens place are added, the digits in the hundreds place are added, etc.

7. 8.

We regroup or rename numbers in order to add. 79 + 8: add 9 ones and 8 ones and regroup to have 1 ten and 7 tens to make 87. Students may rename 7 tens to make 79 ones to add 8 ones. Emphasize the same units that must be added.

Explain to students that adding decimals is the same as when they add with whole numbers. a.

Digits have different values depending on the position in a number.

Add the same units, such as ones added with ones, tenths added with tenths, and hundredths added with hundredths.

Flexible thinking is done by decomposing your digits and then composing your numbers to combine the values.

Distribute Scenario Cards, a set of colored pencils, and 2 different-colored dry-erase markers to each group. Give a Student Journal to each student. Encourage students to write an equation and to use their Grid Model Mats. They should use their 2 different-colored dry-erase markers to represent the 2 decimals being added together on their grid models. They will then represent their problem using partial sums. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How can we represent our ﬁrst decimal addend on our grid model? Answers will vary. I will represent my tenths place with a rod since they represent one-tenth of the whole, and I will use the units to represent the hundredths place; they are one-hundredth of the whole. Since my ﬁrst addend is 0.33, I will shade 3 columns and 3 units on my model.

DOK-1 How can we represent the addition of our second addend on our grid model? My second addend is 0.50, which is represented by 5 tenths. I will add on 5 tenths to the same grid model.

DOK-1 How can I use my grid model to ﬁnd my total sum? I can ﬁnd the total amount of tenths and hundredths on my grid model. 0.3 + 0.5 + 0.03 = 0.83

FACILITATION TIP Write whole numbers as decimals (for example, 2.00) to help the students understand that there is always a decimal after the ones place of a whole number. Money provides good examples of zeros after a decimal. FACILITATION TIP Use base ten blocks to reinforce this concept if needed. Provide a few practice problems that you can use to access their prior knowledge. Allow peer tutoring for students who are struggling. FACILITATION TIP Practice lining up decimal points using decimals with varying numbers of digits, such as 2, 3.3, and 1.323. Consider using whiteboards for this to check students’ knowledge. FACILITATION TIP Provide examples of possible answers for each section of the Student Journal before starting the activity. STEMscopes Tip The Accessing Prior Knowledge activity, located in the Engage section, helps teachers determine students’ prior knowledge about a concept before engaging in the inquiry process. If students struggle with the task, the Foundation Builder, also found in the Engage section, helps to ﬁll the gaps in prior knowledge.

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Add and Subtract Decimals Explore 1 – Add Decimals d.

e. DOK-2 Why do you think the Grid Model Mat has the place values lined up for partial sums? You need to ﬁnd the total for each place value. You have to combine place values that are the same.

FACILITATION TIP If students are struggling, demonstrate how they can use the base ten blocks to determine partial sums.

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.

DOK-1 How can I use partial sums to represent my equation? I can decompose each of my addends into expanded form.

10.

11. 12.

After each Scenario Card, instruct students to record an equation and represent the number on the grid model using two different-colored pencils to represent each addend, the partial sums strategy, and standard algorithm on their Student Journals. Students should repeat this process for each Scenario Card. After Part I, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-2 How did you use the grid models to add your decimals? I used one of my colored pencils to shade in the decimal of my ﬁrst addend. I then used a second color to shade in my second addend on the same grid model. Finally, I counted all the shaded parts of my grid to ﬁnd the total sum. DOK-2 How is the partial sums method similar to the standard algorithm? In both strategies, we need to make sure our place values are lined up and that we add our tenths place to our tenths place and our hundredths place to our hundredths place.

Part II: The Food 1. FACILITATION TIP Access the students’ prior knowledge of the use of place value mats and disks through a review of previous scopes. FACILITATION TIP

2. 3.

Provide base ten blocks for students who are struggling to use the place value disks to represent each decimal. 5.

FACILITATION TIP After each group models the ﬁrst scenario, allow them to review other groups’ models and give peer feedback. Provide examples of guiding questions the students can use for giving feedback. 106

Read the following scenario to the class: After a long, fun day of family reunion games, it is time to eat some food. Help your family ﬁgure out how much food was consumed at the family reunion. Give a Place Value Mat and a set of Place Value Disks to each group of students. Instruct each group of students to analyze their place value disks; identify the disks that represent the ones, tenths, and hundredths; and place them in the correct spot on their Place Value Mats. Quickly check each group’s mat for understanding. Encourage students to collaborate to solve the problems using their Place Value Mats and their place value disks to represent each decimal and then record their work using the partial sums method and standard algorithm method 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 can we use our place value disks to represent the decimal amount of pizza that you ate? Well, it says that I ate 0.25 of the pizza. This will be represented with 2 tenths and 5 hundredths, so I will place these disks on the correct place on my Place Value Mat.

DOK-1 How can we represent the addition of our second decimal addend to our Place Value Mat using our place value disks? It states that Maria ate 0.52 of the pizza, which is represented with 5 tenths and 2 hundredths. I will add these disks to the current disks in the correct spot on the Place Value Mat.

DOK-2 Do any of our place value disks need to be regrouped? Explain. No, in order to regroup, we would need to have 10 or more in one place value, and currently, each place value has fewer than 10 disks in each spot.

DOK-2 How can we use our place value disks to ﬁnd the total? We can add each place value spot and its disks together. For example, 0.2 + 0.5 = 0.7 and 0.05 + 0.02 = 0.07. Finally, 0.7 + 0.07 = 0.77. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

e. DOK-2 How can we use our place value disk models to help us solve using the partial sums method? The place value disks help represent the expanded form of each number. I see that 0.25 = 0.20 + 0.05 and 0.52 = 0.50 + 0.02. 6.

7. 8. 9.

Instruct students to use their place value disk models to help them solve using partial sums on their Student Journals. Students can then check their work using the standard algorithm. Explain to students to always check that their decimals are lined up and that tenths are lined up with tenths and hundredths with hundredths. Once students have completed their Student Journals, they will answer the reﬂection questions. After Part II, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

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.

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Math Chat DOK-2 What strategy did you ﬁnd most helpful when adding decimals? I found adding with place value disks most helpful because it allowed me to have a visual model to then add using partial sums and then the standard algorithm. • DOK-1 What did you have to do if there were 10 or more place value disks in one place value? We had to take 10 place value disks and regroup them for one of the next-highest place values. When we added that one on, we had to make sure we included that regrouped amount in 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.

FACILITATION TIP This Exit Ticket can be used as a preassessment for some students prior to this Explore activity.

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Add and Subtract Decimals Explore 2 – Subtract Decimals ACTIVITY PREPARATION Students focus on ﬂuently subtracting decimals to the hundredths place.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.6 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

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

•

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Scenario Cards for each pair of students. For students who need more support in recalling information, please see our Base Tens and Decimal Place Value Mat elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks and Place Value Disks)

PROCEDURE AND FACILITATION POINTS Part I: Silent Auction 1. FACILITATION TIP Students may be unfamiliar with auctions and silent auctions. Although this is not relevant to the concept, the lack of understanding could serve as a distraction from the learning. Take the time to explain a silent auction to the students. FACILITATION TIP Provide a brief review of subtraction regrouping with zeros prior to beginning the activity.

2. 3.

Read the following scenario to the class: Your family is headed to a state fair to see some animals, ride some roller coasters, eat some good food, and ﬁnd some new toys in a silent auction. Your parents are giving you and your siblings a different amount of money, depending on your age, to use in the silent auction. You will be helping your siblings determine how much money they are left with if they win the silent auction. Give a Student Journal to each student and the Silent Auction Scenario Card to each pair of students. Invite students to collaborate to solve each of the problems on their Student Journals. Instruct students to make a diagram, write an equation, and show their work solving each problem. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How would you set up a diagram for this problem? We know the question is asking how much is left, so we will need to subtract two numbers. By looking at the diagram, I can see the boxes are different sizes based on the decimal values. We can place the greater number in the top section and the number with less value in one of the bottom sections. A variable, such as m for money, can go in the other bottom section because that is what we are trying to ﬁnd.

DOK-1 How can you write an equation for the diagram? We will write the greater number ﬁrst and subtract the smaller number from that greater number. The equation will equal the variable because that is the unknown quantity we are trying to ﬁnd.

FACILITATION TIP Explain that a variable is a placeholder for a currently unknown number. FACILITATION TIP Brieﬂy review comparing and ordering decimals to ensure that the students can determine which decimal is the largest. 108

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Explore

Explain

Elaborate

Evaluate

DOK-2 Does the order of the numbers in my equation matter for a subtraction problem? Explain. Yes, the order of the numbers in a subtraction problem matters because in this case the money we are spending can’t be greater than the money that we have.

Intervention

Acceleration

FACILITATION TIP If students are struggling, use base ten blocks or coins to demonstrate the concept.

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

Math Chat DOK-1 What did you notice about the numbers and decimals in the Show Your Work section of your Student Journal? I noticed that all my numbers and decimals were lined up. The tenths were lined up with the tenths, the hundredths were lined up with the hundredths, and so on. • DOK-2 What number did you have to place into empty place value boxes in order to solve? Explain. I had to place a zero into empty place value boxes because a zero does not change the number, but it does allow us to have the same number of digits after the decimal point. • DOK-1 When is regrouping necessary in a subtraction problem? Regrouping is necessary in a subtraction problem when a digit in my bottom number has a greater value than the digit in the top number. I will need to borrow a group of tens from a greater place value and add it to the current place we are subtracting from in order to make the top digit greater than the bottom digit. •

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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.

Part II: Contest Craze 1. 2.

4. 5.

Give the Contest Craze Scenario Card to each pair of students. Read the following scenario to the class: Each of you and your siblings decided to compete in multiple contests at the state fair. Each contest lasts for ﬁve minutes, and the goal is to eat as much food as possible during that time in order to win. Below are the results. Discuss the information in the table. a.

DOK-1 What do you notice about the decimals in this scenario? I notice that some of the decimals go up to the tenths or hundredths place.

DOK-2 What do you think you might have to do in order for all the decimal numbers to have the same number of digits after the decimal? I might have to add zeros after my digits in the decimal places so my decimal numbers have the same number of digits after the decimal.

Tell students the numbers represent the amount of pie or hot dogs eaten by each sibling during the whole contest. Encourage students to collaborate to solve the questions on their Student Journals. Students will make a diagram and write an equation. Student pairs will then solve their subtraction problem in the table labeled Show Your Work and write a solution statement for their answer. Use the following questions to assess understanding: a.

DOK-2 How would you set up a diagram for this problem? We know the question is asking how many more, which means we are trying to ﬁnd the difference between one sibling’s number and another sibling’s number. By looking at the diagram, I can see that the boxes are different sizes based on the decimal values. We can place the greater number in the top section and the number with less value in one of the bottom sections. A variable, such as p for pies or h for hot dogs, can go in the other bottom section because we are trying to ﬁgure out how many more pies or hot dogs.

DOK-1 How can you write an equation for the diagram? We can write the greater number ﬁrst and subtract the smaller number from that greater number. My equation will equal my variable because that is the unknown quantity we are trying to ﬁnd.

FACILITATION TIP Take time to ensure that the students understand that adding zeros to the end of any number after the decimal does not change the value of that number. Emphasize that this applies to whole numbers as well. Monetary amounts provide good examples of this concept.

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. 109

ADD AND SUBTRACT DECIMALS

Add and Subtract Decimals Explore 2 – Order Decimals 7.

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. FACILITATION TIP This Exit Ticket might also serve as an effective pre-assessment for some students prior to this Explore activity.

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

Math Chat DOK-2 How is solving a subtraction problem with whole numbers similar to solving a subtraction problem with decimals? In both subtraction problems with whole numbers and decimals, we must make sure to line up our place value positions—ones to ones, tens to tens, etc. With decimals, we need to make sure we line up our decimals and our tenths to tenths and hundredths to hundredths. • DOK-2 How is a diagram helpful in solving a real-world problem? A diagram is helpful when solving a real-world problem because it can give a visual aid on what operation is needed in order to solve. It also allows us to see which number is greater in value compared to another number and what unknown quantity we are trying to solve for. •

Post-Explore 1. 2. 3. 4.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Add and Subtract Decimals Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

Add Decimals 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

Subtract Decimals 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

The Backyard Shed

Franchise Owner

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 Saturday Well Spent

Addition and Subtraction Models with Decimals to the Hundredths and Thousandths Places

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

ADD AND SUBTRACT DECIMALS

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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

Ice-Cream Sundaes

Add and Subtract Decimals to the Hundredths and Thousandths Places

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

113

Students who are still acquiring the concept and need remediation

ADD AND SUBTRACT DECIMALS

Add and Subtract Decimals

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can solve problems involving the addition of decimal numbers to the hundredths place using a variety of strategies.

What prompts will be used?

What does mastery look like?

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I can solve problems involving the subtraction of decimal numbers to the hundredths place using a variety of strategies.

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SCOPE 1

Multiply Multi-Digit Whole Numbers Scope Introduction SCOPE SUMMARY Students apply their knowledge of place value (base-ten system) and the distributive property (properties of operations) of multiplication to compute partial products as they begin to multiply multi-digit whole numbers. They then connect partial products to the standard algorithm for multiplication and use this to solve real-world and mathematical problems involving multi-digit whole numbers. Student Expectations

5.NR.2.1 Fluently multiply multi-digit (up to 3-digit by 2-digit) whole numbers to solve authentic problems.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Fourth-grade students build on these concepts to apply their understanding of multiplication models (arrays and area models) and partial products to ﬁnd the products of multi-digit whole number multiplication problems. In fourth grade, students are expected to multiply a whole number (up to four digits) by a one-digit whole number. They are also expected to multiply two two-digit numbers, using place value strategies or the properties of operations.

Sixth-grade students will extend their ﬂuency in using area models, partial products, and the standard algorithm as they work to solve multiplication problems involving multi-digit decimal numbers. Base-ten concepts expand to include negative numbers, with which seventh graders then learn to compute arithmetic. The distributive property and concepts using base-ten computation will continue to be important throughout high school mathematics.

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

analyze a variety of solved multiplication problems to identify the correctly used strategies and errors.

•

describe the errors in the multiplication problems.

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 multiplication and division to solve two-step problems.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 116

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Explore 1

EXPLORE ACTIVITIES Partial Products and the Standard Algorithm In this exploration, students will work with peers to solve a scenario involving the need to ﬁnd the area of carpets. Students will: •

multiply 3-digit by 2-digit numbers.

•

draw an area model.

•

write the partial products to ﬁnd the total product.

The exploration concludes with an Exit Ticket; then, students revisit the Hook to apply their learning and solve.

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Multiply Multi-Digit Whole Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students analyze various solved multiplication problems to ﬁnd correctly used strategies and errors. This activity is intended to assess mastery of the following standard(s): 4.NR.2.3 Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Materials

Preparation

Printed •

•

1 Student Handout (per group or student)

•

Plan to have students work in groups of 3 or 4 or individually to complete this activity. Print the Student Handout for each group or student.

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

Give a Student Handout to each group or individual student, and ask students to look at each of the four problems. Remind students that there are many ways to solve multi-digit multiplication problems and that each problem is solved using a different strategy. Tell students that they will be responsible for solving each of the problems by using a strategy they are comfortable using. Students will compare their work to each of the problems and identify the correct solutions. Facilitate a class discussion about the mistakes that were made in solving the problems. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

Each of the incorrect problems has an incorrect partial product (for example, 20 × 5 = 100, not 10).

Each of the incorrect problems made a place value mistake (for example, 2 × 5 is not correct; it should be 20 × 5 because the 2 means 2 tens).

FACILITATION TIP The goal here is for students to be exposed to a variety of calculator strategies. While students may not be familiar with all of them, they should decide whether or not they agree with the calculation by working out the problem using any strategy of their choice. FACILITATION TIP Keep an ongoing list of computation strategies that students can add to and reference throughout this scope. Strategies may include using an algorithm or vertical calculation, decomposing by place value with base-ten models, repeated addition, area models and partial products, rectangular arrays, estimation, and the relationship between multiplication and division.

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Multiply Multi-Digit Whole Numbers Hook – Inventory Time ACTIVITY PREPARATION Students ﬂuently multiply multi-digit whole numbers using the standard algorithm.

Materials

Preparation

Printed •

• •

1 Inventory Time (per group)

Reusable • • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Whiteboard or sheet of scratch paper (per student) 1 Dry-erase marker (per student)

Plan to show the Phenomena Video. Plan to have students work in groups of 4 to complete this activity. Print an Inventory Time for each group. Cut each sheet apart so that each student will receive one table.

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

FACILITATION TIP Allow the students to share about building playsets made of interlocking bricks. Bring in some examples to provide context for students.

FACILITATION TIP Brainstorm as a whole group how to solve this problem. Use this time to review the various strategies and models students have used previously to solve problems. Give them time to attempt to solve the problem using one of these strategies. Save their predictions for use during the Post-Explore.

DOK-1 What do we want to know? We want to ﬁnd out how many total pieces there are in all the sets that are the same.

DOK-2 What would we have to know in order to ﬁnd the total pieces? We would need to know how many interlocking bricks are in each set and how many of each set we have in our toy store’s inventory.

DOK-2 What operation do you think you would use to ﬁnd the total interlocking bricks in each set? I think we would use multiplication since it would be the same number of pieces multiple times and since there are multiple sets of each kind of set.

Move on to complete the Explore activities. Notes

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

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

DOK-1 What do we want to know? We want to ﬁnd out how many total pieces there are in all the sets that are the same.

Give each student a whiteboard or scratch paper and dry-erase marker. Divide the class into small groups of 4 students. Give one Inventory Time table to each student. Review the problem, and allow students to solve it. As students are working in groups, walk around and check for understanding. Gather students in a whole group, and discuss the following questions: a.

DOK-3 What did you do to ﬁnd out how many total interlocking bricks there are in sets of the same kind? I knew that I needed to multiply. On my table I had one interlocking brick set that had 389 pieces in it. I had 66 of those sets. I knew that I would be adding 389 sixty-six times. Another way to do repeated addition is to multiply. I multiplied using the standard algorithm. It looked like this.

FACILITATION TIP

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Review the previous brainstorm ideas and predictions. Discuss which strategies could be used to solve the problem. Include a justiﬁcation discussion for those strategies that could and could not be used.

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.

So, this type of interlocking brick set had 25,674 total pieces in the 66 sets my store has in inventory. 5.

Have other students share their algorithms. You can also have students with the same inventory table share their answers to see if they got the same total pieces per set.

FACILITATION TIP Have a member of each group come to the board to complete a step of the problem.

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Multiply Multi-Digit Whole Numbers Explore 1 – Partial Products and the Standard Algorithm ACTIVITY PREPARATION Students connect the area model strategy for three-digit by two-digit multiplication with partial products and the standard algorithm.

Standards for Mathematical Practice • • •

MP.1 1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • • •

•

1 Student Journal (per student) 1 Area Model Template (per group) 1 Set of Digit Cards (per group) 1 Standard Algorithm Work Mat (per group) 1 Exit Ticket (per student)

• •

•

Reusable • •

1 Clear sheet protector (per group) 1 Dry-erase marker and eraser (per group)

Consumable •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Digit Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them in resealable bags, one for each place value. Print an Area Model Template and Standard Algorithm Work Mat, on card stock for durability, for each group of students. Place the Area Model Template inside a clear sheet protector. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids elements in the Intervention section.

5 Resealable bags (per group)

PROCEDURE AND FACILITATION POINTS Part I: Partial Products 1.

2. FACILITATION TIP The Area Model Template is a scaffold for the area model. The area model is a scaffold for students to complete the partial product equations. Each of these can be removed as students appropriate the desired skill. 122

3. 4.

Read the following scenario to the class: Aladdin’s Carpets is the biggest carpet store in the area. Businesses like to buy their carpets from Aladdin’s because they have a large variety of carpets in stock and ready to deliver. Four businesses in the area would like to buy carpet from Aladdin’s and have sent Aladdin’s their floor dimensions. Aladdin’s Carpets would like to give them a quote for the cost of carpet and installation, but they first need to find the area of each building. Please help Aladdin’s Carpets find the area of each business’s building. You may need to remind students that area is found by multiplying the length by the width. Give a Student Journal to each student, and give each group an Area Model Template and a dry-erase marker. For each building, students should use the Area Model Template to multiply the numbers. Students should record their partial products for each part of their area model on their Student Journals. Model this as needed. Be sure to relate each section of the area model to the numbers they would be multiplying in the problem and what partial product it produces. © 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 How did you make this area model? Answers may vary. I used the expanded form of the length, 100 + 80 + 4, and the expanded form of the width, 50 + 2, to make the area model. I multiplied each length by width to get the partial products of the sections.

b. DOK-1 How did you use the information in the area model to help you with the partial products? I used the equations from the area model on the partial products. Each partial product is like one section of the area model. c.

DOK-2 How are area models and partial products similar? Both area models and partial products decompose the numbers so they are easier to multiply. DOK-3 What is the advantage of using partial products instead of area models? Answers may vary. You are still ﬁnding the partial products; you just don’t have to draw the area model. It is easier to add the partial products to get the ﬁnal product.

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

Math Chat DOK-2 How is multiplying three-digit numbers by two-digit numbers similar to multiplying three-digit numbers by one-digit numbers? You still break apart the numbers into place values before you distribute them. • DOK-1 Which place values do you use from each number to find partial products? I use them all. I multiply each place value in the first number by each place value in the second number, and then I add all the partial products together. • DOK-2 How does the place value of the factors affect the partial product? If I am multiplying tens by tens, I know I will get hundreds because 10 groups of 10 is 100. If I am multiplying tens by ones, I know I will get tens because I am finding the total of ___ groups of 10. • DOK-2 How does an area model work to find partial products? The rectangle is split up into smaller rectangles based on place value. You find the area of each of those smaller rectangles. Those are called “partial products” because they are just part of the total. Then, you add them up to find the area of the whole rectangle, which is the final product. •

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.

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Part II: The Standard Algorithm 1.

Read the following scenario to the class: Aladdin’s Carpets was able to sell carpeting to the four businesses, but now they have carpet remnants, or pieces, left over. Aladdin’s would like to sell them, but since they sell remnants by the square foot, they need to know the size of each carpet remnant in square feet. Please help Aladdin’s Carpets price the carpet remnants by ﬁnding the area of each piece. Give the Standard Algorithm Work Mat and Digit Cards to each group. Notes

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Multiply Multi-Digit Whole Numbers Explore 1 – Partial Products and the Standard Algorithm 3.

Work through the ﬁrst remnant size to show students how to use the Digit Cards. Give the following instructions: a.

First, you will need to ﬁnd the Digit Cards for the numbers in your multiplication problem. i. The length of Remnant 1 is 362 feet, and the width is 27 feet. ii. DOK-1 What do we need to do to ﬁnd out the total area? We need to multiply 362 × 27. iii. DOK-1 So which digit cards do we need to get out? We need 3 hundreds, 6 tens, 2 ones, 2 tens, and 7 ones. iv.

Place these cards over the dotted rectangles on the Standard Algorithm Work Mat. i. Do NOT glue down the digit cards. ii. Make sure the top row reads “3 hundreds, 6 tens and 2 ones” and the bottom row reads “2 tens and 7 ones”. iii. Now we can start multiplying. Let’s start with the ones places.

FACILITATION TIP Allow the students time to brainstorm and attempt this process before you demonstrate it. Move around the room, observing their interactions and discussions. Address concerns during your demonstration.

DOK-1 There are 7 groups of 2 ones. How many ones does that give us? It gives us 14 ones.

vi.

DOK-2 We can’t write 14 in the ones place. What can we do? We can trade 10 of those ones for 1 ten. i. Students should place the “4 Ones” card in the Ones column, and the “1 Ten” card they regrouped will go ABOVE the Tens column to be added on later. Students should record this step on their Student Journals.

Next, we have 7 groups of 6 tens. i. DOK-1 How many tens does that give us? It gives us 42 tens. ii. DOK-1 Remember that we had to regroup some tens because we had too many ones. So how many tens do we have now? We have 43 tens. iii. DOK-2 We can’t write 43 in the tens place. What can we do? We can trade 40 tens for 4 hundreds.

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.

i. Students should place the “3 Tens” card in the Tens column, and the “4 Hundreds” card they regrouped will go ABOVE the Hundreds column to be added on later. Students should record this step on their Student Journals. iv.

DOK-1 Do we have a digit in the hundreds place to write our regrouped hundred above? Yes, we have 3 hundreds.

DOK-1 There are 7 groups of 3 hundreds. How many hundreds does that give us? It gives us 21 hundreds.

vi.

DOK-2 Remember, we had to regroup the 40 tens that were in the tens place to 4 hundreds. What do we do with those 4 hundreds? We add them to the 21 hundreds we got from multiplying 7 groups of 3 hundreds.

vii. DOK-1 How many hundreds are there now? There are 25 hundreds. viii. DOK-2 We can’t write 25 in the hundreds place. What can we do? We can trade 20 hundreds for 2 thousands. i. Show students how they can place the “5 Hundreds” card in the Hundreds column and the “2 Thousands” card in the Thousands column in the ﬁrst partial product. ii. Students should record this step on their Student Journals.

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Explore

Explain

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Evaluate

Intervention

Acceleration

Now, we have multiplied each place value in the top number by the ones place in the bottom number. We need to do the same thing with the tens place in the bottom number (refer to the area model, if needed). (Have students ﬁnd 20 groups of 2; optionally, it may be easier to think of it as 2 groups of 2 tens.) i. DOK-1 How many tens does that give us? It gives us 4 tens. ii. DOK-1 How many ones do we have? Since we are ﬁnding groups of 10, we have 0 ones. i. Show students how to place the “0 Ones” card in the Ones column for the second partial product and a “4 Tens” card in the Tens column right next to it. ii. Students should record this on their Student Journals.

Next, we have 20 groups of 6 tens. i. DOK-1 How many hundreds does that give us? It gives us 120 tens, which is 12 hundreds.

e. We can’t write 12 in the hundreds place. i. DOK-2 What can we do? We can trade 10 hundreds for 1 thousand. i. Students should place the “2 Hundreds” card in the Hundreds column and the “1 Thousand” card they regrouped will go ABOVE the Thousands column to be added on later.

FACILITATION TIP

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ii. Students should record this step on their Student Journals. f.

Finally, we will ﬁnd 20 groups of 3 hundreds. It’s 20 groups because we are using the “2 Tens” card. i. DOK-1 So how many thousands do we get? It gives us 60 hundreds, which is 6 thousands. ii. DOK-2 Remember, we had to regroup the 10 hundreds that were in the hundreds place to 1 thousand. What do we do with that 1 thousand? We add it to the 6 thousands we got from multiplying 20 groups of 3 hundreds. iii. DOK-1 How many thousands are there now? There are 7 thousands. i. Show students how to place the “7 Thousands” card in the thousands place in the second partial product. ii. Students should record this step on their Student Journals. iv.

Now that we have multiplied each place value in the bottom number by each place value in the top number, we can add up our partial products to ﬁnd the total.

There are some blank cards for each place value. Find a blank card for each place; this is where you can write your answer in.

vi.

Let’s add up the Ones column now: 4 + 0 = 4.

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.

i. Write a 4 on your blank Ones card, and place it in the Ones column below the answer line. vii. Let’s add up the Tens column now: 3 + 4 = 7. i. Write a 7 on your blank Tens card, and place it in the Tens column below the answer line. viii. Let’s add up the hundreds column now: 5 + 2 = 7. i. Write a 7 on your blank Hundreds card, and place it in the Hundreds column below the answer line.

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Multiply Multi-Digit Whole Numbers Explore 1 – Partial Products and the Standard Algorithm ix. Let’s add up the Thousands column now: 2 + 7 = 9. i. Write a 9 on your blank Thousands card, and place it in the Thousands column below the answer line. x. DOK-1 So the product is 9 thousands, 7 hundreds, 7 tens, and 4 ones. What is another way to say this number? 9,774 FACILITATION TIP

If time is limited, after successfully using the work mat allow students to only record the answer on the Student Journal.

Before students clear their Standard Algorithm Work Mats for the next problem, make sure students have recorded their work on their Student Journals. Students should follow the same procedure to ﬁnd the areas of Remnant 2 and Remnant 3. The values are listed on their Student Journals. If students seem ready, have them try to multiply the numbers using the standard algorithm without the Digit Cards. Discuss the following questions: a.

DOK-1 What is the ﬁrst step in solving using the standard algorithm? I multiply my bottom number, starting in the ones place, by all the digits in my top number. When I multiply by the top number, I work from the smallest place value to the largest place value. I write my ones place for my product in the ﬁrst row for my total and regroup as needed.

DOK-1 What is the second step in solving using the standard algorithm? I multiply my bottom number, starting in the tens place, by all the numbers in my top number. When I multiply by the top number, I work from the smallest place value to the largest place value. I write my tens place for my product in the second row for my total and regroup as needed.

DOK-1 What happens when you multiply the number in the tens place on the bottom number by the number in the ones place on the top number? Since I am ﬁnding groups of ten, there are 0 ones, so I write a 0 in the ones place and the number of tens in the tens place.

DOK-1 How do you find the total product using the standard algorithm? I add the two products from my first row and second row in order to find my total product.

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.

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

Math Chat FACILITATION TIP Identify some additional real-world applications for being ﬂuent with multiplying multi-digit numbers without a calculator. Sometimes, students connect with needing to being skilled enough to not get taken advantage of or easily confused in real-life transactions.

•

• •

•

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DOK-2 How does the standard algorithm compare to using area models? You are still using place value to multiply. Each digit gets multiplied by the digits in the other number. They are just recorded in a different way. DOK-2 How are these methods different? In the standard algorithm, you don’t see the rectangles to break the area (or the product) into several parts. You have to really pay attention to the place value so you don’t regroup numbers to the wrong place. DOK-2 How is the standard algorithm similar to using partial products? You multiply each place in the ﬁrst number by each place in the second number. DOK-2 How is it different? You’re not writing out six different equations to add up. Instead, you write each step as part of the answer below the problem and regroup where necessary. DOK-2 Why did we regroup at times? Sometimes when you multiply, you end up with too many of one place value. If you have 10 of something, you can regroup those 10 for one of the next-highest place value.

Engage

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Intervention

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Post-Explore 1. 2. 3. 4.

FACILITATION TIP Before completing this Exit Ticket, provide some repeated independent/partner check practice with whiteboards. After ﬁnishing this Explore activity, consider completing the Exit Ticket during a separate session.

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Multiply Multi-Digit Whole Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

Partial Products and the Standard Algorithm 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

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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

Building a Doghouse

Landscaper

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

How We See Video

Multiplication Algorithms

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

The Ultimate Field Trip

Multiplication Problem Solving with Multi-Digit Factors

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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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

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Multiply Multi-Digit Whole Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

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

Engage

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Explain

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Evaluate

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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 eﬃcient strategies based on knowledge of place value and properties of operations to ﬂuently multiply multi-digit whole numbers.

What prompts will be used?

What does mastery look like?

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I can ﬂuently multiply multidigit whole numbers to solve authentic problems.

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SCOPE 1

Divide Multi-Digit Whole Numbers Scope Introduction SCOPE SUMMARY Moving from one-digit divisors to two-digit divisors is a huge leap for many students. This scope continues the work with strategies and models, such as rectangular arrays, area models, and algorithms. Numerous opportunities are needed for students to continue to build understanding of place value and the properties of operations as they relate to division. Representations and explanations are expected. Student Expectations

VERTICAL ALIGNMENT

5.NR.2.2 Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.

Background Knowledge

Future Expectations

Fourth grade extends division to include whole number quotients and remainders with up to fourdigit dividends and one-digit divisors. Students divide by using strategies based on place value, the properties of operations, or the relationship between multiplication and division.

Division strategies learned in ﬁfth grade are extended to dividing multi-digit numbers including decimals by using place value, arrays, area models, and the standard algorithm in sixth grade. Students also use their understanding of division to divide fractions by fractions.

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

use area models to solve division equations.

•

relate division to multiplication

•

solve for partial dividends, whole dividends and partial quotients for multi-digit problems using area models.

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: •

divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors using various strategies.

Students move onto the Explore activities and come back at the end of the explorations to complete 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. Notes

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Explore

Explain

Elaborate

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Intervention

Acceleration

Rectangular Arrays In this exploration, students will be designing parking lot layouts for different car dealerships’ designs to determine how to arrange their total number of cars into equal rows. Students will: •

use manipulatives to build array models by decomposing the totals.

•

describe the solution and write an equation.

Explore 2

Explore 1

EXPLORE ACTIVITIES

In this exploration, groups of students will solve a realworld problem about a farmer. Students will: •

model division of larger numbers (up to 4 digit by 2 digit) using area models.

•

write a solution.

•

write an expression.

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

Area Models

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Algorithms In this exploration, students will: •

connect the use of area models to using partial quotient models by ﬁrst estimating

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

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Divide Multi-Digit Whole Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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ACCESSING PRIOR KNOWLEDGE Students use area models to solve division equations and relate division to multiplication. This activity is intended to assess mastery of the following standard(s): 4.NR.2.4 Solve authentic division problems involving up to 4-digit dividends and 1-digit divisors (including whole number quotients with remainders) using strategies based on place-value understanding, properties of operations, and the relationships between operations.

Materials

Preparation

Printed •

•

Print the Student Handout for each student.

1 Student Handout (per student)

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

Distribute the Student Handouts to all students. Ask students to look at the ﬁrst problem. Explain that the model is showing a division problem. Discuss the following question: a.

5. 6. 7.

Give students time to ﬁnd each of the partial dividends and the whole dividend. Have students look at the second problem. Discuss the following question: a.

8. 9.

10.

Can you use another operation to solve for the dividend? Yes, multiplication

How is this problem similar to the ﬁrst problem, and how is it different? We are still using area models to break down the solution, but now we are ﬁnding the partial quotients and not the partial dividends. We will use division to complete the problem.

FACILITATION TIP Refresh students about how multiplication and division are opposite operations. Provide students with two or three examples to access prior knowledge. FACILITATION TIP Direct attention to how the tables are different and the written expressions are different.

Give students time to ﬁnd each of the partial quotients and the whole quotient. Facilitate a class discussion about the students’ answers to the division problems. 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 this gap in prior knowledge before moving on to other parts of the scope. Notes

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Divide Multi-Digit Whole Numbers Hook – Carnival Fundraiser ACTIVITY PREPARATION Students divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors by using various strategies.

Materials

Preparation

Printed •

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1 Carnival Fundraiser (per group)

Part II

Reusable • • • •

Plan to show the Phenomena Video.

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1 Phenomena Video (per class) 1 Projector (per class) 1 Whiteboard or piece of paper (per student) 1 Dry-erase marker (per student)

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Plan to have the students work in groups of 3 or 4 to complete this activity. Print the Carnival Fundraiser for each group. Alternatively, plan to project Carnival Fundraiser for the class.

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

FACILITATION TIP

Have students write down the information from the scenario and what are possible strategies to solve the 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.

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DOK-1 What do we know? We know that three grade levels will be combining their totals before dividing them equally among the teachers that teach those grade levels.

DOK-2 What is the first thing you think we would need to know to solve the problem, and what operation would you use? We need to know how much each grade level raised during the carnival. I think we would need to add the totals raised by kindergarten and first and second grade together and then the third, fourth, and fifth grades together.

DOK-1 What operation would we need to use to equally split the money among the teachers that taught those grade levels? I think we would need to divide since they said they would equally share the money.

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Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

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

DOK-1 What do we know? We know that three grade levels will be combining their totals before dividing them equally among the teachers that teach those grade levels.

Give each student a whiteboard or sheet of scratch paper and dry-erase marker. Divide the class into small groups of 3 or 4 students. Give a Carnival Fundraiser to each group, or project it for the class. Allow students to determine how much money each teacher will receive. Review the problem, and allow students to solve it. As students are working in groups, walk around to check for understanding. Discuss the following questions: a.

DOK-2 What did you do to find out how much money the kindergarten and first and second grade teachers were given from the fundraiser for their students and classrooms? We first added the amounts raised by all three grade levels. We added 358 + 439 + 409 = 1,206. We knew that we needed to divide the money raised by the total number of teachers that teach kindergarten and first and second grade. Since there are 18 teachers, we knew we needed to divide $1,206 by 18. We used an area model to divide. It looked like this:

FACILITATION TIP Have students review their ideas from the beginning of the lesson. With the additional information, ask students: “What operations, data and strategies are needed to address the problem?”

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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.

FACILITATION TIP Kindergarten and ﬁrst and second grade teachers each got $67 to spend on their classrooms.

Be sure students are adding the correct grade levels while monitoring. Have students check their work when ﬁnished with another group.

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Divide Multi-Digit Whole Numbers Hook – Carnival Fundraiser b.

STEMscopes Tip

DOK-2 How much money did the third-, fourth-, and ﬁfth-grade teachers get for their classrooms? We used an equation to solve this problem. We added the money raised by the three grade levels ﬁrst. We got a total of $1,664 raised by all three grade levels. We then used a partial quotients model to divide. It looked like this:

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.

Third-, fourth-, and ﬁfth-grade teachers got $104 each for their classes. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Divide Multi-Digit Whole Numbers Explore 1 – Rectangular Arrays ACTIVITY PREPARATION Students model division of larger numbers using base ten blocks to build arrays.

Standards for Mathematical Practice • • •

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

Materials

Preparation

Printed • • •

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

• • • •

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Scenario Cards for the class. Place 4 sets of base ten blocks into containers for each group so they can be distributed and collected easily. •

Reusable • • •

4 Sets of base ten blocks (per group) 5 Laptops (per group, optional) 4 Containers (per group)

•

Prepare 5 stations around the room with the following materials: • • •

• •

Due to the size of the numbers students will be decomposing and dividing, they will need access to large quantities of blocks. Several sets will be needed at each station to create these large arrays. Another option is to have students use digital manipulatives.

1 Scenario Card 4 sets of base ten blocks 5 laptops, if available, to practice using digital base ten block manipulatives

For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Students will be using array models to solve the problems. Arrays are a series of rows and columns that are evenly distributed. FACILITATION TIP Arrays allow students to visualize and adjust the base ten blocks to solve the problem. 140

2. 3. 4.

Read the following scenario to the class: You own a business in which you help car dealerships design their parking lot layouts to determine how to arrange their total number of cars into equal rows. The criteria for each dealership you will be helping is listed on the Scenario Cards. Figure out how to arrange the cars at each dealership so they will best ﬁt on the lot. Make sure base ten blocks are available for each group of students. Assign each group of students a station to begin working at. Give each student a Student Journal. Students can use the base ten blocks or the digital manipulatives to represent cars needing a parking space. Before starting on the scenarios at their stations, practice in a whole group setting. Read the following scenario to the class: Anderson Automotive will receive 1,242 cars by the end of the week. They have enough space for 23 rows of cars. Plan how to arrange the dealership’s parking lot to determine how many cars they should park in each row. © Accelerate Learning Inc. - All Rights Reserved

6. 7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

Instruct students to build a model of the arrangement of cars. They should record their plans on the backs of their Student Journals. Be sure to remind students that their arrays need to be rectangular, meaning they have an equal number of units in each row and column. Give student groups an opportunity to share how they ﬁgured out their arrangements of cars. Record student thinking visually so students can see there is more than one way to solve the problem. This can be done using the virtual base ten blocks, or it can be drawn on the board. Discuss the following questions: a.

DOK-1 When you build a rectangle with the same number of pieces in each row, what is that type of model called? It’s called an array.

DOK-1 Is this scenario looking for the number of groups or the number in each group? Number of cars in each group/row. DOK-2 How do you know? The problem told us the number of groups/ rows is 23, and we have to ﬁnd how many cars will go in each row.

DOK-1 What number in your equation and model represents the number of groups? 23

DOK-1 What number in your equation and model represents the number in each group? 54

Intervention

Acceleration

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.

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e. DOK-2 What number sentences can we use to represent our seating arrangement? 23 rows × 54 in each row = 1,242 cars; 1,242 cars ÷ 23 rows of cars = 54 in each row f.

DOK-3 Explain how you decomposed the number to build your array. I started by building my number with thousands, hundreds, tens, and ones. I then regrouped thousands/cubes into hundreds/flats. I started building my array by using two flats and 3 rods to create my 23 rows from the problem. I kept lining up my remaining flats and rods until I saw they would not make an equal rectangular array. I had to regroup some flats into rods and then finally some rods into units. I ended up with a rectangular array that had 23 rows with 54 (5 tens and 4 ones) in each row.

Sample student models using the digital manipulatives:

FACILITATION TIP Have students direct you how to build an array using the virtual base ten blocks.

h. There is more than one equation that can represent the array. Use the FACILITATION TIP pen tool on the virtual manipulative screen or draw on the board to show Challenge students to decompose the students how the array can be decomposed by place value. Lead them numbers and create another equation to through the process using the following questions: represent the array. i. DOK-1 How many thousands did we use? None, we had to regroup. FACILITATION TIP ii. DOK-1 How many ﬂats/hundreds did we use? 10 ﬂats = 1,000, You should be modeling the process for the so 10 hundreds students. Chunk the process into smaller iii. DOK-1 How many rods/tens did we use? What is the value of tens? pieces for students to implement. 23 rods = 230 © Accelerate Learning Inc. - All Rights Reserved

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Divide Multi-Digit Whole Numbers Explore 1 – Rectangular Arrays iv.

DOK-2 What expression could we use to show just how we divided up the tens? First, we distributed the rods among the 3 rows we had left to form in the divisor, so we used 150 ÷ 3 = 50. We still had 8 tens (80) to distribute, so we divided that by the 20 rows that were already made in the divisor, so we used 80 ÷ 20 = 4.

DOK-2 How can we show this step? We can use parentheses to show the expressions by themselves.

vi.

DOK-1 How many ones did we use? What is the value of them? We have 12 ones/units left.

vii. DOK-2 What expression can we use to show how we divided up the ones? 12 ÷ 3 = 4 viii. DOK-2 We can break apart, or decompose, an array and represent it using more than one equation. How can you represent with an equation the breaking apart or decomposition of an array so that each expression in parentheses represents a section of the array and is the same as saying 1,242 ÷ 23 = 54?

FACILITATION TIP Have students write both equations on their Student Journals for Scenario 1.

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.

FACILITATION TIP Informally assess students and arrange groups to support different levels of students.

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Once students have completed the practice scenario problem in a whole-group setting, they will begin working on the scenarios at their assigned stations. Students can draw squares for ﬂats, lines for rods, and dots for units. They will then rotate to the remaining stations and repeat the process. a.

Students may use base ten blocks or use the digital manipulatives on the laptops for support.

Students may need to start by drawing a model of the dividend before drawing the array. Students could always try to solve the problems using drawings and check their work with the blocks.

11.

12. 13.

14.

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 is given in the problem? Answers will vary.

DOK-1 What information are you trying to ﬁnd? Answers will vary.

DOK-2 Are you solving for the number of groups or number in each group? How do you know? Answers will vary.

DOK-2 How did you decompose the total to build your array? Answers will vary.

Once all groups are done, allow students to share how they solved each problem using the Math Chat guiding questions below. As each group shares their thinking, record their thoughts visually or allow them to demonstrate their own thoughts. This can be done using the virtual base ten blocks, or it can be drawn on the board. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 How did you decompose each total and use your knowledge of base ten to build each array? I built each number first and then started moving them into the given number of rows or columns to start creating my array. When I got to a point of unequal rows or columns, I had to regroup some blocks for smaller place values until I finally created a rectangular array with equal rows and columns. • DOK-3 How did you solve the problem? Student responses will vary based on which problem is being discussed. We used the blocks to build the number and then divided it out between the number of rows we needed. Sometimes we had to trade in a block for smaller place values. • DOK-2 What is the relationship between the array and your equations? The total amount shown in the array is the dividend in my equation. It is the total we are splitting up into equal groups. The second number in the equation is the divisor, which is either our groups or size of groups. The final number is our quotient, which is either our groups or size of groups. • DOK-2 How could you use your arrays to help check your work? I could use multiplication by multiplying the rows by columns to see if my answer equals the original total in each problem. •

FACILITATION TIP Different group members can rotate with different roles like reading the scenario, creating the array model, and writing the equations.

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.

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FACILITATION TIP Remind students that conceptualizing these values with the array model is a helpful thinking tool for later math standards. Reassure them that ﬂuency with these visualizations will help them solve more diﬃcult problems in later standards and in real life.

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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Divide Multi-Digit Whole Numbers Explore 2 – Area Models ACTIVITY PREPARATION Students model division of larger numbers using area models.

Standards for Mathematical Practice • • •

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

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Area Model Cards (per pair) 1 Set of Crop Design Cards (per pair) 1 Exit Ticket (per student)

•

Reusable •

•

1 Dry-erase marker (per pair)

Consumable •

•

1 Resealable bag (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 Area Model Cards, on card stock for durability, for each pair of students. Cut the cards apart, and place them in a resealable bag. Test to make sure student desks can wipe clean after being written on by a dry-erase marker. If not, plan to use another dry-erase surface, such as a whiteboard. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS 1. 2. 3. FACILITATION TIP

Students will be using area models as a different strategy than array models.

5. 6. FACILITATION TIP Model as a class how to create an area model for the ﬁrst scenario. Students will need to determine if they are solving for length or width. 144

Give a set of Area Model Cards and a dry-erase marker to each pair of students. Give a Student Journal to each student. Introduce students to the Area Model Cards by showing them that the 1,000 card represents a row of 1,000, a 100 card represents a row of 100, and so on. Invite students to model the following numbers using the cards: a.

1,265

2,078

931

3,609

Discuss the relationship of the cards to the place value of each digit in the given number. Read the following scenario to the class: Farmer Bill wants to designate several areas on his farm for growing different crops. He has given you some details, such as the area of the space and either the length or width of each crop’s area. He needs your help drawing a model of each space. He will use this information later to plan how much soil and how many seeds he needs to purchase. Can you help him draw an area model for each crop’s space on his farm? Give each pair of students a set of Crop Design Cards. © Accelerate Learning Inc. - All Rights Reserved

10.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What information are you given? We know the space is 1,078 square feet, which is our total. We know the space measures 14 feet wide, so that is our number of groups.

DOK-1 What information are you solving for? Are you solving for the width (number of groups) or the length (number of objects per group)? We are solving for the length of the space, which is the number of feet per row.

Allow time for students to talk with their partners about how they will represent and solve this problem. Challenge students to use the Area Model Cards to build a model of the problem. Once each group has ﬁnished their model, discuss the following questions: DOK-2 How did you know how to build your model? I knew we could put 5 tens in each row since 50 × 14 = 700; then, there is 378 left. I knew we could put 2 tens in each row, since 20 × 14 = 280; then, there is 98 left. Since we could not put any more tens, we had to move to ones, and 14 × 7 = 98, so we knew we could put 7 ones in each row. So 14 groups of 50 plus 14 groups of 20 plus 14 groups of 7 = 14 groups of 77.

DOK-2 Why couldn’t you use any 100s cards? We couldn’t use any 100s cards because 14 rows of 100 would equal 1,400, and that is more than our total. I had to trade in 10 100s cards for 10s cards.

DOK-2 How is this model similar to your base ten arrays from Explore 1? I can see from my model my groups of tens and ones. In the base ten array, the total 1,078 is the same as if we were to total all the ﬂats, rods, and units in the array. For the area model, I could not use any 100s cards because that would put us over our total, so we had to trade in those cards for 10s cards.

DOK-2 What were the dimensions of the crop of corn? The width of the crop was 14 feet, and the length was 77 feet.

e. DOK-1 What was the total area of your model? The total area was 1,078 square feet.

12. 13.

Acceleration

Read the ﬁrst Crop Design Card as a whole group. As a class, discuss the following questions:

11.

Intervention

Have students outline their models on their desks (or other dry-erase surfaces) using the dry-erase markers. Students should draw a line between the tens and the ones. Students should remove the cards and label the dimensions of their drawings and the area of each piece. Explain that this is called an “area model.” The inside of the rectangle is the area, or the total. The number on the left is the divisor. It shows how many rows or groups there will be. The numbers across the top combine to make the quotient, or how many will be in each row or group. a.

FACILITATION TIP Students will need to decompose the total number using the the factor provided. Provide base ten blocks to assist students.

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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.

FACILITATION TIP Relate the area model to previous knowledge of calculating area using the formula length x width.

DOK-2 What equations could we use to represent this problem? 1,078 ÷ 14 = 77 or (700 ÷ 14) + (280 ÷ 14) + (98 ÷ 14) = 77 i. Reinforce how we can use expressions in parentheses to represent each piece of an area model. When we combine them, we can create a new equation to represent the problem. Notes

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Divide Multi-Digit Whole Numbers Explore 2 – Area Models 14.

FACILITATION TIP

15.

Monitor groups and check students’ area models. Address misunderstandings by modeling and guiding students through the process.

FACILITATION TIP If students understand how to create an area model, they can use it to complete the rest of the Crop Design Cards.

16.

Encourage students to collaborate to solve the remaining problems on their Student Journals by using the Area Model Cards. For each area model they build, they should trace it on their dessk with the dry-erase markers and label the dimensions and area of each piece. Students should record what their drawings look like on their Student Journals. a.

Students should always start with the largest place value and think, “How many [largest place value] can I place in each row?”

Have students trade in, or regroup, larger place values for smaller place values, just like they did with the base ten blocks.

Student knowledge of basic multiplication and division facts can help them when dividing each place value.

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

DOK-2 How is this model similar or different from the arrays you have built before? It is similar because we are still building a rectangle. It is different because the area model just shows the total of one piece, while an array shows each piece.

DOK-2 How did you ﬁgure out how many tens and ones went into each row? Answers will vary. We had to trade in the _____, combine them with the _____ we already had, and divide those between each group. We ended up with _____. This allowed us to place _____ in each group because _____ × _____ = _____.

DOK-2 What equation could we use to represent the problem? We could use _____ ÷ _____ = _____.

DOK-2 What is another way we could write this equation? We could use expressions for each piece of the model.

DOK-1 Challenge students who are ready to use an area model to divide larger numbers even if we have no cards or blocks. Give students the equation 1,175 ÷ 25 = ?. We know we are splitting up the total into 25 groups. a.

DOK-1 Draw a vertical line that will become the left side of the area model. Label it 25.

DOK-2 We know the total on the inside is 1,175 and there are 25 rows. We need to ﬁgure out how many are in each row so we know the length of our model. Let’s start with the greatest place value ﬁrst. Our dividend goes to the thousands place. Can we put a thousand in each row? Explain. No, we only have one thousand, so we will need to split it up into hundreds.

DOK-2 How many hundreds did you end up with, and how many could you put in each row? We now have 11 hundreds, but that will not ﬁt in 25 rows.

DOK-2 What can we do to ﬁt 11 hundreds in the 25 rows? We need to regroup the hundreds into tens.

FACILITATION TIP With area models, a rectangle is decomposed into smaller rectangles with each length and width being the factors.

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.

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Explore

Explain

Elaborate

Evaluate

e. DOK-2 If we have 4 tens in each row, what is the value we’ve placed in each row? How much of the total have we used up? We put 40 in each row. We have used 1,000 because 40 × 25 = 1,000. i. DOK-1 Draw this ﬁrst section of the area model, and record how much of the total has been used.

DOK-2 Now that we have split up all the hundreds, what’s next? We do not have enough hundreds or tens to ﬁt in 25 rows. We need to regroup the hundreds and tens into ones. 1 hundred = 100 ones added to 7 tens = 70 ones added to 5 ones that we already have. That makes 175 ones.

DOK-2 If we have 7 ones in each row, what is the value we’ve placed in each row? How much of the total have we used up? We have put 7 in each row because 7 × 25 = 175. We have used up the remainder of the total. ii. DOK-1 Draw the next section of the area model, and record how much of the total has been used.

Intervention

Acceleration

FACILITATION TIP Different group members can rotate with different roles like reading the scenario, creating the array model, and writing the equations.

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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.

h. DOK-2 What expression could we use to represent the ﬁrst section of our area model? We could use (1,000 ÷ 25). i. DOK-2 What expression could we use to represent the second section of our area model? We could use (175 ÷ 25). j. DOK-2 How could we combine those expressions into one equation to represent the quotient? We could add each expression together: (1,000 ÷ 25) + (175 ÷ 25) = 47. k. 17. 18. 19. 20.

DOK-2 What is another equation we could use to represent the quotient? We could use 1,175 ÷ 25 = 47.

Have students work together as groups to draw area models to represent problems on their desks using the dry-erase markers. Students should follow the same process of drawing the left side of the area model and ﬁnding each piece, starting with the greatest place value. Ask students to record two equations for each model and a statement that explains the quotient on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

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Divide Multi-Digit Whole Numbers Explore 2 – Area Models Math Chat • FACILITATION TIP In the Math Chat, have students discuss which strategy they prefer between the area model or the array model.

•

FACILITATION TIP

•

Remind students that conceptualizing these values with models is a helpful thinking tool for later math standards. Reassure them that ﬂuency with these visuals will help them solve more diﬃcult problems in later life.

•

DOK-2 How are your area models similar to your base-ten arrays? These models are a rectangle like our base-ten arrays. The area model shows the total of the different sections of the base-ten array. For example, the area model shows the total of all of our 100s, 10s, and/or 1s we used to build our base-ten array. DOK-3 How did you determine if you were finding the groups or the size of the group? We know when building an array that our rows are our groups and our columns are the size of the group. In each problem, width and length helped us draw our model and determine if we were finding the group or size of the group. DOK-3 Why do you think we are modeling division in this way? Division is the opposite of multiplication. You can use multiplication to find the total on the inside, using both sides. This means you can use the total and one side to divide and find the missing side. DOK-2 Why would we start with the greatest place value first? That takes the most away from the dividend, and you can see if you need to break up a large piece into smaller pieces. DOK-2 Why does this model work when finding the size of each group as well as the number of groups? Each row could represent a group. You can use this model to divide any amount into equal groups.

Post-Explore 1. 2. 3.

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

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Explain

Elaborate

Evaluate

Intervention

Acceleration

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Divide Multi-Digit Whole Numbers Explore 3 – Algorithms ACTIVITY PREPARATION Students use area models, partial quotients, and the standard algorithm to divide up to a four-digit number by a two-digit number.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Preparation

Materials Printed • • •

• • •

1 Student Journal (per student) 1 Algorithms Work Mat (per pair) 1 Exit Ticket (per student)

Reusable • • •

•

1 Box of colored pencils (per student) 1 Dry-erase marker (per pair) 1 Sheet protector (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 the Algorithms Work Mat, on card stock for durability, for each pair of students. Place the work mat inside a sheet protector so students can use it as a dry-erase surface. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Part I: Division Strategies

Consider warming up with some choral skip counting of familiar multiples. Provide students with multiplication tables as needed.

FACILITATION TIP Refresh students understandings of both the array models and area models with a practice problem. 150

3. 4.

Read the following scenario to the class: The concert for this year’s hottest band just let out, and there are so many people! There are 1,134 people waiting for a shuttle to the train station, 2,464 people waiting for a bus, and 1,325 cars sitting in the parking lots, waiting for their owners. a.

Each shuttle can hold only 18 people.

Each bus can hold only 16 people.

There are 25 parking lots.

You need to help the people in charge of traﬃc ﬂow determine how many shuttles they need, how many buses they need, and how many cars are in each parking lot. Give a Student Journal to each student. Have students solve the problem on their Student Journals using an area model as a review from Explore 2. Have base ten blocks or Area Model Cards available for those students who need the added support.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Have students use a different colored pencil for each part of the problem (dividend, divisor, and quotient). Their model should look similar to the example below:

FACILITATION TIP 6. 7.

8. 9. 10.

Give an Algorithms Work Mat and a dry-erase marker to each pair of students. Students used the partial quotients strategy to solve division problems in fourth grade. Explain to students that this partial quotient model is the same except that there is a two-digit divisor instead of a one-digit divisor. Model for students how to use the same colored pencils to record what they did on the area model, but this time using the partial quotients strategy. Have students write the dividend and divisor on their Student Journals in the same colored pencil they used to write the divisor on the area model. Ask the following questions: a.

DOK-2 Can we evenly distribute 1,000 into 18 groups? Explain. No, we cannot evenly distribute 1,000 into 18 groups. Since there is more than 1 group, we will need to trade the 1 thousand for 10 hundreds. Now we have 11 hundreds.

DOK-2 How can we evenly distribute the 11 hundreds into 18 groups? We won’t be able to evenly distribute them into 18 groups, so we need to trade them for groups of ten. Now we will have 113 groups of ten.

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For the partial quotient model, students need to be very neat in the vertical alignment of each place value.

FACILITATION TIP As you are modeling the process, also model the estimating and thinking out loud for students.

i. The ﬁrst three digits in the dividend are 113, which is the same as 113 tens. Explain this relationship as you introduce the students to the Divisor Skip Count Area on the Algorithms Work Mat. 11.

Explain that the Divisor Skip Count Area on the Algorithms Work Mat can be used to write the multiples of the divisor, which will help them find the partial quotients. Instruct students to write at least the first six multiples of 18 in the skip count area of the Algorithms Work Mat (18, 36, 54, 72, 90, 108). Ask students to find a factor they could multiply 18 by to get as close to 113 as possible. a.

DOK-1 What is the ﬁrst partial quotient? The ﬁrst partial quotient is 60.

DOK-2 How did you get that partial quotient? We used skip counting to ﬁnd the multiples of 18. We knew we needed to get as close to the dividend as possible. We looked at our skip counting and saw that 113 is not a multiple of 18, but 108 is, so we knew that 1,080 could be divided evenly into 60 groups of 18. This is our ﬁrst partial quotient.

DOK-2 If you hadn’t skip-counted, what other method could you use to ﬁnd the partial quotient? We could round 18 to 20 to ﬁnd a reasonable number that was close to the divisor. We know 20 × 6 = 120, which is close to 113, so we multiplied 18 × 6 and got 108. We knew 1,080 could be divided evenly into 60 groups of 18.

FACILITATION TIP The area model, array model, and the partial quotient model are different strategies that students can use to solve division problems.

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Divide Multi-Digit Whole Numbers Explore 3 – Algorithms 12.

FACILITATION TIP Have students write partial quotient on their Student Journals for all of the scenarios.

FACILITATION TIP

13.

Project an area model on the board and discuss the similarities to the partial quotient model. 14. 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.

15.

16.

Students should write the partial quotient on the right-hand side of the line (60) with the same colored pencil they used in the area model. Students should write the amount that was distributed below the dividend with the same colored pencil they used in the area model. Students should then subtract the amount that was distributed from the dividend and write the difference with the fourth colored pencil. Ask the following questions: a.

DOK-1 What is the difference between the two numbers? The difference is 54.

DOK-1 How will you ﬁnd the partial quotient? Since we skip counted the divisor to ﬁnd multiples, we know that 3 groups of 18 is 54.

Students should write the partial quotient on the right-hand side of the line (3) in the same colored pencil they used in the area model. Students should then write the amount that was distributed below the remaining dividend with the same colored pencil they used in the area model. Students should subtract the amount that was distributed from the remaining dividend and write the difference (0) with the fourth colored pencil. Have students complete the remaining two problems using the Algorithms Work Mat. Students should transfer their information from the Algorithms Work Mat to their Student Journals using the same colored pencils they used in the ﬁrst model for each part of the problem (dividend, divisor, quotient, and difference). Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How is the partial quotients strategy similar to the area models strategy? They are similar because you are dividing out chunks of the total and adding up parts of the answer.

DOK-2 How do you know how many of a certain place value could go into each group? I skip counted the divisor to ﬁnd multiples. For example, I saw that 18 × 6 is 108, which is less than 113. Since I had only 113 tens, I knew I could put 6 tens in each group of 18 and would have some left over.

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

Math Chat FACILITATION TIP Use the Print Files to project the Math Chat questions and record student responses and any additional questions.

DOK-2 What 3 steps do you repeat at each place value when you are using the partial quotients strategy? Figure out how many of each place value can go in each group to get the partial quotient. Then, multiply the divisor by the partial quotient, and subtract that amount from the dividend that’s left. • DOK-2 Why do you subtract in the middle of a division problem? We divide one place value at a time. Once we are able to distribute some of the total, we need to subtract it from the dividend to figure out how much is left to divide. • DOK-2 How does estimation help you find partial quotients? Estimation can be used to divide rounded numbers to find a reasonable way to divide the dividend •

by the divisor. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Division Algorithm 1. 2.

Using the same scenario and the ﬁrst partial quotients example from Part I as a guide, students will solve the division problem using the standard algorithm. Have students write the dividend and divisor in Part II of their Student Journals in the same colored pencil they used to write the divisor on the partial quotients example. Ask the following question: a.

Students should write the partial quotient of 6 above the tens place using the same colored pencil used to write the partial quotient in the partial quotients example. Explain that since students are writing the 6 above the tens place, it represents 6 tens, or 60. Ask the following question: a.

For the partial quotient model, students need to be very neat in the vertical alignment of each place value.

DOK-1 What was the second operation you used? We multiplied the partial quotient of 60 by the divisor of 18. We wrote the product of 1,080 under the dividend.

DOK-1 What was the third operation you used? We subtracted the product of 1,080 from the dividend of 1,134.

Students should subtract 108 from 113 using the same colored pencil used to write the difference in the partial quotients example. Show students how to draw an arrow down from the next digit in the dividend (4) and use the same colored pencil used to write the difference of 5 to rewrite the 4 next to it, making the difference 54. Ask the following question: a.

FACILITATION TIP

Students should write 108 below the dividend, lining up the place values, using the same colored pencil used to write the product of 18 × 60 on the partial quotients example. Explain that since you are writing the product in the thousands, hundreds, and tens place, 108 represents 1,080. Ask the following question: a.

DOK-1 After you wrote the dividend and divisor in the partial quotients model, what was the first operation you used? We divided. We looked at how many times the divisor of 18 would go into the first two digits of the dividend, which were 11. The divisor wouldn’t go into 11, so we used the first three digits of the dividend, which were 113, to determine the partial quotient. We skip counted by 18 and saw the closest partial quotient was 60.

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DOK-1 What did you do with the difference of 54? We divided 54 by 18, which gave us a partial quotient of 3.

Students should write a 3 in the ones place using the same colored pencil used to write the partial quotient on the partial quotients example. Ask the following question: a.

DOK-1 What did you do next? We multiplied the partial quotient of 3 by the divisor of 18 and got 54. We wrote the product of 54 below the remaining dividend of 54.

Students should write a 54 below the remaining dividend of 54 using the same colored pencil used to write the remaining dividend on the partial quotients example. Ask the following question:

Students should subtract 54 from 54 using the same colored pencil used to write the difference on the partial quotients example.

STEMscopes Tip Spiraled Review, located in the Elaborate section, provides students with a contextual scenario used to solve four different problems. This activity helps students maintain essential knowledge, see how mathematical skills connect from one topic to the next, and experience real-world applications of previously learned skills.

DOK-1 What did you do next? We subtracted 54 from 54 and got 0.

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Divide Multi-Digit Whole Numbers Explore 3 – Algorithms 10.

Explain to students that the standard algorithm uses the same three-step process used in the partial quotients model. a.

Divide: How many times will the divisor go into the first two digits of the dividend? i. If the answer is 0, look at the first three digits. ii. Write this number above the hundreds place (or tens place, if you had to look at the first three digits) in the same colored pencil used to write the partial quotients.

i. Write it below the dividend, lining up the place values, using the same colored pencil used to write the product.

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.

ii. The ones place of the product should be in line with the number written on top during the division step. c.

12.

Take time during the Math Chat to reassure students that being able to ﬂuently divide multi-digit numbers may keep them from getting confused or taken advantage of in the future. This skill is also a thinking tool that will help in problem solving in real life and later math standards.

Subtract: Subtract that product from the ﬁrst two (or three) digits of the dividend. i. Draw an arrow down from the next digit of the dividend, and rewrite that number next to the difference, using the same colored pencil used to write the remaining dividend in the partial quotients example.

11.

FACILITATION TIP

Multiply: Multiply that number by the divisor.

Repeat those three steps until there is no dividend remaining.

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

DOK-2 How is the standard algorithm similar to the partial quotients strategy? In both strategies, we divide the total amount into groups determined by the divisor, multiply the partial quotient by the divisor, subtract the product from the dividend, and repeat the process until there is no dividend remaining.

DOK-1 If you subtract the product from the remaining dividend and the difference is greater than the divisor, what does that mean? It means the dividend could have been divided into more groups.

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

Math Chat DOK-2 What is the relationship between using partial quotients and the standard algorithm? In the standard algorithm, we wrote digits in place values instead of writing the whole value. Otherwise, the process is almost the same for both strategies. • DOK-1 If you subtract the product from the remaining dividend and the difference is greater than the divisor, what does that mean? It means the dividend could have been divided into more groups. •

Post-Explore 1. 2. 3. 4.

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Divide Multi-Digit Whole Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

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

Anchor Chart

Show What You Know, Part 2

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

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

Algorithms 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

Care Packages

Janet Norwood

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

Joining the Family Business

Division Algorithms with Remainders

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

Let the Games Begin!

Division Problem Solving with Multi-Digit Divisors

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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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

DIVIDE MULTI-DIGIT WHOLE NUMBERS

Divide Multi-Digit Whole Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

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

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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 divide up to four-digit whole numbers by two-digit whole numbers using what I know about place value, properties of operations, and the relationship between multiplication and division.

What prompts will be used?

What does mastery look like?

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I can use base-ten models, rectangular arrays, area models, and equations to illustrate and explain calculations that result in a whole-number quotient.

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SCOPE 1

Numerical Expressions Scope Introduction SCOPE SUMMARY

Student Expectations

Fifth-grade students understand the purpose of grouping symbols in numerical expressions and how expressions are affected by their use. Students use their knowledge of mathematical operations and the algebraic order of operations to solve expressions. In addition, students write simple expressions that represent given situations (for example, 3 more than 15 is shown as 3 + 15). Expressions are also examined by considering the relationships of the numbers without having to actually solve the problems. For example, 4 × (75 + 25) is four times as large as the sum of 75 and 25.

5.NR.5.1 Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

These specific concepts are not taught prior to fifth grade. However, prerequisite skills are introduced beginning in third grade. Students apply properties of operations to multiply and divide. In fourth grade, students are tasked with interpreting a multiplication problem as a comparison. These two skills help to prepare students to work with expressions in fifth grade.

As students move from ﬁfth-grade mathematics into sixth, they will continue to build on these concepts. Sixth graders will begin to read, write, and evaluate expressions that represent operations with numbers and variables in realistic situations. They apply their understanding of the properties of operations to equivalent expressions as well as learning how to write and evaluate them. The concepts in this scope will also become relevant in sixth grade as students begin to develop their understanding of the greatest common factor and least common multiple.

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

represent verbal statements as multiplication equations.

•

compare verbal statements for similarities, differences, and type of operation.

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: •

write and interpret simple numerical expressions using parentheses without having to calculate the solutions.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 160

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Acceleration

Order Matters In this exploration, students will discover the value of a standard order of operations. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

realize how failing to follow the order of operations can change the value of an expression.

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

Grouping Symbols In this exploration, groups of students will solve a scenario where they determine how much money a catering company spent at the kitchen supply store. Students will: •

create expressions based on word problems.

•

evaluate and compare numerical expressions that do not involve exponents using parentheses.

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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. Interpreting Expressions In the ﬁnal exploration, students will help solve a scenario about helping sort through booth sales. Students will: •

write, interpret, and compare numerical expressions without evaluating them.

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

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Numerical Expressions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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ACCESSING PRIOR KNOWLEDGE Students write multiplication sentences for given word expressions. This activity is intended to assess mastery of the following standard(s): 4.NR.2.2 Interpret, model, and solve problems involving multiplicative comparison.

Materials

Preparation

Printed •

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1 Slideshow (per class)

Reusable •

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Plan to have students work in groups of 2 or 3 to complete this activity. Prepare to project the Slideshow for the class, or print the Slideshow for each group.

1 Projector or document camera (per class)

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

Project the Slideshow for the class, or distribute to each group. Read the ﬁrst bullet with students, and ask students to convert the words into an equation. Invite students to share their equations with the class. Facilitate a class discussion about their equations. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Discuss the following question: a.

6. 7.

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.

Is there exactly one way to represent this number sentence? Answers may vary. There is only one way to represent the problem. The two factors, 6 and 4, can be in either order, and the outcome will still be 24.

Repeat steps 2–5 with the other three problems. Discuss the following questions: a.

Are there any similarities among all of the problems? They are all showing multiplication; they have repeated groups; there is a total in each.

Are there any differences? Some sentences start with the total and then give the factors; some start with the factors ﬁrst and then give the total; some are real situations.

Explain what operation these equations are related to, and explain why. Multiplication and division are inverse operations; therefore, they are related.

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

FACILITATION TIP Cover up all of the phrases and only reveal one at a time. Take time to assess student knowledge. Converting words into math equations or expressions is an important skill that will be used frequently in algebra.

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Numerical Expressions Hook – Bake Sale Statistics ACTIVITY PREPARATION Students write and interpret simple numerical expressions using parentheses without having to calculate the solutions.

Materials

Preparation

Printed • •

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1 Set of Equation Cards (per pair) 1 Student Handout (per pair)

Part II •

Reusable • •

Plan to show the Phenomena Video.

• •

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

Plan to have students work in pairs to complete this activity. Print the Student Handout for each pair of students. Print a set of Equation Cards for each pair. Cut the cards apart, and place them in a resealable bag.

Consumable • •

1 Piece of scratch paper (per pair) 1 Resealable bag (per pair)

PROCEDURE AND FACILITATION POINTS 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.

Part I: Pre-Explore 1.

4. 5. FACILITATION TIP

DOK-2 What steps will need to be taken to solve the problem? We will think about the situation carefully, use the cards to set up the equation, record the equation on the Student Handout, and solve (if we want to do the bonus). Then, we will create a scenario/problem for our classmates, set up the equation to solve it, and solve it (if we want to do the bonus). We will also solve a scenario our classmates created for us.

FACILITATION TIP

In addition to having them recall the term distributive property, ask students to explain what they do in a math equation to apply this property.

DOK-1 What property are we using when we multiply numbers that are being added inside parentheses? Distributive

DOK-3 Is there more than one way to solve a problem like this? Explain. Yes, we could use the distributive property (multiply each number within the parentheses and add them together), or we could ﬁnd the sum of the addends inside the parentheses and then multiply them.

Allow the students to discuss the problemsolving steps in groups before they share the steps with the class.

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DOK-3 Do you think it will be more diﬃcult to solve the problem that already exists or to create your own problem? Why? Answers will vary. Use this question to promote discussion about mathematical thinking. Accept all answers that have reasonable explanations.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

3. 4.

8. 9. 10.

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

DOK-2 What steps will need to be taken to solve the problem? We will think about the situation carefully, use the cards to set up the equation, record the equation on our Student Handout, and solve (if we want to do the bonus). Then, we will create a scenario/problem for our classmates, set up the equation to solve it, and solve it (if we want to do the bonus). We will also solve a scenario our classmates created for us.

DOK-1 What property are we using when we multiply numbers that are being added inside parentheses? Distributive

DOK-3 Do you think it will be more diﬃcult to solve the problem that already exists or to create your own problem? Why? Student answers will vary. Use this question to promote discussion about mathematical thinking. Accept all answers that have a reasonable explanation.

Assign students a partner or let them choose partners. Give each pair of students a bag of Equation Cards, scratch paper, and the Student Handout. Instruct students to set up the equation for Victoriana using the Equation Cards, and then write the equation on the Student Handout. Explain to students if they do want to find the numerical value of the solution, that is a bonus. Encourage students to do this based on their abilities and interest levels. Give students about 5 minutes to solve the bake sale problem. When time is up, have each student pair meet with another pair to compare how they think the problem should be solved and their reasoning. The equation should represent the scenario and solve for the answer. Then, have students return back to their original pairings. Give students 5 minutes to create a new scenario. Have each pair find the appropriate equation to solve the problem (and solve it if they choose) on scratch paper so they leave the blank Student Handout for the other group to use. They should then pass their scenario to the pair they worked with earlier and receive a scenario from that pair. Give students 5 more minutes to figure out the equation that would solve the new scenario. Again, as a bonus, student pairs may actually solve the problem if they choose, but this is not required. Walk around during the group work, and assist any groups who are having trouble coming up with a scenario or finding equations or solutions. After the 5 minutes, have the two student pairs meet and discuss the two scenarios, the equations, and solutions (if applicable) that they found. Discuss the following questions: a.

Intervention

Acceleration

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.

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FACILITATION TIP Review with students the problem-solving strategies that they discussed at the beginning of the lesson.

FACILITATION TIP To support students in creating their own scenarios, brainstorm a few ideas as a whole class. You may need to consider scenario ideas before the lesson to guide the students if needed.

DOK-2 How did you solve the problems? We read each problem carefully. We used the cards to lay out the equation that we felt would solve the problem. We then recorded the equation. We solved the problem as a bonus.

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Numerical Expressions Hook – Bake Sale Statistics

FACILITATION TIP Have partners discuss their levels of understanding of the distributive property and describe what still confuses them about it.

DOK-2 What was the equation you created for the bake sale problem for Victoriana to use? 7 × (40 + 100) = ?

DOK-1 Did you solve the bake sale scenario? Answers will vary. If yes, the solution should be 980 (280 cupcakes and 700 cookies).

DOK-1 Do you feel that you have a strong understanding of the distributive property and how to set up and solve numerical expressions? Answers will vary based on students’ success during the activity and conﬁdence level.

e. DOK-3 Which was more diﬃcult—creating a problem for your classmates or solving the problem your classmates created for you? Answers will vary. Accept any answer accompanied by a reasonable explanation. Notes

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Numerical Expressions Explore 1 – Order Matters ACTIVITY PREPARATION Students discover the value of a standard order of operations and how failing to follow the order of operations can change the value of an expression.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

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

Reusable • • • • • •

1 Projector (per class) 1 Set of 4 chenille stems (per station) 4 Sets of base ten blocks (per class) 6 Sets of 100 color tiles (per class) 1 Dry-erase marker (per student) 6 Plastic bins (per station)

• • • • •

•

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Station Cards, on card stock for durability, for the class. Cut the cards apart and place each card at different locations around the classroom. Gather 3 sets of base ten blocks. Gather sets of chenille stems for each group. Each group will use a set of chenille stems for Part I of this Explore activity. Those same chenille stems will be placed at stations for Part II of this Explore activity. Gather 6 sets of 100 color tiles. Each group will use a set of color tiles for Part I of this Explore activity. Those same color tiles will be placed at certain stations for Part II of this Explore activity. For Part II of this Explore activity, place the manipulatives as follows: The Eggs and Cotton stations will each have a set of 100 color tiles and a set of chenille stems placed in a plastic bin at that station. • The Carrots, Corn, Potatoes, and Apples stations will each have a set of base ten blocks and a set of chenille stems placed in a plastic bin at that station. •

• • •

Prepare to project the Scenario Card for the class. 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 and Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS Part I: Cows FACILITATION TIP Create a connection with students’ experiences with farms. How many have family members that work on or own farms? How many have a garden that they use to grow food? Who has been on a ﬁeld trip to a local farm?

2. 3. 4.

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Read the following scenario to the class: Farmers are an essential part of keeping our country fed. Without farmers, we would have an extreme lack of meat, fruits, vegetables, grains, dairy products, and so much more. Farmers put in long hours, and they need your help on the farm to keep track of everything they produced and collected for the day. Project the Scenario Card for the class, and give a Student Journal to each student. Give a set of color tiles and chenille stems to each group. Encourage each group to use the color tiles to solve the problem. © Accelerate Learning Inc. - All Rights Reserved

7. 8.

10.

11.

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Explain

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

DOK-1 How can you ﬁgure out how many gallons of milk was collected? I know that one cow produced 15 gallons of milk, so I will represent that amount with 15 color tiles. I also know that 3 cows produced 9 gallons of milk each, so I will make 3 groups of 9 color tiles. I can combine those amounts to ﬁnd the total.

DOK-2 What two operations are you using to solve this problem? Explain. We are using multiplication and addition. We can multiply the 3 groups of 9 to ﬁgure out how many gallons the three cows produced and then add on the 15 gallons the other cow produced.

Engage

DOK-2 Does it matter which operation you need to do ﬁrst in order to solve? Explain. Yes, the order of operations matter because if we add ﬁrst, that will mess up the number we will be multiplying by.

Tell students to use the dry-erase marker to write an expression on their desk that would represent the entire problem and write their solution to the problem. Have each student pair share their expression with another student in their groups and discuss their thinking. Write the expression 15 + 3 × 9 on the board. Encourage students to write this same ﬁrst expression on Part I of their Student Journals. Ask questions such as the following: a.

DOK-1 What is the root word of evaluate evaluate?? Value

DOK-1 Why do you think we call this process evaluating an expression? We are ﬁnding out its value.

DOK-1 How could we evaluate this expression? Answers may vary. We could perform operations from left to right or multiply and then add.

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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.

Invite students to solve this problem in two different ways. Encourage students to multiply and then add but then to also try solving by adding ﬁrst and then multiplying. a.

DOK-1 What value did you get when you solved from left to right? We got 162 gallons of milk.

DOK-1 What value did you get when you multiplied ﬁrst and then added? We got 42 gallons of milk.

DOK-2 We used the same operations for the same answers but got different values. Why are the values different? Answers may vary. When we perform operations in a different order, we are affecting other numbers within the problem, which will then change the ﬁnal value. If we do the operations in the correct order for what is being explained in the problem, then we can ﬁnd the correct value.

Explain to students that sometimes certain parts of expressions need to be grouped together and evaluated ﬁrst, rather than just evaluating an expression from left to right. Depending on the problem, it might be necessary to do operations in a certain order other than simply left to right. There are symbols we can use to organize these steps. Encourage students to analyze their color tiles and work together with their groups on answering and modeling the following questions: a.

DOK-2 How can you use the chenille stems to represent the grouping for an operation? I can use the chenille stems to group the color tiles representing the 3 groups of 9. This shows me that I will be multiplying these numbers ﬁrst. Once we have found the product, we can add on the 15 gallons of milk from the other cow.

FACILITATION TIP Pause here to use the Picture Vocabulary and explain the order of operations step by step. The order of operations can be compared to the rules of the road that must be followed so that all drivers are kept as safe as possible and get to where they want to go. Mathematicians use the order of operations so that they can all communicate with symbols and numbers clearly.

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Numerical Expressions Explore 1 – Order Matters b.

12. FACILITATION TIP

13.

The order of operations will be a key concept for students as they attempt more complex math standards.

14.

Edit the original expression on the board to now include parentheses: 15 + (3 × 9). Encourage students to write this second expression on Part I of their Student Journals. Explain to students that there are also rules we can use to organize the steps when solving expressions. These rules make up a standard procedure used in mathematics called the order of operations. Tell students that the ﬁrst thing to do in the order of operations is to solve what is in parentheses. Ask students the following question: a.

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.

15.

16. 17. 18.

19.

20.

DOK-2 What does the addition of parentheses do for this expression, and how does this new version relate to the original problem? The parentheses group the steps we need to perform together before we perform another operation. The parentheses make the expression match the order of the problem. With the parentheses, we get the value of 42.

DOK-1 How are multiplication and division related? Division is the opposite of multiplication.

Explain that since division is the opposite, or inverse, of multiplication, they create related equations, as in 8 × 4 = 32 and 32 ÷ 4 = 8. Therefore, multiplication and division expressions are done ﬁrst in the order in which they appear, working left to right. Emphasize that neither is more important than the other, so they are performed in order from left to right. DOK-1 How are addition and subtraction related? Subtraction is the opposite of addition. Explain that since subtraction is the opposite, or inverse, of addition, they create equivalent equations. In other words, 3 + 4 = 7 and 7 – 4 = 3. Therefore, addition and subtraction expressions are done next in the order in which they appear, working left to right. Neither one is more important than the other, so they are performed in the order they occur in the expression from left to right. Challenge students to record their cow milk model on Part I of their Student Journals. They will then determine whether the ﬁrst expression or second expression is correct by evaluating those expressions to see which one matches what is happening in their model. They will then describe their process in solving and write a solution statement. After allowing enough time for students to record their work for Part I, quickly check each group’s responses.

Part II: Working on the Farm FACILITATION TIP Post these expectations at each station: First, solve using manipulatives. Second, create an expression that represents the problem.

Tell students that there is a farming problem that needs to be solved at each station. Their task is to solve the problem by ﬁrst using the manipulatives placed at each station and then to create an expression that represents the problem, using parentheses when needed to get the correct solution. Note that not every scenario needs parentheses. Explain that once they have written their expression, they should evaluate it using the correct order of operations. They should be on the lookout for times when parentheses must be used to ensure the correct order of operations is performed. Assign each group of students to a station. As students are working, monitor and check for understanding. Ask questions such as the following: a.

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DOK-2 What operations will you need to use to solve this problem? Explain. Answers will vary based on the station. I will need to multiply and subtract because I have four rows of carrots with 278 carrots in each row. We then need to subtract the inedible carrots from that total.

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Explain

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DOK-2 Does it matter which operation needs to be completed first? Explain. Explanation may vary. Yes, it matters which operation needs to be completed first because if we subtract the numbers first before we multiply, then the value of our expression will be different from if we multiplied first and then subtracted.

DOK-1 How can we represent which operation we need to solve first within our expression? Answers may vary. We can use the chenille stems to place parentheses around the part of our model that we need to solve first. We can use parentheses in our expression to represent which operation we need to solve first. We know that in the order of operations, multiplication and division are solved first, followed by addition and subtraction, so we will follow the order of operations.

DOK-2 Do we always need to include parentheses in our expression? Explain. No, we do not need to always include parentheses. Sometimes we can ﬁnd the correct answer by just following the order of operations, solving multiplication or division ﬁrst, followed by addition or subtraction.

e. DOK-2 How can creating a model help us determine a solution to our problem? Creating a model helps by giving us a visual representation to act out the problem, to show us what is happening in our problem, and to help us determine the correct order of operations in order to solve.

DOK-2 Will you get the same answer when solving left to right versus solving using the order of operations? Answers may vary depending on the scenario. No, we got different answers when solving from left to right versus solving using order of operations.

DOK-2 What can you do if you get different answers when solving from left to right versus order of operations? Read the scenario again, and make sure your expression and model matches what happens in the scenario. Then, make sure you ﬁnd your answer using the order of operations correctly because this will give you the correct answer.

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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.

Allow groups enough time to rotate through and solve the problem at each station. Once the groups have completed all the stations, they will work with their groups 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-1 What does evaluate mean, as in “evaluate an expression”? It means to perform all the operations in an expression until you have one value. • DOK-2 Why is it important to solve using the correct order of operations? It is important to solve using the correct order of operations because if we solve the operations in a random order or from left to right each time, then we will most likely find a different answer. • DOK-1 What is the correct order of operations? Perform the operations in grouping symbols first. If there is more than one set, simplify them in the order they occur. Then, perform multiplication and division, left to right. Finally, perform addition and subtraction, left to right. • DOK-2 How can using parentheses in an expression help you determine a solution? Using parentheses in an expression can help us determine which operation we need to solve first to find the correct answer. They are necessary when addition or subtraction precedes multiplication or division or when any part of an expression should be evaluated before others that would normally be performed first. •

FACILITATION TIP Engage students with the comparison of using the mathematical order of operations in ﬁfth grade to real-world computer programming or cooking. The order of operations is like a very speciﬁc set of directions or a step-by-step recipe.

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Numerical Expressions Explore 1 – Order Matters •

DOK-2 How can creating a model help you determine the correct order of operations? A model can help you determine which operation needs to be solved ﬁrst to match what is happening in the problem. We can show whether or not we need to use parentheses to group manipulatives together to show we perform that operation ﬁrst.

FACILITATION TIP

Post-Explore

When you preview this Exit Ticket with students, allow time for questions or read alouds to ensure that students comprehend the scenario.

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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Numerical Expressions Explore 2 – Grouping Symbols ACTIVITY PREPARATION Students create expressions based on word problems. They will also evaluate and compare numerical expressions that do not involve exponents using parentheses.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

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1 Student Journal (per student) 1 Set of Problem Tents (per class) 1 Exit Ticket (per student)

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Consumable •

Plan to divide the class into 8 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Problem Tents, on card stock for durability, for the class. Fold each problem along the center line to form a tent to place at each station. Make 8 stations around the room, with one Problem Tent at each station. Note: More than one set of Problem Tents can be printed to allow for fewer students at each station.

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8 Sheets of card stock (per class) •

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PROCEDURE AND FACILITATION POINTS 1. 2. 3.

4. 5.

FACILITATION TIP Have students ﬁgure out their own mistakes and then discuss them with partners, using sentence stems such as these: “The error I made was . . . Next time, I will . . .” 174

Give a Student Journal to each student. Instruct students to ﬁnd the ﬁrst problem on their Student Journals. Read the following scenario to the class: Catie owns a catering company. She shops at a kitchen supply store. She bought three mixers for $74 each and two pans for $26 each. How much did she spend at the kitchen supply store? Allow students two minutes to collaborate with their groups to write a mathematical expression that matches the problem scenario. Encourage students to share their expression for the scenario by asking the following question:

DOK-1 What expression can help us determine how to solve this scenario? Answers will vary. (74 × 3) + (26 × 2).

Remove the parentheses. Ask students to evaluate the expression without the parentheses to see if they get the same value.

10.

11. 12. 13.

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Explain

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Intervention

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Discuss the following question. a.

Engage

DOK-1 What would happen to the value of the expression if we removed the parentheses and did not follow the order of operations? Answers may vary. The value is not the same because if we solve from left to right, 74 × 3 = 222 + 26 = 248 × 2 = 496 is not the same as 74 × 3 = 222 + (26 × 2) = 52, for a total of 222 + 52 = 274.

Explain to students that the parentheses in an expression can help us represent which operation needs to be solved ﬁrst. Without parentheses, the operations in an expression will be solved using the order of operations. Discuss the following questions: a.

DOK-1 What is the order of operations? The order of operations helps us determine the order in which we must solve an expression. When solving an expression from left to right, we must solve the multiplication and division operations ﬁrst, followed by addition and subtraction.

DOK-1 In Catie’s scenario, what should be evaluated ﬁrst? Either multiplication problem inside the parentheses can be evaluated ﬁrst since they are both multiplication.

DOK-3 What do you think those parentheses mean? They represent the two different parts of a problem we have to evaluate ﬁrst.

DOK-1 What operation does Catie need to solve after performing the operations in the parentheses? She needs to add the two values found for the operations inside of the parentheses to determine how much she spent at the kitchen supply store.

Inform students that they will visit 8 stations. At each station, they either will have to create an expression based on a scenario or they will be given an expression to evaluate. For all problems, they will need to evaluate the expressions given or created. Students will also be asked to evaluate expressions and compare their values. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How is the card asking you to solve using expressions? Answers will vary based on the card. The card is asking me to place grouping symbols within the expression to make it a true statement.

DOK-3 How can parentheses change the value of the expression? Answers will vary. Parentheses help us determine which operations we will need to solve ﬁrst. Depending on the value found within the parentheses, that can make the value of our expression greater or less than if we would’ve solved without parentheses.

DOK-2 (For stations 7 and 8) How do the two expressions compare? The ﬁrst one is (less than or greater than) the second.

DOK-2 (For stations 7 and 8) Why is the ﬁrst expression less or greater? When an expression is evaluated, the value of that is compared. The greater value indicates a greater expression.

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 Give roles to each student in the group that can be rotated as they move through each station. FACILITATION TIP Model exactly how students are to show their methods for evaluating the expressions. Students will be tempted to skip showing steps which can lead to errors. You will be better able to help with error analysis if you can see their steps. FACILITATION TIP Pay attention to each group’s whiteboard. You may need to address mistakes in the math or in the order of operations.

Allow students enough time to rotate through all the stations and record all their work on their Student Journals. Once the students have completed all the stations, they will work with their groups 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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Numerical Expressions Explore 2 – Grouping Symbols Math Chat •

• FACILITATION TIP Create total physical and choral responses to help students remember the complex process of order of operations. Consider hand signals or songs and repeat as needed.

•

DOK-3 Why do we have a standard order of operations? There are certain values you need to calculate before you can do the rest of the problem. Having a standard order helps us all arrive at the one correct answer. If we are all following the same rules, we can use expressions to accurately communicate information. DOK-3 Describe the process for evaluating expressions. Any expression in parentheses should be performed first. Then, any multiplication or division should be done from left to right. Finally, any addition or subtraction should be performed from left to right. DOK-2 How do you write an expression based on a real-world problem? When given a real-world problem, you have meaning for each number. You have to determine which numbers need to be grouped together and the order that operations need to be performed based on the context. You can use grouping symbols in the expression to help others know which operations to do first. DOK-3 What is the purpose of parentheses in evaluating expressions? They group certain parts of the expression together to ensure they are performed first or ahead of others. They are also another way of indicating multiplication. DOK-2 What should you do if you have more than one set of parentheses in an expression? You should start with the set of parentheses on the left and work to the right. You must evaluate each expression within parentheses using the correct order of operations.

Post-Explore FACILITATION TIP Prior to students completing this Exit Ticket, provide some simple practice for evaluating expressions. Students may need time to practice the steps without being required to comprehend scenarios and translate them into words.

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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Numerical Expressions Explore 3 - Interpret Expressions ACTIVITY PREPARATION Students write, interpret, and compare numerical expressions without evaluating them.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Preparation

Materials Printed • • • • •

• • •

1 Student Journal (per student) 1 Set of Booth Displays (per class) 1 Set of Matching Cards (per class) 1 Set of Inventory Cards (per pair) 1 Exit Ticket (per student)

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Reusable • •

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 Booth Displays, on card stock for durability, for the class. Place the Booth Displays at different stations around the classroom. Print a set of Matching Cards, on card stock for durability, for the class. Cut the cards apart, and separate them into 4 resealable bags to be placed with their corresponding Booth Displays. •

4 Resealable bags (per class) 1 Paper clip (per group)

• •

•

Note: More than one set of Booth Displays and Matching Cards can be printed to allow for fewer students at each station.

Print a set of Inventory Cards, on card stock for durability, for each pair. Cut the cards apart, and put them together with a paper clip. For students who need more support in recalling information, please see our Base Tens and Grid Paper Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION POINTS Part I FACILITATION TIP

This scenario is an excellent real-world example of why ﬂuency with the order of operations is necessary for success in a business.

2. 3. 178

Read the following scenario to the class: Mrs. López was recording sales from the four booths she and her family set up at the local Farmers Market over the weekend. She recorded the sales of the various produce in two different ways so she could double-check that her records were accurate. She had just ﬁnished laying the slips of paper beside the matching expressions when a strong gust of wind pushed the door open and blew the slips on the ﬂoor all out of order! She started to match the expressions but ran out of time. Can you help Mrs. López sort through the remaining sales? Explain to students that there are different stations around the classroom and they will rotate through each one with their partners. Tell students that at each of the four stations, there are several of Mrs. Lopez’s expressions that need matching, and not all of the expressions will be used. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

2. 3.

Acceleration

As students collaborate at each station, use guiding questions like the ones below to help assess understanding: a.

DOK-1 What do you notice about the description or expression given on the Booth Displays? Answers will vary. I notice that the expression contains parentheses, which means that operation only applies to the numbers within the parentheses. I notice important vocabulary such as times/sum/less than, which means to multiply/add/subtract.

DOK-2 How did you know what each part of the expression asked you to do? Answers will vary. “Less than” tells me that the number has less value—usually that means a number is subtracted. “A fourth of” means divide by 4 or multiply by one-fourth. “Twice” means multiply by 2 because it is doubled. “More than” means the number is greater, so that usually means an amount is added. “Sum” is the answer to an addition expression. “Difference” is asking for the answer to a subtraction expression. “Product” asks for the answer to a multiplication expression.

DOK-1 How could this expression be written in a different way? Answers will vary.

DOK-2 How can the description or expression help you determine a value? Answers will vary. The grouping symbols let me know which operation needs to be performed ﬁrst. Then, once we have that value, we can apply the second operation to determine a value for the expression. The description explains the operations and in which order we need to solve them so that we can determine the value.

FACILITATION TIP Have students brainstorm some words they need to use to transfer the equation into written form. Provide sentence stems and other transition words if needed.

Allow each group enough time to complete each station and to record their work on their Student Journals. STEMscopes Tip

Part II 1.

Intervention

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Read the following scenario to the class: The López family was so impressed by your work that they would like you to help with one more analysis. They need your help to compare the inventory from last month to this month for certain fruits. Help them double-check the inventory by writing their ﬁrst inventory list a different way. Give a set of the Inventory Cards to each group. Encourage students to work with their partners to look over the cards and discuss what they notice about the vocabulary and the values within the expressions and the descriptions. Engage students in a discussion to share their observations about interpreting words into numerical expressions. Invite students to share with their partners before sharing with the class. Ask students to share examples. a.

DOK-1 What do you notice about the values of the numbers used in each expression and description? I notice that the values of the numbers used in each expression and description are the same. Each card has the numbers 27, 3, and 532.

DOK-1 What pattern have you noticed for words that call for addition? Sum, more than, increased by

DOK-1 What pattern have you noticed for words that call for subtraction? Less than, difference, decreased by

DOK-1 What pattern have you noticed for words that call for multiplication? Times, equal groups, product, triple, double, twice

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.

FACILITATION TIP Create a table on the board, and list the terms with their associated properties.

e. DOK-1 What pattern have you noticed for words that call for division? Half of, third of, quotient

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Numerical Expressions Explore 3 - Interpret Expressions 5.

Explain to the class that they will be using the Inventory Cards either to interpret an inventory as a numerical expression into words or interpret an inventory written in words into a numerical expression. They will record their interpretations onto their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP

Have students think out loud about what is happening in each expression. Groups can estimate their answers and then solve to verify.

DOK-2 How can you tell which expression will yield the greater value? Answers will vary. If whole numbers are multiplied, the values are greater than when the same numbers are added. If whole numbers are divided, the result is less than if the same numbers are subtracted.

DOK-2 Which fruit produced the greatest sales? How do you know? Cucumbers. All of the expressions contain the same numbers. The expression with the greatest value is the one that multiplies the largest numbers and then adds the smallest number. Multiplying the largest numbers makes the outcome much greater than adding or subtracting the largest numbers.

DOK-2 Which fruit produced the least sales? How do you know? Apples. The expression with the least value is all numbers added. Every other expression contains multiplication.

7. 8. 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.

Allow students enough time to work together to interpret each Inventory Card and to answer the 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 How did you use your understanding of operations to determine either a word interpretation or a numerical expression? It helped to know what the different operations do to numbers. If I was combining equal groups or splitting something into equal groups, I knew I would need to multiply or divide. If I was just increasing or decreasing the value by a certain amount, I would add or subtract. • DOK-3 What were some patterns you observed in the words that led to a particular operation? We noticed that “sum,” “increase,” and “more than” would typically result in addition. We also noticed that “less than,” “decrease,” and “difference” were typically used for subtraction. For multiplication, we saw “product,” “_____ more times than,” “double,” and “triple.” Division would typically talk about a “quotient” or “a half of.” • DOK-3 What were some challenges you had as you were interpreting different expressions? What would you caution other students about? One of the challenges is knowing how to group the expressions. I would caution other students that the grouping affects the outcome. We need to read the expressions and see what is grouped together. •

Post-Explore FACILITATION TIP When you preview this Exit Ticket with students, consider having them ﬁrst focus only on the scenario and try to understand the solution. After examining the scenario, they can look at the two expressions. You can project the scenario alone on the document camera or encourage students to fold their paper or cover up the bottom of the ticket.

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Numerical Expressions 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

Order Matters 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

Grouping Symbols 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

Interpret Expressions 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

Sophie and Sloan Host a Movie Night

Elon Musk

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

Twenty-Three Skiddoo

Simple Numerical Expressions

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

Welcome to My House

Numerical Expressions

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

NUMERICAL EXPRESSIONS

Numerical Expressions

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

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What prompts will be used?

What does mastery look like?

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I can write, interpret, and evaluate numerical expressions made up of mixed operations.

I can use grouping symbols within an expression to interpret and evaluate the order of operations.

I can use parentheses, brackets, or braces to write, interpret, and evaluate expressions.

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SCOPE 1

Compare and Order Fractions and Mixed Numbers Scope Introduction SCOPE SUMMARY Students plot, order, and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators. Instruction includes using an appropriately scaled number line and reasoning about relative sizes of fractions. Students reason about distances of each fraction from benchmark fractions. Comparisons are made by using the symbols >, <, or =, accompanied with a justiﬁcation of the comparison. Student Expectations

5.NR.3.2 Compare and order up to three fractions with different numerators and/or different denominators by ﬂexibly using a variety of tools and strategies.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In fourth grade, students compare 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 by using models, number lines, and benchmark fractions. These tools and strategies help students recognize and reason about the sizes of fractional parts and that comparisons are only valid when the two fractions refer to the same whole.

By the time students reach sixth grade, they are able to apply their understanding of the relative sizes of fractions to add, subtract, multiply, and divide fractions and mixed numbers by using a variety of strategies, including but not limited to concrete models, visual fraction models, student-generated strategies, a standard algorithm, or other strategies based on numerical reasoning to represent and solve problems. The prior knowledge gained from these various strategies allows students to make sense of and strategically solve problems by using eﬃcient methods that are most comfortable for and make sense to them.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

compare two fractions with the same numerator or denominator.

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

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

compare fractions with unlike numerators and denominators.

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.

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In this exploration, students will use <, > and = symbols to compare fractions and mixed numbers.Students will:

Explore 3

•

Explore 2

Compare Fractions with Models

create models using the fraction circles or fraction tiles.

Compare Fractions with Number Lines In this exploration, students will compare fractions and mixed numbers using number lines. Students will: •

create a list of paint colors and determine how much paint needed to complete paint projects.

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

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

Compare Fractions with Benchmarks

Order Fractions with Number Lines

In this exploration, students will compare fractions and mixed numbers with different numerators and denominators using benchmark fractions. Students will: •

Explore 4

Explore 1

EXPLORE ACTIVITIES

review the daily screen time usage amounts and determine which children are spending the most or least amount of time on a screen.

In this exploration, students will order fractions and mixed numbers with different numerators and different denominators by plotting them on a number line. 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.

ordering fractional amounts from least to greatest to determine the pizza party winner for each grade level.

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

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COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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

Tuesday

Wednesday

Thursday

Friday

188

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students compare two fractions with the same numerator or denominator and decide whether the justiﬁcation of the conclusion using symbols, words, and pictorial models is true or false. This activity is intended to assess mastery of the following standard(s): 4.NR.4.2 Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole.

Materials

Preparation

Printed •

• Plan to have students work in groups of 3 or 4 to complete this activity. • Prepare to project the Slideshow for the class, or print a Slideshow for each group.

1 Slideshow (per class)

Reusable •

1 Projector or document camera (per class)

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

Project the Slideshow for the class, or distribute Slideshows to groups. Read the first problem, and show students the first set of fractions and the justification. Students who agree with the conclusion should give a thumbs-up; students who disagree with the conclusion should give a thumbs-down. Facilitate a class discussion about their choices. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

Repeat the process for the second set of fractions. a.

The statement ___ > ___ is false. The number of pieces in the whole or 10 10 set, 10, is the same. The pieces would be the same size. Six is less than eight, so the symbol should be the less-than symbol. Nicole has completed more of her bracelet than Samantha. 3

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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FACILITATION TIP Before students participate in the discussion that follows, challenge them to adjust the false statement to make it true. FACILITATION TIP If students struggle to understand the comparison, refer to fraction tiles, fraction circles, or fraction towers to model the fractional sizes. If needed, use the Foundation Builder for further support with this type of investigation.

The statement that __5 is greater than __8 is true. When there are more pieces in the whole or set, the pieces get smaller. Penny has eaten more of her dog food than Rocko.

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

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Compare and Order Fractions and Mixed Numbers Hook – Pizza Deliveries ACTIVITY PREPARATION Students compare fractions with unlike numerators and denominators to determine whether a larger fraction of pizzas ordered was delivered to homes or businesses.

Materials

Preparation

Printed •

•

1 Student Handout (per student)

Part II

Reusable • • •

Plan to show the Phenomena Video.

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Colored pencil (per student)

• •

Plan to have students work in groups of 3 or 4 to complete this activity. Print the Student Handout for each student. Gather enough colored pencils for each student to have one.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1. FACILITATION TIP In the Engage section, the Foundation Builder activity can be used to informally assess students’ understanding and to activate their prior knowledge.

DOK-2 Would __3 and __5 be easy to compare? Maybe if I shaded in the models, I would be able to compare. The model helps, but I am still not positive which fraction is greater.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2. 3. 4.

5. 190

Discuss the following questions: a. DOK-1 What information have we been given? We know the amount delivered to homes and businesses one weekday.

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.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: DOK-1 What information have we been given? We know the amount delivered to homes and businesses one weekday. 1 2 DOK-2 Would __3 and __5 be easy to compare? Maybe if I shaded in the models, I would be able to compare. The model helps, but I am still not positive which fraction is greater. Review the problem, and allow students to solve it. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Give a colored pencil and Student Handout to each student. Have each student complete their own handout. Have students discuss how to solve the problem with their groups. Discuss the following questions: a. DOK-1 What was one of the ﬁrst things you did to ﬁnd the solution? 1 2 I shaded the top model to show __3 and the bottom to show __5.

DOK-1 Did one fraction seem greater than the other after shading the 2 1 models? It appeared that __5 was greater than __3. It was close, so I was not positive.

DOK-3 The bottom of the Student Handout asks you to ﬁnd a common denominator. Why would that be needed? Once I found a common denominator, I could compare the fractions easily and feel conﬁdent in my comparison by comparing the numerators like I would whole numbers.

d. DOK-2 How did you know what the common denominator was? I thought of the smallest multiple that 3 and 5 have in common. I know that 15 is a multiple of them both. That is the common denominator. e. DOK-2 How did you adjust the model to show ﬁfteenths instead of thirds? I know that 3 × 5 = 15. I knew that I needed to add 5 lines to the thirds. I added 5 horizontal lines to the thirds and then had 15 equal 5 5 1 1 5 parts. So, __3 = ___ , because __3 × __5 = ___ . 15 15 f. DOK-2 How did you adjust the model with ﬁfths? I know that 5 × 3 = 15. I knew that 3 lines needed to be added, and I did that horizontally to the 6 6 2 2 3 model. So, __5 = ___ , because __5 × __3 = ___ . 15 15

Intervention

Acceleration

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.

FACILITATION TIP Use the Virtual Manipulative – Fraction Tiles to model for students how a whole can be broken into different but equal 5 1 parts. For example, __3 equals ___ . 15

FACILITATION TIP

Students may need to explore different manipulatives to see how each piece can be broken down to ﬁnd the common denominator.

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g. DOK-1 Did homes or businesses get more pizza delivered? Businesses 5 6 got more pizza delivered since ___ < ___. 15 15 Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Compare and Order Fractions and Mixed Numbers Explore 1 – Compare Fractions with Models ACTIVITY PREPARATION Students use <, >, and = symbols to compare fractions and mixed numbers. They justify their reasoning by using concrete manipulatives and visual models.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure

Materials Printed • • •

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

Preparation • • • •

• • • • • •

Reusable • •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Roadway Station Cards, on card stock for durability, and place them around the room to create 6 stations. Each station will need the following manipulatives:

4 Sets of fraction circles (per class) 6 Sets of fraction tiles (per class) • •

Gold Gator Way – 2 sets of fraction tiles Georgia Parkway Roundabout – 2 sets of fraction circles Featherstone Road – 2 sets of fraction tiles Bulldog Trail Roundabout – 1 set of fraction circles Eagle Landing Trail – 2 sets of fraction tiles Yellow Jacket Roundabout – 1 set of fraction circles

For students who need more support in recalling information, please see our Fraction Circles and Fraction Strips Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles and Fraction Tiles)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

2. 3.

Take time to carefully review numerator, denominator, whole and mixed numbers, and equivalent. FACILITATION TIP

192

Provide templates for students to trace if needed. Fraction strips are provided in the Intervention section.

Read the following scenario to the class: The local government roadway association has hired you and your team to be in charge of the construction on newly approved roads in your town. The roadway association has a goal of how much of each road needs to be completed after a year’s worth of construction. You and your team will be documenting the completion of each road at a year’s time and comparing it to the goal set to determine if you are on track, behind schedule, or ahead of schedule on each roadway project. Give a Student Journal to each student. Explain to the class that there are Roadway Station Cards around the room that their groups will be rotating through in order to check the status of each roadway project. Some stations will have fraction tiles for roads or fraction circles for roundabouts. Explain to the class that a roundabout is a circular road without stop signs in which oncoming traﬃc yields to cars already in the roundabout. Each Roadway Station Card will have fractions and mixed numbers with different numerators and different denominators. Explain that they have to collaborate with their groups to create models using the fraction circles or fraction tiles at that station to help them create fractions that are easier to compare. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

Encourage groups to explore ways to create equivalent fractions so the fractions they are comparing have the same numerator or the same denominator. Students then use the models to decide if the roadway construction projects are on schedule, ahead of schedule, or behind schedule. Each decision should be recorded and explained in their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 What do you notice about the fractions/mixed numbers on your Roadway Station Card? Answers will vary depending on the card. I notice that the numerators and denominators are different. I notice that the whole numbers are the same in the mixed numbers. I notice that one fraction is given for the goal and one fraction is given for how much has been completed.

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.

b. DOK-1 Is the whole, or road, on your Roadway Station Card the same for the goal and the amount completed? Yes c.

DOK-3 Why is it important that the whole, or road, are the same size in the given problem? It is important that the roads are the same size in the problem because if they were different sizes, we would not be able to compare them accurately. For example, if one whole is bigger than 3 3 the other whole, then __4 in a bigger whole will not be the same size as __4 in a smaller whole.

d. DOK-2 How can you use the fraction manipulatives to represent the problem? I can start by using the fraction tiles or circles to represent the two given fractions in the problem. I can then ﬁnd an equivalent fraction with the same numerator or same denominator to convert one of the given fractions. We can then use that equivalent fraction we created to compare it to the remaining given fraction. e.

g. DOK-1 How do you know which fraction is greater or less? If one model is larger than the other, then that fraction is greater. h. DOK-1 How could you represent your choice using symbols? I could use symbols like >, <, and = to show which fractions are greater, less, or equal.

8. 9. 10.

Demonstrate that fraction tiles and fraction circles are not equal by placing the manipulatives on top of each other.

DOK-1 How do the denominators affect the size of the fraction? If the denominators are the same, then look at the numerator. The larger the numerator, the greater the fraction. If the numerators are the same, then look at the denominators. The smaller the denominator, the greater the fraction.

f. DOK-2 How can you ﬁnd equivalent fractions for the ones you are comparing? We can trade out the pieces for smaller pieces and ﬁnd a fraction that is the same size. We are breaking up each unit fraction into smaller pieces.

FACILITATION TIP

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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DOK-2 Is it important to draw an accurate representation of the fraction models? Explain. If we misrepresent the drawings of the whole or fraction into larger or smaller sizes, then it will be hard to compare our models with accuracy.

FACILITATION TIP Consider encouraging students to use a standard-sized rectangle to model the fractions. Stacked, aligned rectangles are easier to compare for most students. Drawing the models the same size can be complex. Provide a template to support accurate representations.

Allow students enough time to rotate through each station and record their work on their Student Journals. After the class has ﬁnished rotating through each station, allow the groups to work together 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.

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Compare and Order Fractions and Mixed Numbers Explore 1 – Compare Fractions with Models Math Chat •

• 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.

•

DOK-3 What connections did you make while you were working on this Explore activity? I noticed that each model is composed of unit fractions. I noticed how a smaller denominator means the whole is only broken into a few pieces, so the pieces are larger. I noticed we could make equivalent fractions by breaking each piece into equal smaller pieces. DOK-3 Describe the process you used to make your decision on each card. I looked at the two fractions or mixed numbers and built a model of each. I then created an equivalent fraction so the fractions I was comparing either had the same denominator or the same numerator. I then used those fractions to compare the goal to how much was completed to determine if they were on schedule or not. DOK-2 What would happen if the whole wasn’t the same size? We wouldn’t be able to tell which one was actually larger or smaller. The models wouldn’t be helpful. DOK-2 What if you didn’t have the math tools in front of you—what could you do? We could draw fraction circles or fraction tiles. As long as the whole is the same size on both models and it is partitioned evenly, we could use our drawings to compare the fractions. I could also use the drawn model to create equivalent fractions so they have the same numerator or denominator. That would help me compare them without having math tools. DOK-2 Why is it helpful to create equivalent fractions with the same numerator or denominator? If two fractions have the same numerator or denominator, I can easily decide which is greater by thinking about the number of pieces or the sizes of the pieces.

Post-Explore FACILITATION TIP

Depending on your students, consider providing standard rectangle templates for students to create accurate models to compare.

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.

194

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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195

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

Compare and Order Fractions and Mixed Numbers Explore 2 – Compare Fractions with Number Lines ACTIVITY PREPARATION Students compare fractions and mixed numbers using number lines.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

•

1 Student Journal (per student) 1 Paint Checklist (per group) 1 Set of Number Lines (per group) 1 Exit Ticket (per student)

• • •

Reusable • • •

•

1 Dry-erase marker (per group) 1 Dry-erase eraser (per group) 2 Clear sheet protectors (per group)

•

Consumable •

1 Sheet of chart paper (per teacher, optional)

•

Plan to have students work in groups of 2 or 3 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Paint Checklist, on card stock for durability, and place it in a clear sheet protector to create an erasable surface. Print a set of Number Lines back to back. Put them in a clear sheet protector for each group. Gather enough dry-erase markers and dry-erase erasers for each group to have one. For students who need more support in recalling information, please see our 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. (Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP

Take time to carefully review numerator, denominator, whole and mixed numbers, and equivalent.

3. 4.

FACILITATION TIP Have students use the fraction tiles to create a model for each amount. Then, students can transfer the distances to the number lines on their Student Journals. 196

Read the following scenario to the class: You and your family are ready to redo the paint colors in your home. After years of paint projects for friends and neighbors, your family has collected a bunch of leftover cans of paint in your garage. Instead of going out and buying more paint, your family decides to use what you have ﬁrst. You are helping out your family by creating a list of paint colors and writing down how much paint you will need to complete the paint projects and how much paint you have left over. It is your job to inform your family if they need to buy more paint, have more than enough paint, or just the right amount. Give a Paint Checklist and a set of Number Lines to each group. Give each group a dry-erase marker and eraser. Give each student a Student Journal. Tell students that they will be working together to analyze the Paint Checklist and compare how much paint they have versus how much paint they need to complete the paint projects. Instruct them to use the Number Lines to compare the two numbers. Brieﬂy review how to model fractions using number lines with the following questions: © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 What do you notice about the Number Lines? I notice that one of the Number Lines goes from 0 to 1, and the other Number Line goes from 0 to 1 to 2. I notice that the Number Lines are the same length.

b. DOK-2 How do we know that the wholes for each measurement of paint are equal or the same size? We know the wholes for the paint are the same because we are measuring in gallons of paint. c. DOK-2 How can we determine which Number Line to use? If the fraction doesn’t contain a whole number, we can use the Number Line that goes from 0 to 1. If the fraction is a mixed number, we can use the Number Line that goes from 0 to 1 to 2. d. DOK-2 How do we know how many pieces each whole in the Number Line will be separated into? The denominator of each fraction determines how many pieces the whole of each Number Line will be separated into.

FACILITATION TIP Model carefully for students how to create equal-sized pieces.

e. DOK-3 Why is it important to create equal-sized pieces when modeling fractions on a number line? If I make some pieces big and some pieces small within the same whole of a number line, it will be hard to get an accurate representation when comparing the fractions or mixed numbers. 6.

7. 8.

Challenge students also to generate equivalent fractions and find a common numerator or denominator in order to check their work they modeled on the Number Lines. Students will collaborate to complete each table until they find an equal numerator or denominator for the given fractions. Using a piece of chart paper, briefly review how to find equivalent fractions. Create the tables below on the board.

FACILITATION TIP Use a multiplication chart to model how to find equivalent fractions by sliding left to right along the columns after finding the first fraction (For example, locate 4 over a 5 and slide over to look for equivalent fractions in the next columns).

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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4 5 6 STEMscopes Tip

8 9. 10.

11.

Invite students to create equivalent fraction tables on their desks with dry-erase markers. Challenge them to generate equivalent fractions and ﬁnd a common numerator or denominator. Students will collaborate to complete each table until they ﬁnd an equal numerator or denominator for the given fractions. Call on volunteers to come up to the board and complete the tables until an equal numerator or denominator is reached. Students may quickly see that multiplying the numerator and denominator in a fraction by 2, then 3, then 4 results in skip counting by each. This strategy can be used to quickly generate equivalent fractions. 4

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.

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Compare and Order Fractions and Mixed Numbers Explore 2 – Compare Fractions with Number Lines 12.

Students will circle their fractions with equal numerators or equal denominators. 32 12 ___ 12 24 24 30 They should circle ___ , , ___, ___, ___ and ___ . Ask them what the denominators and 15 16 30 32 40 40 numerators for these fractions are. Students should see that the denominators and numerators are different. Discuss the following questions: a.

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.

13. 14.

15.

16.

DOK-1 How can we compare these fractions now that we have equal numerators or denominators? We can look at the denominators or numerators and compare the fractions based on those. Since the numerators are the same, we know that the same amount of pieces are shaded, so looking at the denominator can help us determine the size of the pieces in the whole. The bigger the denominator, the smaller the piece. The smaller the denominator, the bigger the piece. Alternatively, since the denominators are the same, we know the size of the pieces will be the same for both fractions. The bigger the numerator, the more pieces shaded.

Emphasize the usefulness of having a common numerator or denominator when comparing fractions. Once students have modeled their fractions and mixed numbers on number lines and found a common numerator or denominator, they will then write two comparison statements to justify their answers in their Student Journals. Allow students enough time to complete the comparisons for each paint color on their checklist. When students ﬁnish modeling and comparing each paint color, they will place a check mark on their checklist to show whether they do not have enough paint, whether they have just the right amount of paint, or whether they have more than enough paint. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What do you notice about the numerators in these fractions? They are different.

b. DOK-1 What do you notice about the denominators in these fractions? They are different.

STEMscopes Tip

c. DOK-2 How can we compare these fractions and mixed numbers? We can represent them on separate number lines to see which fraction is larger or smaller. We could also look at the number line to see which fraction is closer to one. We can also compare by creating a table and ﬁnding multiples of the numerator and denominator until we have a common numerator or denominator.

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.

d. DOK-2 Are the fractions equivalent? How do you know? Answers may vary. Yes they are because when I created my number lines and marked each fraction or mixed number with a point, I noticed they are the same distance from zero. e. DOK-1 How can you determine if there is not enough paint? If I look at my number lines and the fraction/mixed number for the paint we have is less than the amount of paint we need, then I know we don’t have enough paint. f. DOK-1 How can you determine if there is more than enough paint? If I look at my number lines and the fraction/mixed number for the paint we have is greater than the amount of paint we need, then I know we have more than enough paint.

FACILITATION TIP

198

Using a number line for this Explore activity will help students when they need to visualize decimals and percents on a number line as well. Reassure students that ﬂuency with physical models will help them to conceptualize more complex scenarios as they get older.

g. DOK-1 How did the Number Line help you compare these two numbers? Once I placed the numbers on the Number Line, I could easily see the number that was closer to 0 was the smaller number. 17. 18.

Allow students enough time to record all their work 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. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat DOK-2 How can we compare fractions when the numerators and denominators are different? We can model the fractions using number lines and look at the number line to see which fraction is closer or farther away from 0. We can ﬁnd a common numerator or denominator and compare the equivalent fractions. • DOK-2 Why is it helpful to use number lines to compare fractions or mixed numbers? When we model a fraction or mixed number on a number line, it creates a visual model that can better show us which number is closer to or farther away from 0. • DOK-2 How do you know whether you had enough paint, not enough paint, or more than enough paint? If I look at my number lines and the fraction/mixed number for the paint we have is less than the amount of paint we need, then I know we don’t have enough paint. If I look at my number lines and the fraction/ mixed number for the paint we have is greater than the amount of paint we need, then I know we have more than enough paint. • DOK-2 Why is it helpful to ﬁnd a common numerator or denominator? If I have a common denominator, I could look at the numerators and determine which was smaller or larger since the equal denominators tells me the size of the pieces will be the same for both fractions. If I have common numerators, I can judge which pieces are larger or smaller based on the denominator because I know I have the same number of pieces. •

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.

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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COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

Compare and Order Fractions and Mixed Numbers Explore 3 – Compare Fractions with Benchmarks ACTIVITY PREPARATION The students compare fractions and mixed numbers with different numerators and denominators using benchmark fractions.

Standards for Mathematical Practice • • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Screen Time Station Cards (per class) 1 Set of Number Lines (per station) 1 Exit Ticket (per student)

• •

Reusable • • • •

•

2 Sets of fraction tiles (per station) 1 Dry-erase marker (per group) 1 Dry-erase eraser (per group) 1 Clear sheet protector (per group)

•

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Screen Time Station Cards, on card stock for durability, and place them around the room to create 6 stations. Place 2 sets of fraction tiles at each station. Print a set of Number Lines back to back. Put number lines in a clear sheet protector for each group. Gather enough dry-erase markers and dry-erase erasers for each group to have one. For students who need more support in recalling information, please see our 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 Tiles and Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

STEMscopes Tip The Standards-Based Assessment is found within the Evaluate section for Grades 2–5. Students demonstrate mastery of the concepts covered in the scope using multiple-choice and gridded response questions aligned to the scope standard(s). This assessment can be assigned and scored digitally, printed, or edited to meet students’ individual needs.

3. 4. 200

Read the following scenario to the class: The amount of screen time a person spends watching TV, on their phone, or playing video games can have a positive or negative effect on an individual. Some parents have decided to limit the amount of screen time in their house so their children have enough time in the day to play, eat, help out around the house, or get schoolwork done. The parents document the screen time of each child to make sure they don’t exceed the 2-hour daily limit. The parents need your help to review the daily screen time usage amounts and determine which children are spending the most or least amount of time on a screen. Explain to students that the parents will use the whole numbers 0, 1, and 2 to represent the hours their children can spend using screen time. Discuss the following question: DOK-2 Why do you think the parents would use the whole numbers 0, 1, and 2 to compare their children’s screen time usage? Answers may vary. It is easier to ﬁgure out what whole number a fraction or mixed number is closest to instead of ﬁguring out which fraction of an hour your given fraction is closest to.

Give a Student Journal to each student. Assign each group of students to a station. Allow students a few moments to discover their materials and discuss how they relate to the scenario. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Explain to students that they will compare two or three fractions with different numerators and denominators. Using benchmark numbers makes comparing fractions easy because we know the benchmark numbers and can compare different fraction amounts to them. Instruct students to decide whether they would like to model their scenario with the number lines or fraction tiles. Explain to students that 0, 1, and 2 are the benchmark numbers they will use when comparing fractions. Students will draw their model on their Student Journals and explain how they can compare their model using benchmark numbers. They will then write two comparison statements and write their answer to the problem. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What do you notice about the information given in the scenario? Answers will vary. I notice that there are a mix of fractions and mixed numbers. I notice that both of the screen time fractions are mixed numbers.

Intervention

Acceleration

FACILITATION TIP Review or reteach benchmark numbers using Picture Vocabulary. FACILITATION TIP Depending on your students, consider using only one type of manipulative at a time to start. You can accurately model and assess if students are comparing appropriately. FACILITATION TIP Encourage students to use a standardized size of rectangle when they draw their models. Rectangular fraction models and number lines can be used for fraction division and multiplication. Rectangles are also more functional for visualizing than circles in later math standards.

b. DOK-2 Which tool do you think would be the best option in modeling this problem? Explain. Answers will vary. I think the best tool to represent the FACILITATION TIP information in this problem is the fraction tiles because I can easily pull Before students begin working the two whole number tiles, model the information in the scenario, and see which one is the most or least based on how close they are to the 0, independently or collaborating, clarify your expectations for drawing the models. Some 1, and 2 represented by the fraction tiles. students may use an algorithm or common c. DOK-2 How can you figure out which benchmark number to use to sense to quickly solve without drawing. compare the fractions given in the problem? If I am looking for the least screen time, I will find the fraction that is closest to 0 or the mixed number that is closest to 1. If I am looking for the most screen time, I will find the fraction that is closest to 2. STEMscopes Tip

d. DOK-2 How do you compare numbers that have a set of data that contains a fraction and a mixed number? I know the fraction will always be less than the mixed number because having a whole number will always be greater than just a fraction of something. I know the mixed number will always be greater than the fraction because having a whole number makes that mixed number greater than 1, and the fraction will be less than 1. 9. 10. 11.

Allow students enough time to rotate through each station and to record their work on their Student Journals. After the class has ﬁnished rotating through each station, allow the groups to work together 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 knowing whether a fraction is greater or less than a benchmark number help you compare fractions? When comparing fractions, if you know that one fraction is greater than one benchmark number and another fraction is smaller than that benchmark number, you can immediately tell which fraction is greater without doing any more work. • DOK-3 Are benchmark numbers similar to another math concept used before? How? They are similar to rounding and estimating because you don’t need an exact answer. •

Post-Explore 1. 2. 3.

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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.

FACILITATION TIP In addition to these Math Chat questions, include some relevant engaging real-world examples for why quickly comparing fractions is helpful. For example: sale prices, construction purchases, and creative design projects.

FACILITATION TIP

Have students complete the Exit Ticket to formatively assess their understanding Before this Exit Ticket, clarify how students should show their thinking. Consider that of the concept. some students may want to calculate Complete the Anchor Chart as a class. equivalent fractions rather than draw Have each student complete their Interactive Notebook. models.

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Compare and Order Fractions and Mixed Numbers Explore 4 – Order Fractions with Number Lines ACTIVITY PREPARATION Students order fractions and mixed numbers with different numerators and different denominators by plotting them on a number line.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Fraction Cards (per class) 1 Equivalent Fraction Work Mat (per station) 1 Exit Ticket (per student)

Reusable • • •

Preparation • • •

• •

1 Sheet protector (per station) 1 Dry-erase marker (per station) 1 Resealable bag (per station)

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 Fraction Cards, on card stock for durability, for the class. Cut the cards along the dotted lines, and place the different grade-level cards in separate resealable bags. Print an Equivalent Fraction Work Mat, on card stock for durability, for each station. Place each work mat inside a sheet protector. Set up 6 stations around the room. Each station includes Fraction Cards, an Equivalent Fraction Work Mat, and a dry-erase marker. The stations are as follows: • • • • • •

•

Kindergarten First Grade Second Grade Third Grade Fourth Grade Fifth Grade

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

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Project this scenario and read it along with students. Encourage students to read it more than once and guide them to ﬁnd the relevant math phrases and values. A common error with ordering problems is to reverse the order. Support careful reading for the words least to greatest and greatest to least. FACILITATION TIP Project images of pies or cakes that are different sizes, and have students order them from least to greatest in size. 202

2. 3.

Read the following scenario to the class: Chávez Elementary School is participating in a canned goods food drive. Each class for each grade level has a goal of collecting 100 cans. Of course, they are always welcome to surpass the goal and collect more than 100 cans if possible. The class that collects the most cans in the grade level will win a pizza party. At the end of the fundraiser, each class must display the fractional amount of the 100-can goal that they were able to collect. The school needs your help ordering those fractional amounts from least to greatest so the school principal can determine the pizza party winner for each grade level. Give a Student Journal to each student. Explain to the class that around the room are stations for each grade level from Chávez Elementary School and the fraction data for each classroom for the number of canned goods they collected in relation to the 100-can goal. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Quickly model how students work together at each station by explaining that when each group gets to their station, they remove the Fraction Cards from their resealable bags and analyze each fraction. They should notice that the fraction data includes different numerators, different denominators, and mixed numbers that they must order and plot on the number line. Discuss the following questions: a.

DOK-3 How do you think we can order fractions with different numerators and denominators on a number line? I think we will need to make equivalent fractions where all the fractions have the same denominator.

b. DOK-3 How can the number line help us determine what denominator all of our fractions should have? The number of parts on our number line between one whole number and the next will help us determine the denominator for our fractions. 6.

7. 8. 9.

Challenge students to use the Equivalent Fraction Work Mat to help them ﬁnd equivalent fractions in order to better help their groups plot and order their fractions on the number line. Model how they place their Fraction Cards in order to ﬁll out their Student Journals. Assign each group to a station, and encourage students to get started plotting and ordering their fractions. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

Intervention

Acceleration

FACILITATION TIP To engage students, have them collect canned food from home to bring to class to donate.

FACILITATION TIP Have students fold a sticky note in half and then in half again. Have students compare 2 1 the size of __4 to the size of __2 to make the connection that they are equivalent.

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.

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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DOK-1 What are the different denominators for each of your fractions and mixed numbers? Answers will vary.

b. DOK-3 How can the number line help us determine what denominator all our fractions should have? The number of parts on our number line between one whole number and the next will help us determine the denominator for our fractions. c. DOK-2 What factor can we multiply the original fraction by in order to ﬁnd our equivalent fraction? Answers will vary depending on the original fraction. d. DOK-3 Describe your strategy for plotting your fraction/mixed number on the number line. I will make sure my denominator matches the total parts for each whole on the number line. Then, I will analyze my numerator and will start at zero and move from line to line on my number line until I’ve reached the same number as my numerator. I will place my point on that line and label the teacher for that point. e. DOK-3 Why is it important to label the points on your number line? It is important to label the points so you can remember whose classroom represents that data. f. DOK-3 How can we use our number line and plotted points to list our fractions and mixed numbers from least to greatest? We can read our number line from left to right. As I come across a point, I will ﬁnd what teacher that is and put his or her Fraction Card into the correct order.

FACILITATION TIP If students struggle to ﬁnd a common denominator, explain that a simple way to do so is to multiply each denominator by the other denominator.

FACILITATION TIP Monitor groups to ensure that students are labeling the points on the number line for each teacher. Demonstrate as needed.

g. DOK-2 How can you use your ordered fractions and mixed numbers to ﬁnd the winner of the pizza party? Well, the winner of the pizza party is the class that collected the most canned goods, so I will ﬁnd the greatest fraction, and that teacher’s class will be the winner of the pizza party. 10. 11.

Once students have completed ordering their fractions together, instruct them to use that information to individually record their work on their Student Journals. Allow students enough time to rotate through each station and to record their work on their Student Journals.

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Compare and Order Fractions and Mixed Numbers Explore 4 – Order Fractions with Number Lines 12. 13.

When students have completed all their stations, challenge 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 How can you use equivalent fractions to help you plot your points on a number line? Equivalent fractions can help me ﬁnd a fraction with the same denominator for the number of increments between the whole numbers on my number line. I can then use that equivalent fraction to correctly plot that fraction on the number line. • DOK-3 How can a number line be used to order fractions? I can use a number line to order fractions by placing all my fractions in the correct place on the number line and then reading the number line from left to right to ﬁnd the order of my fractions from least to greatest. If I read the number line from right to left, then it would order my fractions from greatest to least. • 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.

Post-Explore 1. 2. 3. 4.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

Compare Fractions with 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

Compare Fractions 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

Compare Fractions with Benchmarks

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

Order Fractions with 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

Launch Day

Erno Rubik

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 Special Baseball

Compare Fractions and Mixed Numbers

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

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

Problem-Based Task

PhET Interactive Simulation

Summer Garden

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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207

Students who are still acquiring the concept and need remediation

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

Compare and Order Fractions and Mixed Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

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 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can compare and order fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.

I can use fraction models and number lines to compare fractions.

What prompts will be used?

What does mastery look like?

COMPARE AND ORDER FRACTIONS AND MIXED NUMBERS

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I can recognize that comparisons are valid only if both fractions refer to the same whole.

I can record comparisons using the symbols >, =, or <.

I can use benchmark fractions to compare fractions.

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SCOPE 1

Add and Subtract Fractions Scope Introduction SCOPE SUMMARY

Student Expectations

5.NR.3.3 Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.

Students have ample opportunities to understand and apply a wide variety of concepts regarding operations and fractional numbers. They apply equivalent fraction concepts (learned in fourth grade) along with adding and subtracting fractions with unlike denominators. These need to be changed into equivalent fractions with like denominators before the sum or difference can be calculated. In this scope, students learn to focus on number sense, redirecting their understanding of fractions as numbers that are found between whole numbers on a number line. When the topic centers on fractions, number sense also refers to being able to move between these fractions, as well as decimals, to locate equivalent fractions. Students apply their understanding of benchmark fractions and number sense to estimate and assess the reasonableness of solutions to fraction addition and subtraction problems.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In fourth grade, students extend their knowledge of fractions by composing and decomposing fractions and mixed numbers with a sum of fractions. They then begin modeling addition and subtraction of fractions and mixed numbers with the same denominators, using models and equations.

As students move into higher-level mathematics, they will build on their understanding of equivalent fractions, operational computation, and assessing for reasonableness of solutions. In sixth grade, students engage in adding, subtracting, multiplying, and dividing fractions and mixed numbers, using a variety of strategies, including but not limited to concrete models, visual fraction models, studentgenerated strategies, a standard algorithm, or other strategies based on numerical reasoning to represent and solve problems. The prior knowledge gained from these various strategies allows students to make sense of and strategically solve problems using eﬃcient methods that are most comfortable for and make sense to them.

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

estimate and solve a problem involving addition of fractions using benchmark diagrams and bar diagrams.

•

estimate using benchmark fractions.

•

solve using a bar diagram.

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: •

understand how to represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole, using objects, pictorial models, and properties of operations.

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. 210

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Addition and Subtraction Using Benchmark Fractions In this exploration, learning occurs through solving scenarios where students help ﬁgure out how much paint is in each bottle for art projects and how much was used for each. Students will: •

solve problems involving addition and subtraction of fractions that refer to the same whole.

•

use benchmark fractions to mentally estimate and assess the reasonableness of answers.

Explore 2

Explore 1

EXPLORE ACTIVITIES

•

use pictorial models to ﬁnd common denominators.

•

add and subtract fractions.

ﬁnd common denominators to add and subtract fractions.

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

Explore 4

Explore 3

In this exploration, students will be tasked with solving scenarios about the amount of ingredients needed for a food truck. Students will:

In this exploration, students will use manipulatives and resources to solve a scenario about helping determine how many crops are being used on a farm. 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. Subtraction with Unlike Denominators Using Equivalent Fractions

Addition with Unlike Denominators Using Equivalent Fractions

ADD AND SUBTRACT FRACTIONS

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

Problem Solve with Visual Models In this exploration, students will help a director set up for a 10k marathon. Students will: •

use manipulatives, number lines, and models to add and subtract fractions.

•

create models, write equations and complete a solution sentence for each scenario.

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

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Add and Subtract Fractions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

212

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students estimate and solve a fraction addition problem using benchmark fractions and diagrams. This activity is intended to assess mastery of the following standard(s): 4.NR.4.6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Materials

Preparation

Printed •

•

1 Student Handout (per group)

• •

Reusable •

Plan to have students work in groups of 2 or 3 to complete this activity. Prepare to project the Student Handout for the class. Print one Student Handout for each group of students.

ADD AND SUBTRACT FRACTIONS

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1 Projector or document camera (per class)

Procedure and Facilitation Points 1. 2. 3.

Project the Student Handout for the class. Give one Student Handout to each small group of students. Read the scenario with students, and ask students to discuss how they will solve the problem. a.

4. 5. 6.

Before ﬁnding the actual answer, students will use benchmark fractions to estimate the total. Allow students time to work through their estimated sum before sharing their reasoning with the class. Facilitate a class discussion about how they estimated the sum. This provides an opportunity to gain an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

7. 8.

We are looking for a total time, so we will need to add the 2 amounts 3 1 (__4 of an hour and 1 __4 hours) to each other. We can use a model to help us to solve the problem.

3 __

Challenge early ﬁnishers to compare their answers to another group. Groups can explain their thinking and their strategy.

is very close to 1, so we can estimate __4 of an hour to be about 1 hour. 1 1 1 __4 is also close to 1 hour, so we can estimate 1 __4 to be about 1 hour. If we add 1 hour + 1 hour, our estimated sum is 2 hours. Jamal’s time is about 2 hours. 4

FACILITATION TIP

After estimating, students will use the diagram to ﬁnd the actual sum. Discuss with students how they solved the problem. Also discuss the need to show the portion of each hour in the diagram and that the whole must be equal for each model. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Encourage students to justify their reasoning by using benchmark fractions, number lines, and bar diagrams to complete the activity.

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Add and Subtract Fractions Hook – Pizza Portions ACTIVITY PREPARATION Students add fractions with unlike denominators by replacing given fractions with equivalent fractions with like denominators to ﬁnd a sum with a like denominator.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Part II

Reusable • •

• •

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

Consumable •

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

Plan for students to work in pairs to complete this activity. Gather enough sets of colored pencils for each pair of students to have one set.

1 Set of colored pencils (per pair)

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

FACILITATION TIP Project a print version of the scenario. Have students read it silently to themselves, then read it together as a class more than once. Guide students to ﬁnd the relevant math phrases and values.

DOK-1 What information do we have and what do we know? We have the 3

amount each person ate. Maddy ate __4, Jim ate __2, and Jacky ate __8 of a

pizza. The pizzas are divided into 8 pieces. The problem asks how much pizza they ate, which tells us that we need to add the fractions together to ﬁnd this out.

FACILITATION TIP In addition to the circle model, include a standard rectangular model for students. The rectangular model will support visualization of multiplication and division with fractions. Rectangles are also easier to divide relatively equally and can be placed above and below each other to visually compare. 214

DOK-2 What steps will need to be taken to solve the problem? We will need to ﬁnd a common denominator. We will use the pictorial models from the Student Handout to help us solve the problem. We will color in the fraction of a pizza that each person ate. We will color each person’s pieces of pizza in a different color. We will then determine how much pizza Maddy and her friends ate. Finally, we will write an equation using fractions with like denominators to represent the scenario.

Engage

Explore

Explain

Elaborate

Evaluate

Part II: Post-Explore 1. 2.

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

6. 7. 8.

Acceleration

FACILITATION TIP

The students should draw visual representations of how much pizza each family member can eat. Although circles are more typical, using rectangles allows a. DOK-1 What information do we have and what do we know? We have the the students to create more accurate 3 5 1 amount each person ate. Maddy ate __4, Jim ate __2, and Jacky ate __8 of a representations. pizza. The pizzas are divided into 8 pieces. The problem asks how much pizza they ate, which tells us that we need to add the fractions together to ﬁnd this out.

Intervention

Divide the class into pairs. Tell them to determine the common denominator they should use in the equation. Once a pair ﬁgures out their common denominator, the students can use that as their password to receive a copy of the Student Handout and a set of colored pencils. Give students about 10 minutes to solve the problem. a.

Students should choose a pencil color for Maddy and a different color for each friend and color the fraction of a pizza that each friend eats in that speciﬁc color.

Have students use the pictorial model from the Student Handout to write an equation using fractions with like denominators that represents the scenario and solve for the answer.

Tell students to use their ﬁngers and hold up the number of pizzas Maddy and her friends ate. Have students use their ﬁngers to hold up the number of leftover pieces of pizza they will have. Gather the students in a whole group, and discuss the following questions: a.

DOK-2 How did you solve the problem? We colored the number of slices of pizza that equal the fraction for each person: 6 for Maddy, 4 for Jim, and 5 for Jacky. We added these up to get 15 slices. In the pictorial model, 15 slices made up 1 whole pizza and 7 slices of a second pizza.

DOK- What equivalent fractions did you use to be able to construct an DOK-2 6 3 4 5 1 equation with like denominators? We used __8 for __4, __8 for __2, and we kept __ 8.

c. d.

DOK-2 What was the equation you created to represent the scenario? 6 __ 4 5 15 __ + + __ = ___ 8 8 8 8

FACILITATION TIP

ADD AND SUBTRACT FRACTIONS

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Using their representations, the students should predict how many of eight pieces of pizza they believe each family member will eat. Keep these predictions for use after the students complete the Explore activities.

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 Use manipulatives and visual representations to help struggling students identify equivalent fractions.

DOK-2 How much pizza did they eat? They ate 15 slices of pizza, or 15/8. The pizzas are divided into 8 slices. 8 slices is 1 whole pizza and they ate 7 slices of the second pizza.

e. DOK-2 How many pieces of pizza will be left over? What fraction of a 1 pizza is left over? 1 piece will be left over. That is __8 of a pizza.

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Add and Subtract Fractions Explore 1 — Addition and Subtraction Using Benchmark Fractions ACTIVITY PREPARATION Students solve problems involving addition and subtraction of fractions that refer to the same whole. Students will use benchmark fractions to estimate mentally and assess the reasonableness of answers.

Standards for Mathematical Practice • • •

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

Materials

Preparation

Printed • • • • •

• • •

1 Student Journal (per student) 1 Set of Benchmark Fractions (per group) 1 Set of Scenario Cards (per group) 1 Set of Paint Bottle Cards (per group) 1 Exit Ticket (per student)

•

Reusable • • •

2 Different colored pencils (per student) 1 or 2 Sets of fraction tiles (per group) 2 Resealable bags (per group)

• • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Benchmark Fractions for each group. When printing the Benchmark Fractions, ensure the printer is set to Print Scale 100% (not Scale to Fit Page) so measurements will be correct. Print a set of Scenario Cards and Paint Bottle Cards, on card stock for durability, for each group of students. Cut the Scenario Cards and Paint Bottle Cards out along the dashed lines. Place each set of Scenario Cards and Paint Bottle Cards in separate resealable bags per group. Label the bags for Paint Bottle Cards “Part I” and for Scenario Cards, “Part II.” Gather sets of fraction tiles so that each group can share 1 or 2 sets. Gather 2 different colored pencils for each student. 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 Tiles)

PROCEDURE AND FACILITATION POINTS 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 I 1.

2. 3. 4.

Read the following scenario to the class: Mr. Esparza was getting ready to have his students start an art project. Before they started, he pulled out his paint bottles to see how full each bottle was. Using benchmark fractions, help Mr. Esparza ﬁgure out about how much paint is in each bottle. Give a Student Journal to each student. Give the Paint Bottle Cards and 1 or 2 fraction tile sets to each group. Explain how students can use fraction tiles to ﬁnd the benchmark fractions. Notes

216

Explore

Explain

Elaborate

Evaluate

Instruct students to look at the ﬁrst paint bottle and notice it has __8 of paint remaining in the bottle. Ask students to use Benchmark Fractions and fraction 1 tiles to discuss with their groups what fraction it is closest to: 0, __2, or 1. a.

Engage

DOK-2 Invite students nts to share their observations. We observed that __8 is 3 1 closest to one whole. It is only __8 away from one whole, but it is __8 from one-half.

Encourage groups to collaborate as they continue working through the scenarios and their Benchmark Fractions and fraction tiles to ﬁll out the Benchmark Fraction column on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How can we ﬁnd benchmark fractions for each paint bottle? I can represent each fraction with the fraction tiles and place them on the Benchmark Fractions. I will round my fraction to the closest benchmark fraction.

DOK-2 What happens if my fraction looks close to two benchmark fractions? I will ﬁnd out how many tiles away my fraction is from either benchmark fraction and choose the one that is fewer tiles away.

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

Math Chat •

DOK-2 Are benchmark fractions similar to another math concept you know? They are similar to rounding.

•

DOK-2 Are there other benchmark fractions we could use to make the rounding 3 1 more accurate? We could use __4 and __4 to make the rounding more accurate 1 because those fractions fall exactly halfway between 0, __2, and 1.

Part II 1.

2. 3.

Intervention

Acceleration

FACILITATION TIP Ask each group to record their representation of the fraction, their answer, and their justiﬁcation on a whiteboard. Have the groups hold up their whiteboards for a quick check for understanding.

FACILITATION TIP

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Encourage students to evaluate and provide feedback to other groups and to allow other groups to evaluate their work as well.

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.

Read the following scenario to the class: Mr. Esparza has planned a fun math and art activity for his students. They will be using fractions to find out how much paint they used on their project. This will not only help him figure out if it is time to order new paint if the bottle is getting low, but it will also help the students see how much of each color went into their project. Use your fraction knowledge to help Mr. Esparza figure out how much paint was used in each project. Explain to students that they will be reading each Scenario Card together and using the fraction tiles to help them represent each problem. Ask students to draw a model that represents what they did with the fraction tiles on their Student Journals. a.

Encourage them to use their different colored pencils to represent the different fractions they added and subtracted.

They will then represent their work and write their solution as both a number sentence and a solution sentence.

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

DOK-1 What benchmark fractions and numbers can you use to help you 1 solve each problem? I can use 0, __2, and 1.

DOK-2 How can you check to see if your answer is reasonable? I could ﬁnd equivalent fractions to add and subtract and compare my answer to my estimate.

FACILITATION TIP The students should include a justiﬁcation statement for each of their responses. FACILITATION TIP Being able to determine reasonableness is an important skill for the students to master. Spend time modeling how to determine and justify reasonableness. 217

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Add and Subtract Fractions Explore 1 — Addition and Subtraction Using Benchmark Fractions

5. FACILITATION TIP In addition to these Math Chat questions, prepare to share some unique real-world applications of when older students or adults need to be able to add and subtract fractions. Make sure to include examples of estimations and exact answers.

DOK-2 How can you ﬁnd if a fraction is close to __2? You can ﬁnd half of the denominator and see if the numerator is a little above or below that number.

DOK-2 How can you ﬁnd if a fraction is close to 1? I can see if the fraction is close to 1 because the denominator tells me how many equal parts the fraction has, and the closer the numerator is to the denominator, the closer the fraction is to 1.

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

Math Chat •

•

DOK-2 What are some strategies you used to add and subtract fractions? We have used fraction circles and fractions tiles or drawn a fraction model to add and subtract like denominators. DOK-3 Is using benchmark fractions a good way to estimate sums and differences of fractions? Why? Yes, it is, because it allows you to quickly estimate what the answer will be. Sometimes you don’t need an exact answer; you just need an estimate.

Post-Explore FACILITATION TIP When you preview this Exit Ticket with students, clarify your expectations for drawing the models. Some students may only want to draw models of the benchmark fractions or the exact fractions. Also, clarify if the number sentence is to be written with estimates or exact values.

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

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Add and Subtract Fractions Explore 2 — Addition with Unlike Denominators Using Equivalent Fractions ACTIVITY PREPARATION Students use pictorial models to ﬁnd common denominators to add fractions.

Standards for Mathematical Practice • • •

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

Preparation

Materials Printed • • • •

• • •

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

•

Reusable • • • • •

•

2 Colored pencils of different colors (per student) 1 Resealable bag (per group) 1 Dry-erase marker (per group 1 Clear sheet protector (per group) 1–3 Sets of fraction tiles (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Number Line, on card stock for durability, and place it inside a clear sheet protector to create an erasable surface. Print a set of Scenario Cards, on card stock for durability, for each group of students. Cut the cards apart and place them in a resealable bag. Prepare the following materials for each group: a bag of Scenario Cards, a Number Line, 2 colored pencils for each student, a dry-erase marker, and a set of fraction tiles. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Tiles and Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Give the students an opportunity to discuss and brainstorm how they will use the information and images provided to solve the scenario. Allow them to use their ideas to direct you as you guide them through the scenario.

2. 3. 4.

FACILITATION TIP 3

Remind the students that “__8” means “three out of eight” or “three parts out of a total of eight parts.” 220

Read the following scenario to the class: Your grandparents have an orchard where they grow different varieties of apple-producing trees. You enjoy visiting their orchard, so you have offered to help your grandparents with collecting the apples during the weekends. They have divided their orchard into several different sections. They need your help determining what fraction of the land is being used for the different varieties of apple trees. Can you help? Give a Student Journal to each student, and distribute materials to each group. Invite students to read scenario 1 together. Explain that your grandparents have divided up an area of land for their Detroit Red trees. Discuss the following question:

DOK-1 What does it mean that __8 of the orchard is being planted with Detroit Reds? It means that out of 8 equal sections, 3 will be planted with Detroit Reds.

Explain that your grandparents have divided up an area of land for their Gala trees.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a. DOK-1 What does it mean that 1/4 of the orchard is being planted with Galas? It means that out of 4 equal sections, 1 will be planted with Galas. b. DOK-2 How can 3/8 and 1/4 be added together? Answers will vary. The two FACILITATION TIP fractions have different denominators. In order to add them, we would need to ﬁnd Ask the students which fraction is greater: a common denominator. 3 1 __ or __8. This will reinforce prior knowledge 4 c. DOK-2 How can this problem be represented on an open number line? Answers and prepare them for estimation with fractions. will vary. Start with the fraction of the east orchard that will be planted with Galas since that is a friendlier unit fraction. Create increments on the open number line for 0, 1/4, 2/4, 3/4, 4/4, or 1. The ﬁrst jump on the number line for the Galas will be from 0 to 1/4. The fraction of the east orchard that will be planted with Detroit Reds is 3/8. Two one-eighths is equal to 1 one-fourth, so 2/8=1/4, 4/8=2/4, 6/8=3/4, and 8/8 = 4/4, or 1. Increments for 1/8, 3/8, 5/8, and 7/8 can be created between the equivalent fractions. The second jump for the Detroit Reds will be from 1/4 or 2/8 to 5/8. 5/8 of the east orchard will be planted with Detroit Reds

FACILITATION TIP

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Ask the students to brainstorm ways that they could adjust the two images so they would have the same number and size of pieces. Guide them toward using the least common multiple to determine how to create a model with the same number and size of pieces.

and Galas. 7.

Explain to students that they may use manipulatives to come up with equivalent fractions for each fraction in order to create common denominators. 8. Invite them to draw number lines or area models and use a colored pencil to indicate the variety of apple tree. Ask them to use these models to answer the questions on their Student Journals. 9. Encourage students to work collaboratively, and challenge them to find different ways to model how they found equivalent fractions. 10. As students are working, monitor and check for understanding. FACILITATION TIP 11. When students finish all four scenarios, they should complete the reflection questions. 12. After the Explore activity, invite the class to a Math Chat to share their observations and Use manipulatives to visually demonstrate learning. this concept if they are struggling to understand. Math Chat FACILITATION TIP • DOK-2 How does the fraction change when you find an equivalent fraction? The value remains the same, the only thing that changes is how the whole is partitioned and the size of As an extension, ask the students to those partitions. This changes the denominator and the numerator, but it still represents the describe the relationship between each of 1 2 same amount. the equivalent fractions. For example, __4 = __8; • DOK-3 Explain how you chose your common denominators. To find common denominators, if you multiply both the numerator and we used models to see the size of one piece of the whole. We then compared different-sized denominator of __1 by two, then you get the 4 2 pieces to see which ones could fill the piece neatly. For example, one-fourth fit two-eighths equivalent fraction of __8. neatly. So that means we can now add two-eighths to three-eighths and get an answer of FACILITATION TIP five-eighths. Another way is to find a common multiple between both denominators. For example, 8 and 4 both have a common multiple of 8. Since we do not have to change the Consider using a multiplication chart or size of the eighth, we left it alone. To change the fourth, we had to multiply 4 by 2. This times table to show students how they can means each fourth is now partitioned into two pieces for a total of eight parts making the slide over left and right to find equivalent whole. So one fourth piece now is made up of two eighth pieces. fractions using multiples. • DOK-2 Why are common denominators necessary when adding fractions? We need common denominators in order to add fractions because we need to make sure we are adding the same-sized pieces from the same-sized whole. 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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Add and Subtract Fractions Explore 3 — Subtraction with Unlike Denominators Using Equivalent Fractions ACTIVITY PREPARATION Students use fraction manipulatives and models to make common denominators in order to subtract fractions with unlike denominators.

Standards for Mathematical Practice • • •

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

Preparation

Materials Printed • • •

•

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

• •

Reusable •

• •

1–3 Sets of fraction tiles (per station)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Handout and an Exit Ticket for each student. Print a set of Ingredient Station Cards, on card stock for durability, for the class. Cut the cards apart, and place them around the classroom. Prepare fraction tiles for each station. 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 Tiles)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Allow each group to choose the manipulatives they would like to use during this activity. 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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2. 3.

4. 5.

Read the following scenario to the class: Your food truck, The Kooky Cookie Co., opened last week to great fanfare. A local social media inﬂuencer loved your cookies so much, she decided to feature you on her page. This means customers! That’s great news, but now you need to keep a closer eye on your ingredient inventory to make sure you don’t run out. At the end of the day, you check all of your ingredients to see how much was used that day. Explain to students that they will be visiting each of the six ingredient stations. Encourage students to use fraction manipulatives to model each problem, draw the model on their Student Journals, and then create an equation that represents that model. Assign each group to a starting station. Allow them a few minutes at each station before moving on to the next one. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What do we need in order to subtract these fractions? Equalsized pieces

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

FACILITATION TIP DOK-2 How can we write numbers greater than one as fractions? The numerator will be greater than the denominator because it has more Model for students using fraction tiles how pieces than the whole. We call them improper fractions. to convert mixed numbers into improper fractions. d. DOK-2 When is it useful to use improper fractions to subtract? When the numerator in the starting number is less than the numerator in the FACILITATION TIP subtracted number—for example, two and one-third minus two-thirds 5 Have students explain why __6 cannot 6. After the Explore activity, invite the class to a Math Chat to share their be reduced. Allow them to share their observations and learning. justiﬁcations. Math Chat c.

•

• •

DOK-2 How is subtracting fractions similar to adding fractions? You need to be able to ﬁnd equivalent fractions so the fractions have common denominators with equal-sized pieces. DOK-1 What is it called when the denominators are the same? Common denominators. DOK-2 What happens to the size of the pieces when you multiply the numerator and denominator by the same number? The size of the pieces changes. 2 For example, if one-fourth is multiplied by __2, this means each piece is being partitioned into two pieces. So now instead of the whole being four equal pieces, there are eight equal pieces.

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Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding When previewing this Exit Ticket, take time of the concept. to clarify your expectations regarding the Complete the Anchor Chart as a class. models. Have each student complete their Interactive Notebook. Notes

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Add and Subtract Fractions Explore 4 — Problem Solve with Visual Models ACTIVITY PREPARATION Students use manipulatives and models to solve problems with the addition and subtraction of fractions.

Standards for Mathematical Practice • • •

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

Preparation

Materials Printed • • • •

•

1 Student Journal (per student) 1 Number Line (per station) 1 Set of Station Cards (per class) 1 Exit Ticket (per student)

• • •

Reusable • • •

•

1 Dry-erase marker (per station) 1 Clear sheet protector (per station) 1–3 Sets of fraction tiles (per station)

•

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 Number Line, on card stock for durability, and place it inside a clear sheet protector to create an erasable surface. Print a set of Station Cards, on card stock for durability, for the class. Cut the cards apart, and place them around the classroom. Prepare the following materials for each station: a Station Card, a Number Line, a dry-erase marker, and a set of fraction tiles. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Tiles and Number Lines)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP As a student reads the scenario cards, other group members should list the fractions needed to solve the problem on their dry erase board. Another student can place the fractions on a number line. FACILITATION TIP You can give students a few fractions to convert using the fraction tiles to refresh students. Then, the students can place the converted fractions on a number line. 224

2. 3. 4. 5. 6.

Read the following scenario to the class: You have decided to help set up the Annual Winter Wonderland 10K Run. The director has asked you to help with the setup before the race. Visit each station, and complete the assignments left to you by the race director. Explain to students that they will be visiting each of the six stations, where they have been given directions to get ready for the race. Encourage students to use fraction tiles and number lines to help create models to solve the problems. Ask them to record how they solved the problem in their Student Journals. Assign each group to a starting station. Provide students with a few minutes at each station to collaborate and solve the problem.

Engage

Explore

Explain

Elaborate

Evaluate

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

DOK-1 What do we need in order to add or subtract these fractions? Equal-sized pieces

b. DOK-1 When we have equal-sized pieces, what happens to the denominators? They are the same. We call them “common denominators.”

Intervention

Acceleration

FACILITATION TIP Be sure students are converting the fractions correctly. Address common misunderstandings as a class during the Math Chat.

8. 9.

DOK-1 How can we write numbers more than one as fractions? FACILITATION TIP The numerator will be greater than the denominator because it has more Ensure that students are fluent with the pieces than the whole. We call them “improper fractions.” terms common denominator and improper When students finish all six stations, they should complete the reflection fractions before moving on to further questions. scopes. After the Explore activity, invite the class to a Math Chat to share their observations and learning. STEMscopes Tip

Math Chat DOK-2 What is the first step when you’re adding or subtracting fractions or mixed numbers? Why is that important? Find the common denominator so the pieces of the whole are all the same size. If the denominators aren’t the same, the pieces can’t be added or subtracted. • DOK-3 When working on the last question, was it hard to draw the models? Would there be an easier way to find a common denominator? The model was hard because there were so many pieces. Instead of drawing a model, I could list multiples or multiply to find a denominator I could change both 8 and 5 into. • DOK-2 When looking at the fractions you added or subtracted, what did you notice about the relationship between the original denominators and the common denominators? You can multiply the original denominators together to get a common denominator because a common denominator must be a multiple of both numbers to create equivalent fractions. •

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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. FACILITATION TIP Provide students with multiplication charts and continue to model how to locate common multiplies and equivalent fractions on the table.

Post-Explore 1. 2. 3. 4.

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Add and Subtract 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

Addition and Subtraction Using Benchmark 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

Addition with Unlike Denominators Using Equivalent Fractions 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

Subtraction with Unlike Denominators Using Equivalent Fractions Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook

Show What You Know, Part 4

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

Problem Solve with Visual Models 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

Yard-Sale Treasurer

Carpenter

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

It Holds the World Together

Add and Subtract Fractions with Unlike Denominators

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

Rock Paper Scissors

Fraction Addition and Subtraction with Unlike Denominators – Models and Equations

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

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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

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Add and Subtract 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

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 visual fraction models to reason about the process for adding and subtracting fractions and mixed numbers with unlike denominators.

What prompts will be used?

What does mastery look like?

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I can reason that when adding and subtracting fractions and mixed numbers, the fractions must refer to the same whole.

I can replace fractions that have unlike denominators with equivalent fractions that have the same denominator.

I can multiply the denominators of unlike fractions to ﬁnd a common denominator.

I can recognize that mixed numbers can be equivalent to improper fractions.

I can use visual fraction models and equations to represent problems involving the addition and subtraction of fractions and mixed numbers.

I can use benchmark fractions and number sense to estimate and assess the reasonableness of an answer.

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SCOPE 1

Multiply Fractions Scope Introduction SCOPE SUMMARY Students use various manipulatives to create area models, diagrams, and number lines to make sense of the process for multiplying a fraction by a whole number. They then interpret these models by writing addition expressions and relating them to a multiplication expression. Students also reason about multiplication as scaling or resizing, meaning the size of the product can be altered based on the resizing of one or both of the factors. They justify their reasoning with pictures, models, or manipulatives. Student Expectations

5.NR.3.4 Model and solve problems involving multiplication of a fraction and a whole number. 5.NR.3.5 Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In fourth grade, students solidify their understanding of equivalent fractions and begin to compose and decompose fractions and mixed numbers. Fourth graders use that knowledge to add and subtract fractions with the same denominators. In ﬁfth grade, prior to this scope, students expand their knowledge of adding and subtracting fractions and mixed numbers with unlike denominators, and they compare and order fractions and mixed numbers.

In sixth grade, students use the number line to make sense of the order, comparison, and absolute value of rational numbers. Sixth-grade students solve problems involving the multiplication of fractions by whole numbers, another fraction, or mixed numbers. The use of fractions is limited to the denominators 2, 3, 4, 5, 6, 8, 10, and 12. Sixth graders can use a variety of strategies, including but not limited to concrete models, visual fraction models, student-generated strategies, a standard algorithm, or other strategies based on numerical reasoning to represent and solve problems.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

choose the model that best represents a fraction equivalent to one-third.

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: •

represent and solve problems involving the multiplication of a whole number.

•

represent a fraction that refers to the same whole, by using objects and pictorial models, including area models.

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

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Equal Groups In this exploration, students will use fraction tiles and fraction circles as models. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

number lines as representations to make the connection that multiplying fractions is the same as repeated addition of fractions.

•

determine that when a fraction and a whole number are multiplied, the product will be less than the whole number.

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

Explore 4

Explore 3

In this exploration, students will model multiplication of fractions in a variety of ways. Students will:

In this exploration, students will recognize that ﬁnding a fraction of a group will involve multiplying to solve. 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.

Area Models

Fractions of a Group

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be introduced to the area model using grid paper.

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

Scaling In the ﬁnal exploration, students will participate in helping solve a real-world scenario that involves sharing plans for a new farm property to compare how each person wants to use the new space. Students will: •

reason about the size of the product based on the resizing of factors.

•

justify reasonings by using visuals, models, or manipulatives.

•

compare their strategies to others.

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

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Multiply 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 1

Students choose the model that best represents a fraction equivalent to __3. This activity is intended to assess mastery of the following standard(s):

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4.NR.4.1 Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fractions, including fractions greater than one, and explain the identity property of multiplication as it relates to equivalent fractions. Generate equivalent fractions using these relationships.

Materials

Preparation

Printed •

•

1 Slideshow (per class)

•

Reusable •

Plan to have students work in groups of 3 or 4 to complete this activity. Prepare to project the Slideshow for the class, or print a Slideshow for each group.

1 Projector or document camera (per class)

Procedure and Facilitation Points 1.

Project the Slideshow for the class, or distribute Slideshows to groups.

Instruct students to think about how to represent fractions equivalent to __3 by using different models.

3. 4.

Have students decide which model best represents represents the fraction. Have students raise one, two, or three ﬁngers to identify which model they agree with most. Students need to be ready to justify their choices. Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Sample student responses include the following:

5. 6.

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.

I think Model 1 best represents a fraction equivalent to __3. I know __6 is 1 equivalent to __3 because the shaded part is the same amount. 1

b. I do not think Model 2 best represents a fraction equivalent to __3. The model 3 1 shows ___ shaded, which is equivalent to __4. I can prove this by multiplying 12 1 the numerator and denominator of __4 by the same multiple of 3. c.

I think Model 3 best represents a fraction equivalent to __3 The model 4 1 shows ___ , which is equivalent to __3. I know this because the point could 12 1 also represent __3 on the number line.

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

FACILITATION TIP When you project the slideshow, have students make observations/notes silently and independently at ﬁrst. After they have made some notes, have them pair up with a shoulder partner and then be prepared to share with the whole class.

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Multiply Fractions Hook – Touchdown Pass ACTIVITY PREPARATION Students represent and solve problems involving the multiplication of a whole number and a fraction that refers to the same whole, by using objects and pictorial models, including area models.

Materials

Preparation

Printed •

•

1 Football Players (per group)

Part II

Reusable • •

Plan to show the Phenomena Video.

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

• •

Plan to have students work in groups of 3 or 4 to complete this activity. Print Football Players, on cardstock for durability, for each group of students.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore FACILITATION TIP

Print and project the text of the scenario. Have students think silently and jot notes ﬁrst; then, have them read it in pairs and prepare to share their ideas with the whole class.

touchdown. He knows that __6 of the players on the team have scored so far this 4. 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.

DOK-1 What information do we have? We know that there are 48 players 2 on the team and __6 of them have scored this year. 2

DOK-2 What does the fraction __6 represent? It represents two equal parts of six, or two equal pieces of six. We also know the denominator is six, which means the whole set is broken into six equal parts.

DOK-2 What are some strategies we learned that could help us ﬁnd __6 of 48? We learned about models, arrays, repeated addition, number lines, etc.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

234

season. How many players have scored a touchdown? Discuss the following questions:

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

DOK-1 What information do we have? We know that there are 48 players 2 on the team and __6 of them have scored this year.

3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

DOK-2 What are some strategies we learned that could help us ﬁnd __6 of 48? We learned about models, arrays, repeated addition, number lines, etc.

Give Football Players to each group. Tell students that the chart lists all of the players’ numbers. They may use the chart to help them model the problem. Discuss the following questions: a.

Intervention

DOK-2 How did your group solve the problem? The football players were divided into 6 groups. Because the denominator is 6, we are looking for 6 equal parts. If we put the football players into 6 groups, there will be 8 players in each group:

FACILITATION TIP When you distribute Football Players to students, take time to ensure that students understand that the players’ numbers are irrelevant values. This chart is an excellent example of how easy it is to be distracted with extraneous numbers that have nothing to do with the solution to a scenario. Consider allowing some time to see if students need clariﬁcation or not.

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FACILITATION TIP 1

This means that __6 of 48 is 8 players. We circled or colored 2 groups of 2 2 8, which would equal __6 of 48; __6 of 48 is 16. This means 16 players have scored touchdowns. b.

DOK-2 Which operation did you use? Explain your answer. Answers may

This rectangular model with equal parts will continue to be helpful as students progress into decimals and percents. Encourage students to use it as a visualization tool and to become ﬂuent at drawing models like this one.

vary. I was multiplying a fraction by a whole number. I used division to ﬁgure out how many pieces would end up in each equal part of the 1

whole. Once I knew how many players were in __6, I added that amount 2

twice to ﬁnd the total in __6.

DOK-3 If you did not have the chart, what strategy could you have used to solve the problem? We could draw a model or use groups to solve the problem. Notes

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Multiply Fractions Explore 1 — Equal Groups ACTIVITY PREPARATION Students use fraction tiles and fraction circles as models and number lines as representations to make the connection that multiplying fractions is the same as repeated addition of fractions.

Standards for Mathematical Practice • • •

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

Materials

Preparation

Printed • • •

• • • •

1 Student Journal (per student) 2 Sets of Station Cards (per class) 1 Exit Ticket (per student)

Reusable • • •

•

12 Sets of fraction tiles (per class) 10 Sets of fraction circles (per class) 8 Rulers (per class)

• •

Consumable • •

2 Strips of manila paper measuring 3 × 18 inches (per student) 2 Dispensers with clear tape (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 and cut apart two sets of Station Cards for the class. Prepare two bins for station 1, each with ﬁve sets of fraction tiles and a Station 1 Card. Prepare two bins for station 2, each with ﬁve sets of fraction circles and a Station 2 Card. Prepare two bins for station 3, each with one set of fraction tiles, four rulers, tape, and manila paper strips for half the students. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS 1. 2. FACILITATION TIP

Take time to engage students and check for prior knowledge about the meaning of batch.

236

FACILITATION TIP

Depending on your students, consider projecting and modeling using each Station Card. Solving these scenarios along with students may simplify classroom movement space as there are only three station cards.

Assign a station where each group will begin. Explain that students will rotate between three stations. At each station, students will be using the concept of equal groups to model a scenario involving fractions. Read the following scenario to the class: Today, you will be thinking about the role of a baker who is making different treats for a bakery. For each type of treat, more than one batch or recipe of sweets are needed to ﬁll the bakery’s needs. As you review the scenarios, you’ll need to be thinking about how much of some of the ingredients are needed to make all the batches. In station 1, you will be thinking about some ingredients used in cookies and cupcakes. In station 2, you will be thinking about some ingredients used in brownies and blondies. Finally, in station 3, you will be thinking about some ingredients used in making pies and pastries. Explain to students there will be different models found in each station. In station 1, students will use fraction tiles to model. In station 2, they will use fraction circles to model. Finally, in station 3, students will use number lines. Assign groups of students to their ﬁrst station. Ask them to review the Station Card at their station. Discuss the following question: a.

DOK-1 What measurements will you base your fraction models on? We will be modeling different amounts of pie and pastry ingredients in the form of cups or sticks. © Accelerate Learning Inc. - All Rights Reserved

10.

11. 12.

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 Can you give me an example of a fraction of a recipe ingredient 2 from your Station Card? An example is __3 of a cup of milk.

Have students discuss with their groups how they can model the scenarios and work together within their station using the materials provided to model and solve the problems. As students work, move from group to group and scaffold as needed. Remind students to draw their models and record their thinking on their Student Journals for each station. a.

Explore

Tell students that when you bake a recipe, you don’t always need whole cups. Sometimes parts, or fractions, of cups are used for the recipe ingredients. Discuss the following question: a.

Engage

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Note for Station 3: Pies and Pastries – Instruct students to each use two of the strips of manila paper and to tape them together along the short ends to make a longer strip. Next, have students use the ruler to draw an unlabeled number line in the middle of the strip, along the full length of the strip. Then, have them place a mark near the left side of the line for 0. Have them use the whole fraction tile to mark the whole-number intervals on the line by laying the whole tile under the number line, starting at 0 and using the other end to mark 1. They can move the left end of the tile to 1 and mark 2, etc. Have students continue until they have at least 4 whole units.

If a group is struggling, ask them to begin by modeling the amount of the ingredient needed to make one batch and to think about how they could represent more than one batch of the ingredient. When students draw a model, look for regrouping strategies. The focus should be that there are repeated groups of fractions. Some students will also start to connect that they are actually multiplying the fractions. Students may need help with writing the multiplication expressions. Remind students that multiplication means the amount in one group times the number of groups. In station 3, students may need help to think about representing each scenario on a number line. Discuss the following: a.

DOK-2 How can you represent a whole cup using a number line? You can use one of the whole fraction tiles.

DOK-2 How can you show the amount of an ingredient if it is less than a whole cup? You can use the other fraction tile models, such as halves, and put marks along the line. Or you could lay them along the top of the number line.

DOK-2 How can you represent the number of batches of the ingredient amount? The recipe amounts are happening over and over; they are being repeated, so we should have several jumps that are all the same number. The number of times the recipe will be made, the batches, will be the number of jumps.

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.

After students have rotated through each of the three stations, lead a discussion about the problems in each station and how the students modeled the situations. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What types of operations are found within the problems? The operations we found in the problems were repeated addition and multiplication. • DOK-2 Why does repeated addition work for these problems? It works because the same amount of the ingredient is in each batch, and there are multiple batches. You add the amount in each batch for the number of times the recipe will be made. •

FACILITATION TIP Before this Math Chat, be prepared with some additional relevant, real-world examples for when students will need to be able to multiply fractions by whole numbers. Look for landscaping, creative design, computer gaming, and construction examples. 237

MULTIPLY FRACTIONS

Multiply Fractions Explore 1 — Equal Groups DOK-2 How does multiplication represent repeated addition? The ﬁrst factor, the fraction, is the portion in each recipe. The second factor, the whole number, is the number of batches, or times the recipe will be repeated or made. • DOK-2 Think about one of the problems. What did you add to solve for the total amount of ingredients needed? We added the numerators over and over and put them over the denominator because we had the same fraction repeated. • DOK-2 Explain how you could use multiplication to solve the same situations. Because the fraction was being repeated many times, instead of repeated addition, we can multiply the fraction by the number of times each recipe is made (batches). • DOK-3 When you use multiplication, you multiply the whole number by the numerator because it is being repeated. The denominator does not change. Why is this true? It is because the size of the share, or part of the cup, is the same 1 throughout the problem. For example, we would be ﬁnding the total number of __2 2 __ cups in 8 batches or the total number of 3 cups in 4 batches. •

FACILITATION TIP Provide some clariﬁcation by showing students that if the word of can be logically placed between two values, it often means to multiply. These examples would be “8 1 2 batches of __2” or “4 batches of __3 .” (The commutative property applies here, but not all students will be ready to note that.)

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.

238

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MULTIPLY FRACTIONS

Home

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Multiply Fractions Explore 2 — Fractions of a Group ACTIVITY PREPARATION Students recognize that ﬁnding a fraction of a group will involve multiplying to solve and that when a fraction and a whole number are multiplied, the product will be less than the whole number.

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.

Preparation

Materials Printed • • •

• • •

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

Reusable • • • •

•

20 Two-color counters (per group) 1 Red colored pencil (per student) 1 Yellow colored pencil (per student) 1 Resealable bag (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Scenario Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag with the twenty two-color counters. 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. (Two Color Counters)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP Print this scenario and project for students. Set a timer and have them think silently and independently for 1 minute (allow notes), then share with a partner for 1 minute, and then prepare to share with the whole group. FACILITATION TIP This scenario provides a good opportunity to show students how the word of can be a clue word for multiplication. If of can be logically placed between two values in a scenario, it usually means to multiply. Emphasize the word of when you read the scenarios to students. For example, “One 3 fourth OF 20 is ? __4 OF 20 is?” 240

Distribute Student Journals and colored pencils to each student and bags with Scenario Cards and two-color counters to each group. Ask students to ﬁnd scenario 1.

Read the following scenario to the class: Makayla collects candles to make her house smell nice. As of right now, she has 20 candles. She complained to her 1 friend, though, that __4 of them are completely burned out. How many of Makayla’s candles are burned out? Have a discussion with the students about what is happening mathematically in this scenario. Discuss the following questions:

DOK-1 How many candles does Makayla have in all? She has 20 candles.

DOK-1 Are all the candles burned out? No

DOK-2 So less than 20 candles are burned out? Yes, it has to be less than 20.

DOK-2 Predict what you think would happen if we multiplied a whole number by a fraction. The product would be less than the whole number because the fraction is less than one.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Facilitate the construction of the ﬁrst model with the following guiding questions: a.

DOK-2 Look at the denominator. The denominator tells you how many parts, or groups, in this case. So what will you do with that information? We will split the 20 counters into four groups.

DOK-2 Do your groups need to be equal? Yes, we’re splitting them equally or dividing the whole into fractional parts.

Distribute your counters so you have four equal groups. DOK-2 How many counters do you have in each group? There are ﬁve counters.

DOK-1 What are we trying to ﬁnd? We are trying to ﬁnd out the number of burned-out candles.

MULTIPLY FRACTIONS

Home

e. DOK-1 What do we know about the burned-out candles? 1 Only __4 of the candles are burned out. f.

5. 6.

Allow students time to answer the questions on their Student Journals below the ﬁrst model. Make sure students understand that scenario 2 is connected to scenario 1. Discuss the following question: a.

7. 8.

DOK-2 Can we look at our model to ﬁnd the number of burned-out candles? Explain. We split the counters into four groups, but only one of the groups is burned out, so we need to look at the number of counters in just one group.

DOK-3 How does scenario 2 differ from scenario 1? This time, we are looking for the candles that are not burned out, so we have to ﬁnd the number of candles in the other 3/4 of her collection of 20.

Ask students to model the scenario. Students should discover that the model is set up the same way as the ﬁrst scenario. Discuss the following questions: a.

DOK-2 Why does your model look the same as scenario 1? There are still 20 counters. They are still divided into four equal groups.

DOK-3 So is the answer the same as in scenario 1? Why or why not? No, 1 the answer is not the same. In the ﬁrst scenario, we were looking for __4, 3 which is one of the groups. In the second scenario, we are looking for __4, which is three of the groups.

DOK-2 How many candles are not burned out? There are 15 candles not burned out.

DOK-2 So how many groups did you circle? We circled three groups.

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.

e. DOK-1 How many candles were in each group? There were ﬁve candles in each group. f. 9. 10.

11.

DOK-1 What expression does that represent? 3 × 5

Allow students time to answer the questions on their Student Journals below the second model and discuss. Student groups will then work together to complete the table using the information they obtained from the models. If students encounter problems completing the Explanation portion of the table, ask them if they notice a relationship among the number in each group, the number of groups selected, and the solution. Students should recognize that they are related by multiplication. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Consider pulling the class back together to complete the reﬂection questions to answer any questions and clarify misconceptions.

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MULTIPLY FRACTIONS

Multiply Fractions Explore 2 — Fractions of a GroupFractions Math Chat • FACILITATION TIP Before this Math Chat, be prepared with some additional relevant real-world examples for when students will need to be able to multiply fractions by whole numbers. Look for landscaping, creative design, computer gaming, and construction examples.

•

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.

•

DOK-1 How did you know how many items to place in each group? The denominator told us how many equal groups of the total number of items we needed to make. We placed an equal number of items in each group. DOK-2 As you and your group solved each scenario, did you see any evidence of repeated addition? Explain what evidence you saw. As we modeled and solved, we did have the same number of items in the groups that were split up. To get the total number of items, we had to add all the items in the groups we selected. DOK-3 Do you see a more efficient way to find the total for the groups you needed once they had been split up? We could also multiply the numerator (which is the number of groups) by the number in each group. 2 DOK-3 Use your own words to explain this statement: 6 is __5 of 15 If we split 15 2 into 5 equal groups, we would have 3 in each group. To find __5, we would have to take 2 of the groups of 3 (2 × 3). Then, our answer is 6. DOK-3 Explain why we are actually multiplying a fraction and a whole number but our answer is less than the whole number. If the factor is less than one, such as with a fraction, then the product is less than the other factor. We are taking part of the whole.

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.

242

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MULTIPLY FRACTIONS

Home

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Multiply Fractions Explore 3 — Area Models ACTIVITY PREPARATION Students model multiplication of fractions in a variety of ways. Students will also be introduced to the area model using grid paper.

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.

Preparation

Materials Printed • • • •

•

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

• •

•

Reusable • •

2 Colored pencils, any color (per student) 1 Resealable bag (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Scenario Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag. Prepare one sheet of Grid Paper and two colored pencils for each student. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS 1. 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.

2. 3. 4.

FACILITATION TIP Be aware that Scenario One refers to 9 1 dozen. Clarify how students are to solve. __3 of 1 9 or __3 of (9�12). 244

Read the following scenario to the class: You will be working together to help a baker at Sweet Dreams Bakery. This baker usually works on jobs with large groups of people and needs help ﬁguring out solutions to some baking situations that have come up. Distribute Student Journals, Grid Paper, and colored pencils to each student and bags with Scenario Cards to each group. Explain to students that they will begin by modeling the scenario on the Grid Paper. They can do this by creating a rectangle to represent the whole. Discuss the following questions: a.

DOK-2 How will you represent the denominator on the Grid Paper? The denominator will tell us how many equal groups in which to partition our rectangular area model.

DOK-2 How could you represent the numerator? The numerator will tell us how many equal groups to color in our rectangular area model.

Students may have diﬃculty generating an expression from their model. Help students see how multiplication can also be thought of as an “of” statement. For 1 example, __3 of 9.

Explain to the class that they will read the Scenario Cards and represent the scenario on their Grid Paper. They will then draw a model and write an expression that represents the scenario on their Student Journals.

8. 9.

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 What does each rectangular area model represent? The rectangular area model represents a set or a whole.

DOK-2 Will you need to draw more than one whole on the Grid Paper? Explain. Yes. Explanations may vary. Scenarios 3 and 4 ask for a fraction of each whole. We will need to combine the fractions of each whole together to ﬁnd a total. You need more than one rectangle to show that it’s a fraction of each whole and not a fraction of a set like scenarios 1 and 2.

Allow students enough time to work together to represent each Scenario Card 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-2 What do you expect the product to be when one factor is less than 1? The product will be less than the other factor.

•

DOK-2 When you were ﬁnding __3 of 9, you multiplied __3 × 9. Does the answer 3

MULTIPLY FRACTIONS

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FACILITATION TIP Depending on your students, consider modeling the ﬁrst scenario and third scenario for them or have student volunteers demonstrate. After this bit of instruction, have them collaborate on scenarios two and four.

1 make sense? se Explain. Yes, 3 is __3 of 9. Our answer should be less than 9 because

not all the 9 dozen were gluten-free.

• •

DOK-2 Is __3 greater than or less than __2? It is less than __2.

DOK-3 Does knowing that help us justify our answer? Yes, it does because our answer is 3, and that is also less than half of 9. 2

DOK-3 Does it make sense that it takes 4 ___ hours to bake all 6 sheet cakes? 10 Why? It does make sense because it takes less than 1 hour to bake each cake, so 7 1 it would take less than 6 hours. Also, ___ is more than __2 an hour, so it will take the 10 baker more than 3 hours. • DOK-2 Explain why scenarios 3 and 4 were multiplication problems. The fractions were being repeated in these scenarios for each of the sheet cakes. We were looking for a total number from equal groups. These scenarios looked like repeated addition.

•

DOK-3 Why is it that in some problems, such as scenarios 1 and 2, the model is a single rectangle and in other problems, the scenario calls for more than one 1 rectangular model? Scenarios 1 and 2 ask for a fraction of a set, such as __3 of a 2 set of 9 cupcakes or __5 of a set of 20 pies. The 20 pies were one whole (set), so we only had one rectangle drawn to represent that whole. Scenarios 3 and 4 ask for a fraction of each whole. We needed to combine the fractions of each whole together to ﬁnd a total. You need more than one rectangle to show that it’s a fraction of each whole and not a fraction of the set of cakes.

FACILITATION TIP Use this question to have students vote, or use a physical response to model the values or comparison symbol. 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.

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, allow a variety of 1 Complete the Anchor Chart as a class. models. Some students may model __6 of Have each student complete their Interactive Notebook. 48, others may need to draw groups within 48, and others may use a number line. Continue to encourage students to draw models and show their thinking even if they “know” the answers.

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Multiply Fractions Explore 4 — Scaling ACTIVITY PREPARATION Students reason about the size of the product based on the resizing of one or both of the factors. Students justify their reasoning with pictures, models, or manipulatives. Students will compare or contrast their strategies with their partners.

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

Preparation

Printed • • •

• • •

1 Student Journal (per student) 3 Sets of Station Cards (per class) 1 Exit Ticket (per student)

Reusable • •

• •

20 base ten blocks, ten rods (per station) 20 base ten blocks, one units (per station)

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print three sets of Station Cards, on card stock for durability, for the class. Cut the cards apart, and place them at different stations around the classroom. Assign four pairs of students to each set of cards. You may want to consider printing each set on different-colored card stock. Decide at which station each pair will begin. Prepare each station with the following manipulatives: 20 base ten rods 20 ones unit cubes

• • • •

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 FACILITATION TIP

As you read this scenario with the class, discuss the possible shapes for the property. Students may wonder if it must be a square, rectangle, or any other shape. 2. 3. FACILITATION TIP Consider providing some grid paper for students to begin to visualize these questions as you think, discuss, and share.

246

Read the following scenario to the class: You and your business partner have invested in a farm and have to plan where everything will go. The two of you have different plans and ideas for the new property. Today, you will share your plans with your business partner and compare how each of you wants to use the space. You are not trying to ﬁnd the exact measurements; you are simply comparing what that space would be for either business plan. Explain that students will work with a “business partner” as they travel to the different parts of their farm. Emphasize that they are not solving for the area; they are simply comparing business plans for their new investment. Challenge the pairs to think, discuss, and share their thoughts about the following questions: a.

DOK-2 What would happen to the area if the length of one side were to decrease? Why do you think that? The area would become smaller. The length and width of a rectangle affect the space in the area. If one of those side lengths were to change, so would that area. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What would happen if the length of one side were to increase? Why do you think that? The area would become bigger. The length and width of a rectangle affect the space in the area. If one of those side lengths were to change, so would that area.

DOK-2 How do you know this would happen? What do you understand about area? When we solve for area, we multiply length × width. If those change, so does the area. If I were to make an array, this means the number of columns and/or rows would change, which would affect the total number of items in the array.

DOK If one side decreases by a fraction — __2, for example—what do you DOK-2 think would happen to the area? Why do you think that? The entire area gets halved, too. This is because half of the length or width gets taken out. If we compare it to an array, half of the items in the array are taken out.

Intervention

Acceleration

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e. DOK-2 What about if both sides get resized? What do you think would happen if I decreased the length or the width by one-half? We would 1 1 have to multiply how they got resized, __2 × __2, and that will be how much the total area gets resized. 5. 6.

7. 8. 9. 10.

Explain that at each area of the farm, pairs will compare how each business partner wants to use the space for the determined purpose. Encourage students to individually reason (using a drawing, models, or manipulatives) about how the space they will use is different and how they know that based on the relationship of the measurements for each plan. Encourage them to show their reasoning differently and record their reasoning in their Student Journals. Invite the pairs to compare their strategies using their Student Journals. Challenge pairs to ﬁnd similarities and differences in each others’ strategies and record ﬁndings in their Student Journals. As students are working, listen for reasoning. If students are thinking of the same strategy, talk to them about other ways to display. a.

11.

DOK-2 You both thought of drawing a rectangle and writing the measurements. What could possibly be another way? One of us could make a rectangle but with base ten blocks and then take some of them away to make the other rectangle. DOK-2 How can you use base ten blocks? For example, the corn and peppers—I modeled the length of a rectangle using 2 ten rods and 2 unit cubes to make 22. Then, I modeled the width using 1 ten rod and 2 unit cubes to make 12. When I modeled the length of the next rectangle, I left the 22 but then added another ten rod and 2 unit cubes to the 12 I already had for the width to make 24. This showed me that since I doubled the width, I would double the area.

Help students ﬁnd similarities and differences with the 2 strategies. Discuss the following questions: a.

DOK-1 Did you both draw the same picture? No, one of us drew the ﬁrst one, and the other one drew the second one.

DOK-1 What stayed the same in both strategies? Length or width

DOK-1 How did the measurements change? __2, __4, __3, etc. of the original size

DOK-1 Do you both agree about the size of the area? Yes

FACILITATION TIP If time and space are limited, consider projecting each scenario one at a time and allowing partners to collaborate for a few minutes to solve. After partners have drawn models, used manipulatives, and reasoned through Corn vs Peppers, bring the whole group together to compare solutions and models. Move on to the next scenario (Barn vs Coop) and allow for collaboration time again and so on.

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.

1 1 1

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Multiply Fractions Explore 4 — Scaling 12.

FACILITATION TIP Print and post this expectation for students to refer to as they collaborate. For example, “Its the process, not the product,” or “Think and reason, don’t rush to results.” FACILITATION TIP Before this Math Chat, take time to ﬁnd some visual real-world examples of scaling to share with students. Encourage them to look for applications in familiar careers or hobbies.

13.

If you notice students actually multiplying the numbers, steer them away from that strategy and remind them that this activity is to just reason. Explain that it’s not the actual product but the resizing comparison you are looking for. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 What connections did you make during this activity? I was able to strategize using rectangles. I could multiply like I would when I find the area of a rectangle. I noticed that my partner and I didn’t have to use the same strategy to come up with the same result. There are many ways to find the same answer. • DOK-2 Was it necessary to multiply to figure out the resizing area? Why? No, because the reasoning is always the same when increasing or decreasing. The area will get larger or smaller based on what happens to one or both sides. •

•

DOK-3 Explain how you determined the resizing. If the length or width decreased 1 1 by __2, __4, or any fraction, the area also decreased by that same amount. If it was 1 half the size, then I knew I had to divide by 2. If it was __4 of the size, I divided by 4. If it doubled, then I knew to multiply by 2. If both sides resized, then I had to multiply both fractions together to determine how the area resized.

Post-Explore 1. 2. 3. 4.

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Multiply 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

Equal Groups 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

Fractions of a Group Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

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

Area Models

Interactive Notebook

Show What You Know, Part 4

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

Scaling

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

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ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

The Fun Run

Paula Deen

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

Fireﬁghters’ Pancake Supper

Multiply Fractions – 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

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Problem-Based Task Grandma’s Spaghetti Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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Multiply 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?

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What does mastery look like?

I can model the multiplication of a whole number and a fraction using a variety of strategies.

I can solve problems involving the multiplication of a whole number and a fraction.

I can reason about how numbers change when they are multiplied by fractions.

I can explain that when multiplying a whole number by a fraction greater than one, the number increases, and when multiplying by a fraction less than one, the number decreases.

I can explain that when multiplying a whole number by a fraction equal to one results in a product equal to the whole number.

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Fractions as Division Scope Introduction SCOPE SUMMARY Students connect fractions with division as they understand that 7 ÷ 3 = __7. Students 3 have many opportunities to explore the relationship between division relationships and numerator/denominator.

VERTICAL ALIGNMENT

Student Expectations

5.NR.3.1 Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Background Knowledge

Future Expectations

In fourth grade, students extend their understanding of fractions by decomposing a fraction into a sum of fractions with the same denominator and comparing two fractions with different numerators and denominators using benchmark fractions and common numerators or denominators. Students also multiply a fraction by a whole number.

Sixth grade will apply and extend students’ understanding of division to perform operations with multi-digit decimal numbers fluently by using models and student-selected strategies. Sixth-grade students will also be asked to multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. They will interpret products and quotients of fractions and solve word problems. Seventh-grade students will understand that integers can be divided and that the quotient makes a rational number. Eighth graders will begin to use rational numbers to approximate irrational numbers. In sixth-grade geometry, students will use their knowledge of multiplying fractions to help them find the area of rectangular prisms. Connections will be made in sixth and seventh grade as students begin working with ratio concepts and reasoning. In sixth grade, students will explore the concept of unit rates, and in seventh grade, students will find the unit rate of fractions. They will use these understandings to apply these principles to real-world contexts.

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

solve whole number problems from given word expressions.

•

share their representations of the problem.

•

explain the concept of a remainder in a class discussion.

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

Hook

Accessing Prior Knowledge

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

solve word problems involving division of whole numbers.

•

write answers in the form of fractions by using visual fraction models and equations to represent the problem.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 254

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Fractions as Division without Remainders In this exploration, students will collaborate with peers to solve a real-world scenario involving an ice-cream shop and helping them read Ice Cream Cards to document how much ice cream or toppings each customer received. Students will: •

use concrete and pictorial models to interpret division with fractional quotients.

•

use multiplication to prove their answers.

Explore 2

Explore 1

EXPLORE ACTIVITIES

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

Fractions as Division with Remainders In the last exploration, students will participate in completing a babysitting scenario where they must solve various issues to ensure everything is in order when the parents return. Students will: •

use visual models to solve division word problems with a quotient that involves a mixed number.

•

interpret fractional remainders and reason what they represent.

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

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Fractions as Division Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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ACCESSING PRIOR KNOWLEDGE Students solve whole number division problems from given word expressions. Students solve problems both with and without remainders. This activity is intended to assess mastery of the following standard(s): 4.NR.2.4 Solve authentic division problems involving up to 4-digit dividends and 1- digit divisors (including whole number quotients with remainders) using strategies based on place-value understanding, properties of operations, and the relationships between operations.

Materials

Preparation

Printed •

1 Student Handout (per group)

Reusable • • •

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• • •

Plan to have students work in groups to complete this activity. Print a Student Handout for each group. Give each group a set of base ten blocks.

1 Set of base ten blocks (per group) 1 Whiteboard (per student) 1 Dry-erase marker (per student)

Procedure and Facilitation Points 1. 2.

Distribute Student Handouts and base ten block sets to student groups. Ask students to think of at least two situations when division would be necessary to solve a problem. a.

3. 4. 5.

6. 7.

Splitting something with your friends or family, making equal groups out of something, separating ingredients in cooking, etc.

Call on students to share the scenarios they thought of for using division. Write their ideas on the board or on large chart paper. Ask students to read Expression 1 and to represent the division problem using models on their whiteboards or by using the base ten blocks. Facilitate a class discussion about students’ representations of the expression. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Repeat these steps for Expressions 2–4. Ask students to explain what it means to have a remainder in Expression 2. a.

There are ounces left that were not evenly divided into the 8 bowls. There are leftover ounces.

Some students may recognize that the 3 remaining ounces can be broken down into smaller parts. These parts will be smaller than 1, i.e., fractions or decimals.

FACILITATION TIP Discuss how division represents the number of equally sized groups or the amount per group, depending on the context of a given situation. FACILITATION TIP Students that rely on using concrete models (such as base ten blocks) may beneﬁt from participating in the Foundation Builder.

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

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Fractions as Division Hook – Fractions and Bubbles and Division – Oh, My! ACTIVITY PREPARATION Students solve word problems involving division of whole numbers leading to answers in the form of fractions by using visual fraction models and equations to represent the problem.

Materials

Preparation

Printed •

• • •

1 Student Handout (per student)

Reusable • • • • • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Gallon-sized container of bubbles (per class) 4 8-Ounce or 12-ounce clear plastic cups (per class) 1 Quart-sized measuring pitcher (per class) 3 1 Measuring cup, __4 cup (per class)

•

Plan to show the Phenomena Video. Print a Student Handout for each student. Gather all supplies: bubble solution, quart-size measuring 3 pitcher, __4 cup measuring cup, and clear plastic cups. Plan to have students work in pairs to complete this activity.

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

2. FACILITATION TIP

As an alternative, present the scenario to the students along with the needed supplies. Have them work in pairs or groups to design a procedure for distributing the correct amount of bubble solution to the sets of partners. Instruct them to include a written explanation, a visual model, and a mathematical equation. FACILITATION TIP If supplies are limited, this scenario can be modeled with colored water instead. FACILITATION TIP Consider printing and projecting the scenario for students to read before demonstrating or providing time for hands-on manipulation.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: I have assigned my science club students a project to design the best bubble wand. Students will be working in partners; there are 4 sets of partners in the club. I have purchased a large container of bubble solution and I will be using 3 cups of solution for the 4 sets of partners. (Pour three cups into the measuring pitcher.) To be fair, I want each pair to have the same amount of bubble solution to test their wands. Because a fraction is an example of division, I know that if I divide 3 cups by 4 sets, I will 3 have 3 ÷ 4, which is the same as __4 , which is said “three fourths.” So, each pair of 3 students will get __4 of a cup of bubble solution. Watch. (Pour the bubble solution 3 from the measuring pitcher into the __4 cup measuring cup, and then dump the contents carefully into one of the clear plastic cups. Do this 4 times. Make sure 3 to measure exactly. The bubble solution should ﬁll the __4 cup measuring cup exactly four times.) Project the Student Handout. Tell students that on the upper half of their Student Handouts, they will draw what they observed during the teacher demonstration. Then, they will write an equation to represent what happened. On the bottom half of their Student Handouts, students will create similar scenarios to use as examples. Examples should show how a fraction is an example of division.

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Allow groups to share their procedures, and follow their steps as they share with the class. If a procedure does not achieve the intended goal, use guided questioning to discuss why it did not work. © Accelerate Learning Inc. - All Rights Reserved

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Discuss the following questions: a. DOK-2 What steps will need to be taken to solve the bubble solution problem? We will need to draw the measuring pitcher containing 3 cups of bubble solution. Then, we will need to show how it was divided 3 equally into 4 portions of __4 of a cup each. After that, we need to write an equation representing the action. b. DOK-2 What will you need to show in the scenario you create with your partner? We will need to show how a fraction represents division because a certain number of items (numerator) will be divided into a certain number of equal parts (denominator). c.

DOK-3 Do you think it will be more diﬃcult to show how to solve the scenario demonstrated by your teacher or to create and solve your own problem? Why? Answers will vary. Use this question to promote discussion about mathematical thinking. Accept all answers that have reasonable explanations.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a. DOK-2 What steps will need to be taken to solve the bubble solution problem? We will need to draw the measuring pitcher containing 3 cups of bubble solution. Then, we will need to show how it was divided 3 equally into 4 portions of __4 of a cup each. After that, we need to write an equation representing the action.

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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.

b. DOK-2 What will you need to show in the scenario you create with your partner? We will need to show how a fraction represents division because a certain number of items (numerator) will be divided into a certain number of equal parts (denominator). c.

3. 4.

5. 6.

7. 8.

DOK-3 Do you think it will be more diﬃcult to show how to solve the scenario demonstrated or to create and solve your own problem? Why? Answers will vary. Use this question to promote discussion about mathematical thinking. Accept all answers that have reasonable explanations.

Assign students partners or let them choose partners. Give each pair of students a Student Handout. Tell students that once they have sketched out the solution to the problem demonstrated, they will need to write an equation to represent how to solve the problem in the Student Handout. Remind students to use the top half of their Student Handouts for this portion of the Hook. Give students about 5 minutes to draw their scenarios and write their equations to the bubble solution problem. Give students 5–10 more minutes to create a new scenario on the bottom half of their Student Handouts. Note that each pair should create a scenario, draw the solution, ﬁnd the appropriate equation to represent the actions, and solve the problem. Walk around during this time, and assist any pairs who are having trouble coming up with a scenario, drawing it, or ﬁnding equations or solutions. Next, have two sets of partners pair up. Give them 3–5 minutes to share their original scenarios, drawings, equations, and solutions. Encourage them to discuss their ideas and to ask and answer questions.

FACILITATION TIP Encourage students to use fractions other 3 than __4. Brainstorm situations in which they might need to separate a substance into fractions: pizza, a soft drink, a bag of candy, and so on.

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Fractions as Division Hook – Fractions and Bubbles and Division – Oh, My! 9.

FACILITATION TIP Share various models as a whole group to encourage the students to think creatively.

Gather students in a whole group and discuss the following questions: a. DOK-2 How did sketching the scenario help you solve the problems? It helped us because it was a visual fraction model that took us step by step through how the original items were divided into equal parts. The equal parts are fractions. b. c.

DOK-2 What was the equation you created for the bubble problem? 3 3 ÷ 4 = __4

DOK-3 Which was more difficult—drawing and finding the equation for the bubble problem demonstrated or creating a new scenario and drawing and finding the equation for it? Answers may vary. Accept any answer accompanied by a reasonable explanation.

d. DOK-1 Do you feel that you have a strong understanding of how a fraction is an example of division? Answers may vary based on students’ success during the activity and on their conﬁdence levels. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Fractions as Division Explore 1 – Fractions as Division without Remainders ACTIVITY PREPARATION Students use concrete and pictorial models to interpret division with fractional quotients. They use multiplication to prove their answers.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• • •

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

Reusable • •

•

4 Sets of fraction tiles or fraction circles (per group) Colored pencils or markers or crayons (per student)

•

Plan to divide the class into 4 groups for this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut apart a set of Ice Cream Cards for each group. Ice Cream Cards can be printed on card stock and laminated for durability if desired. Create sets of fraction tiles or fraction circles for each group. Each group will need 4 sets of either the tiles or the circles. For students who need more support in recalling information, please see our Sharing Mats, 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 Tiles and Fraction Circles)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP For struggling students, provide dry beans, popcorn kernels, or other manipulatives they can use to physically separate into equal groups. Help them connect their groups to the math of each scenario. FACILITATION TIP

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Ensure the students’ understanding that, to distribute equal pieces in this situation, they must return to the whole and not just divide one of the objects.

2. 3. 4. 5.

Read the following scenario to the class: Scoop-tastic sells a lot of ice cream and toppings throughout a business day. However, not every customer receives the same amount of ice cream or toppings. The amount of ice cream or toppings a customer receives depends on the customer’s order and the amount of product Scoop-tastic had at the beginning of their day. Read each Ice Cream Card, and help Scoop-tastic document how much ice cream or toppings each customer received. Divide the class into groups. Give a Student Journal to each student. Distribute 4 sets of either fraction tiles or fraction circles to each group. Explain to students that as they read each scenario, they may notice that they are taking a total and splitting it into equal parts as they distribute items to their customers. Ask the following review questions to engage their prior knowledge. Encourage each group to discuss these questions together before reviewing them with the class: a. DOK-1 What operation could you use to partition items evenly or equally? Division b.

DOK-2 What do you think would happen if there are more people to share with than there are objects to share? Answers may vary. I think this would mean we would need to count how many people we have and © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

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Acceleration

split each item into that many pieces and make sure each person gets an equal-sized piece from each object. c.

DOK-2 Do you think this means people will get whole objects, less than a whole object, or more than a whole object? I think people will get less than a whole object.

d. DOK-2 Why do you think they will receive that much of an object? (This question goes with their response from the previous question.) I think they will receive less than a whole object because there are more people than there are objects, and we need to divide the objects into pieces smaller than a whole for people to get the same amount. 7. 8.

10. 11.

Explain to students that for each Ice Cream Card, they will be working with their groups to ﬁnd each customer’s amount of ice cream or toppings. Explain to students that they will need to select 12 different colors. Each color will represent a different customer’s amount of product received from Scooptastic. They will need these different colors to shade their models for their Explore. Encourage students to use their fraction tiles or circles to represent the problem, and have students draw models of their work using their customer colors and then use an equation from the scenario to represent that model and an inverse operation to check that work. It is up to the group to ﬁgure out the correct operation needed for the equation and the inverse operation to check their answer. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 What operation do you think is being used to solve each scenario? I think we are using division to solve each scenario. b. DOK-1 Why do you think we are using that operation? I think we are using division because you are taking a total and splitting it into parts. c.

DOK-1 How can we split a whole number? We can split a whole number into equal fractional parts.

DOK-1 What is the inverse operation being used to check your work? I will use multiplication to check my work since it is the opposite of division.

12.

DOK-2 How can your colors help you better understand your model and how the Scoop-tastic products were distributed? The colors help me better understand the fractional amount each customer received and how many customers wanted each product.

If students are struggling to ﬁgure out the inverse operation and how to check their work, remind those students about fact families. a.

Give them an example such as 12 ÷ 4 = 3.

b. DOK-1 What multiplication problem would be used to check this division problem. 4 × 3 = 12 13.

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FACILITATION TIP If you do not have enough colored pencils or crayons to have 12 different colors, ask the students to create different patterns such as stripes, dots, or squiggles to represent the different customers. FACILITATION TIP Consider creating a universal color key to be used class wide. This allows for a quick visual check for understanding. FACILITATION TIP Continue to express the importance of always checking one’s work before moving to the next problem.

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.

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

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Fractions as Division Explore 1 – Fractions as Division without Remainders Math Chat • FACILITATION TIP Take time to generate some real-world examples of dividing fractions with no remainders. Provide some visual images of construction sites, landscaping, popular student games, or hobbies.

•

FACILITATION TIP

•

Continue to encourage students to use visual models to show their thinking even as they begin to be able to intuit the solutions to some of these scenarios. Being skilled with models now will support their success on more complex math standards later.

•

DOK-1 What did you need to do to your whole number before you could split the ice cream or toppings between customers? I had to split each whole number into equal fractional parts. DOK-1 How did you know how many fractional parts to split your starting whole number into? I used the number of customers for each scenario to ﬁgure out how many equal fractional parts to divide my starting amount into. DOK-1 What did you notice when we divide a smaller number by a larger number? I noticed that when I divided a smaller number by a larger number, my answer was a fraction. DOK-2 How did the model or manipulatives help you solve each scenario? The model helped me solve because I could represent the parts that each whole number contained and then use that starting number of parts to represent the equal number of fractional parts that each customer received. DOK-2 How did the model or manipulatives help you use an inverse operation to check your work? The model helped me check my work because I could see the fractional value that each customer received and multiply that by how many customers there were and see that it led me back to my starting amount or original whole number.

Post-Explore 1. 2. 3.

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

Instructional Supports 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.

For students who are struggling to connect the concept of fractions as division, reinforce that division is the same as partitioning or splitting into equal parts, which is also how we deﬁne fractions. Ask students to make a personal connection to using fractions to represent division. For example, “How could we share 1 sandwich equally between 3 1 people?” Students will reason that 1 divided by 3 is __3 and that each person will 1 __ get 3 of the sandwich.

For students who are struggling with using fraction manipulatives to understand the concept, give students paper strips to cut apart and distribute into equal groups. For students who interchange the dividend and divisor, create a visual reference tool. Copy an ice-cream problem from this activity, and write the corresponding fractions. Relate the fraction to a division symbol. Draw and label a division symbol next to the fraction—the dot on top represents the numerator, (dividend), and the dot on the bottom represents the denominator, (divisor).

Language Supports The following Language Acquisition Strategy is supported in this Explore activity. See the strategies below for ways to support a student’s language development. As more English is acquired, students will provide speciﬁc and precise verbal descriptions. Beginner: Respect a student’s silence period, and do not force them to speak if they are hesitant. Intermediate: As students work together to create models for each ice-cream shop example, have them verbally describe their the models as they work. Provide sentence frames as needed: We have made ______ wholes because there is ________ of ice cream. We have partitioned the wholes into ______ equal parts because it is being shared equally between _____ customers. Each customer receives _____ of a _____ of _______ ﬂavored ice cream. Advanced: Insist on increasingly correct and precise language. 264

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Fractions as Division Explore 2 – Fractions as Division with Remainders ACTIVITY PREPARATION Students use visual models to solve division word problems with a quotient that represents a mixed number. Students also interpret the fractional remainder and reason what it represents.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems, and persevere in solving them. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials Printed • • •

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

Reusable • • •

Preparation • • • • •

12 Sets of fraction tiles (per class) 4 Sets of fraction circles (per class) 3 Sets of two-color counters (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 and cut apart a set of the Babysitting Cards for the class. The Babysitting Cards can be printed on card stock and laminated for durability if desired. Place the Babysitting Cards around the room as stations. Acquire the 12 sets of fraction tiles, 4 sets of fraction circles, and 3 sets of twocolor counters, and set up the stations around the room as follows: • • • • • •

•

Pizza Night: 4 sets of the thirds in fraction circles Candy Jar: 7 sets of the halves in fraction tiles Toy Box: 1 set of two-color counters Crayons: 1 set of two-color counters Feeding Ducks: 5 sets of the fourths in fraction tiles Books: 1 set of two-color counters

For students who need more support in recalling information, please see our Sharing Mats, 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 Tiles, Fraction Circles, Two-Color Counters)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP Project this scenario and engage students by asking for some examples when sharing between two or three can be complicated.

2. 3.

Read the following scenario to the class: You are babysitting 2 children for the weekend while their parents take a mini vacation. During the weekend, you came across some situations when the kids must share and organize some items so that these items are evenly distributed. Use the tools available to solve each issue so that everything is in order when the parents return. Give a Student Journal to each student. Explain to students that as they read each scenario, they may notice that they are taking a total and splitting it into equal parts. Discuss the following questions: a.

DOK-1 What operation could you use to partition items evenly or equally? Division

b. DOK-1 Can everything always be divided equally? No, sometimes there is a remainder after we divide. 266

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Explain

Elaborate

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c. DOK-1 What can we do with a remainder? A remainder can be dropped from the answer, it can make the quotient add one to its value, or it can be the answer. 4. 5. 6. 7.

8. 9.

Explain to students that they will have to determine what happens to a remainder today as they encounter issues with the kids they are babysitting. Explain to students that their groups will be placed at stations around the room. Encourage students to work with their groups to read each Babysitting Card and use their prior knowledge about division and fractions to create a model to solve. Explain that once they’ve created a model, they will use it to help them write a solution equation and solution statement and to help them answer any other questions pertaining to the scenario. Teacher will give an amount of time for groups to rotate and complete each station. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How can you ﬁgure out which number is your dividend? The dividend is the total amount of an object that is being split.

b. DOK-1 Can your dividend be evenly split using only whole numbers? No, I cannot evenly split the dividend with only whole numbers. c. DOK-2 What do you think you should do to make sure each person gets an equal amount using fraction tiles? Answers may vary. I think I will break the wholes into equal parts based on the divisor and then make sure each person gets an equal amount of fraction tiles.

Intervention

Acceleration

FACILITATION TIP Brainstorm situations in which each of these scenarios might be used. FACILITATION TIP Review the procedures and expectations for moving between and working at stations.

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FACILITATION TIP The Babysitting Cards provide good opportunities for careful, close reading of math scenarios. Encourage students to read them more than once with their group and look for relevant values and math phrases. FACILITATION TIP Use a projected online timer to encourage the students to stay on task and work at an acceptable speed. FACILITATION TIP Continue to reinforce that a fraction describes how many parts out of a whole they have.

d. DOK-2 What does the fractional amount represent when using fraction tiles or circles? The fractional amount represents a whole that was split into equal parts and distributed evenly among each group. e. DOK-1 What did you notice about your quotient? I noticed that my quotient was a mixed number and improper fraction. f. DOK-1 What do you need to do to make sure your two-color counters are divided equally? Answers may vary. I need to make sure each group is the same size. g. DOK-2 What does the fraction represent when using the two-color counters? My fractional amount will represent the remainder of a group that wasn’t a full amount as the groups that were the same size. 10.

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

Math Chat

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.

DOK-2 Why do you think some stations had fraction tiles or circles and some stations had two-color counters? I think some stations had fraction tiles because the items in real life could be split into pieces. I think some stations had twocolor counters because those items can’t be split apart in real life but can still be sorted. • DOK-2 How did you determine what to do with the remainder? Depending on the scenario, I can take the remainder and fractionally split it into the number of parts that is represented by my divisor. The remainder can also represent the leftover pieces that represent a fraction based on a part of a whole. • DOK-1 When is the answer a fraction or a mixed number? The answer is a fraction when the dividend cannot be evenly split by the divisor and you are left with a remainder. Your answer can also be a fraction when you are dividing a smaller number by a bigger number. • DOK-1 What does that fraction represent? The fraction represents the remaining whole or wholes that were left over or a whole that was split equally between groups. •

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Fractions as Division Explore 2 – Fractions as Division with Remainders •

FACILITATION TIP Fractions in between is a critical concept for students. Take time to demonstrate, clarify, and check for understanding.

DOK-2 How can you determine what two wholes an answer falls between? I can determine what whole numbers my answer falls between by looking at the whole number in my mixed number. The whole number in my mixed number will be the ﬁrst number, and the number that follows that whole number will be my other 3 number. For example, if my answer is 2__4, then the two whole numbers my answer is between are 2 and 3. If there is no whole number with my fraction, then my answer falls between 0 and 1.

Post-Explore 1. 2. 3. 4.

Instructional Supports 1. 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.

4. 5.

For students who struggle with the concept of interpreting remainders, use a think-aloud strategy to model the process of dividing at the ﬁrst station. Students can gain a tactile sense of what it means to partition a whole into equal shares by cutting a paper model into fractional parts. To help students retain conceptual understanding of division with remainders, challenge students to write a real-world problem involving sharing something that results in a value that is a mixed number. Showcase examples of student-generated models for students to reference. Post a word wall or anchor chart with examples of the terms dividend, divisor, divisor quotient, and remainder (in fraction form). ). Show that the dividend is the total amount of items, the divisor is the number of people sharing, and the quotient is the amount that each person receives.

Language Supports The following Language Acquisition Strategy is supported in this Explore activity. See the strategies below for ways to support a student’s language development. Students will use background knowledge as a link to understanding the English language. Beginner: Build background knowledge and make connections prior to describing the scenario. Discuss students’ experiences staying with a babysitter and sharing food. Display the pictures on each Babysitting Card, pronounce each word, and have students repeat: pizza, candy, toys, crayons, ducks, books. Intermediate: As students read each Babysitting Card, ask student groups to discuss how the scenario relates to their own lives. Provide students the following stem: When I used/shared _____ with _____, I noticed that _____. Advanced: Pair students, and have students alternate reading a Babysitting Card while the other partner explains the scenario in their own words.

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Fractions as Division 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

Fractions as Division without Remainders Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

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

Fractions as Division with Remainders 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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Explore

Explain

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Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Just the Right Spice

Lars and Jens Rasmussen

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 Backpacking Trip

Fractions as Division Problem Solving

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

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

Problem-Based Task

Interactive Practice

Sharing Candy

City Lights

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

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Fractions as Division 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?

FRACTIONS AS DIVISION

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What does mastery look like?

I can explain the meaning of a fraction as division of the numerator by the denominator.

I can apply what I know about solving problems with whole numbers to solve those involving fractions and mixed numbers.

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SCOPE 1

Divide Fractions Scope Introduction SCOPE SUMMARY To divide fractions, students build on their prior knowledge that fractions are equal parts of a whole and that division is dividing numbers into equal parts. Students divide unit fractions by whole numbers and divide whole numbers by unit fractions. They use fraction manipulatives as well as pictorial models, such as illustrations, number lines, and area models, to solve problems involving division of fractions. Student Expectations

5.NR.3.6 Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In fourth grade, students solidify their understanding of equivalent fractions, including fractions greater than one. They also extend their knowledge of comparing fractions. They begin to compose and decompose fractions and mixed numbers, and they use that knowledge to add and subtract fractions with like denominators. In ﬁfth grade, prior to this scope, students expand their knowledge of adding and subtracting fractions and mixed numbers with unlike denominators as well as comparing and ordering fractions and mixed numbers. They also model and solve problems involving multiplication of a whole number and a fraction. Students understand that the greater the number of parts into which a whole is divided, the smaller each part is. Conversely, the lesser the number of parts into which a whole is divided, the larger the size of each part.

In sixth and seventh grades, students use their understanding of fractions to reason about ratios. Sixth-grade students analyze ratios, rates, and percentages by using tables of equivalent ratios and graph pairs of equivalent ratios in the coordinate plane. Seventh-grade students will compute unit rates associated with ratios of fractions with like or different units. They will analyze graphs, tables, equations, and diagrams to see various ways to discover unit rates.

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

choose the statement that best represents the solutions to addition and subtraction problems using fractions with equal denominators.

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

Hook

Accessing Prior Knowledge

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

represent division of a fraction by a whole number and the division of a whole number by a fraction by using objects and pictorial models.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 274

Engage

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Acceleration

Divide a Whole Number by a Unit Fraction In this exploration, students will model division of a whole number by a unit fraction. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

determine how to split pizzas equally.

In this exploration, students will divide a unit fraction by a whole number by using objects and pictorial models. 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

Divide a Unit Fraction by a Whole Number

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show how to divide models into fractions.

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

Develop Models to Solve Problems In this exploration, students will investigate the angle size and side lengths of triangles to classify them into various categories and subcategories. Students will: •

classify the different types of triangles to organize them on shelves.

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

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Divide Fractions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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ACCESSING PRIOR KNOWLEDGE Students choose the statement that best represents the solutions to addition and subtraction problems using fractions with equal denominators. This activity is intended to assess mastery of the following standard(s):

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4.NR.4.6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Materials

Preparation

Printed • •

•

1 Slideshow (per class) 1 Error Analysis (per class)

•

Reusable •

•

1 Projector or document camera (per class)

•

Consumable •

Plan to have students work in groups of 3 or 4 to complete this activity. Prepare to project the Slideshow for the class, or print a Slideshow for each group. Print the Error Analysis on card stock for durability, and post in different locations around the classroom. Gather enough scratch paper for each student to have one sheet.

1 Sheet of scratch paper (per student)

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

Project the Slideshow for the class, or distribute a printed Slideshow to each group. Tell students that Roberta took a math test in which she had to add and subtract fractions. Have students look at her answers and decide if they are correct. Instruct groups to read the statements from the Error Analysis posted around the classroom and discuss each one as a group. Facilitate a class discussion about the error analysis. 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 agree with Charlene. When you add and subtract fractions with like denominators, you should only add or subtract the numerators.

I do not agree with Adolpho. When you add and subtract fractions with like denominators, you do not add or subtract the denominators.

I do not agree with Nala. Roberta’s addition problem is not correct. She should have only added the numerators and kept the denominators the same.

FACILITATION TIP Provide silent time for students to observe and make notes about Roberta’s answers. Next, provide some shoulder partner time to discuss.

FACILITATION TIP If space is limited or students need to be able to clearly read and see the Error Analysis problems one at a time, consider projecting them for students to read alone/ in partners.

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

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Divide Fractions Hook – Measure Twice, Cut Once ACTIVITY PREPARATION Students represent division of a fraction by a whole number and the division of a whole number by a fraction by using objects and pictorial models.

Materials

Preparation

Reusable • • • • • • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 3 Yards of string or ribbon (per group) 1 Yardstick (per group) 1 Ruler (per group) 1 Pair of scissors (per group) 1 Whiteboard (per group or student) 1 Dry-erase marker (per group or student)

Plan to show the Phenomena Video.

Part II • • • •

Plan to have students work in groups of 2 or 3 to complete this activity. Cut a piece of string or ribbon 3 yards long for each group. Gather enough yardsticks, rulers, and pairs of scissors for each group to have one of each Gather enough whiteboards and dry-erase markers for each group or student to have one of each.

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

FACILITATION TIP Print and project the text of the scenario. Have student think silently and jot notes ﬁrst, then have them read it in pairs, and then prepare to share ideas with the whole class.

DOK-1 What information do we have? We know that Beth has a piece of wood that is 3 yards long. It needs to be divided into pieces of wood 1 that are each __6 of a yard long.

DOK-2 What will your group do with the string to divide it into the correct number of pieces and the correct measurement? For the piece that is 3 1 yards long, we can use a yardstick to measure __6 of a yard. We can then 1 keep measuring __6 of a yard until we get to the end of the string.

Move on to complete the Explore activities. Notes

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Acceleration

Part II: Post-Explore 1. 2.

3. 4.

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

DOK-1 What information do we have? We know that Beth has a piece of wood that is 3 yards long. It needs to be divided into pieces of wood 1 that are each __6 of a yard long.

Give the string, yardstick, ruler, pair of scissors, whiteboards, and dry-erase marker(s) to each group. Give students 5–10 minutes to solve the problem and cut their strings. Tell students that when they are ﬁnished cutting the strings, their group needs to write an equation to represent the scenario and solve for the answer on the whiteboard. Walk around during the group work, and assist any groups who are having trouble with measuring the string. Discuss the following questions:

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FACILITATION TIP Before distributing the string and scissors, be sure that students can easily cut them. Some string and some school scissors make accurate cutting diﬃcult.

FACILITATION TIP a. DOK-2 How did you solve the problem? We used the yardstick to measure 1 __ the string and marked it to be cut into chunks that were each 6 of a yard. Continue to encourage students to use physical models to demonstrate solutions. We cut one piece of string, and then we cut the other pieces, using the Being ﬂuent with models will support ﬁrst cut piece as a template. visualization skills as students move into b. DOK-1 How many pieces did you end up with? We ended up with 18 pieces more complex math standards later. of string. c.

DOK-1 What are the equation and solution that your group wrote down 1 for this problem? We wrote down 3 ÷ __6 = 18.

DOK-2 What does the 18 mean? There are 18 pieces. Each piece is __6 of 1 a yard long. The whole 3-yard board makes 18 groups of __6 of a yard.

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Divide Fractions Explore 1 — Divide a Whole Number by a Unit Fraction ACTIVITY PREPARATION Students explore how to model division of a whole number by a unit fraction.

Standards for Mathematical Practice • • •

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

Preparation

Materials Printed • • •

• • •

1 Student Journal (per student) 3 Sets of Pizza Cutouts (per group) 1 Exit Ticket (per student)

Reusable • • • •

•

3 Paper clips (per group) 1 Resealable bag (per group) 1 Pair of scissors (per student) 1 Set of fraction tiles (per student)

•

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 three sets of Pizza Cutouts for each group of students. Cut apart and paper clip each set of cutouts, and then place the three sets in a resealable bag. DO NOT cut pizzas into fractional parts; students will be responsible for doing this during Part I of the Explore activity. Prepare a set of fraction tiles for each student. This activity may be most effective in a small-group setting so each student can have his or her own set of fraction tiles. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS Part I: Sharing Pizza FACILITATION TIP

Print and project the scenario for students to view as they collaborate.

2. FACILITATION TIP If time is limited, consider having students merely draw on the pizza rather than be required to cut the pizzas.

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3. 4.

Read the following scenario to the class: You and your friends are going to be sharing four pizzas. Two of your friends have an argument about how to split the pizzas equally. a.

Morgan says that if you split the pizza into smaller fractions, you will have more pieces of pizza to share.

Freddy says that if you split the pizza into smaller fractions, you will not have more pieces. Use the pizza pieces to ﬁnd out who is correct.

Ask students to discuss with their group members whether they agree with Morgan or Freddy. Students should explain their thinking. Give a Student Journal and a pair of scissors to each student. Give each group the ﬁrst set of four pizzas. They are asked to split the pizzas into thirds. Students should draw lines ﬁrst and then physically cut the pizzas into thirds. Students should then draw the cut pizzas on their Student Journals and label the number of pieces in each pizza. Ask the following questions: a.

DOK-1 Describe what is happening in your model. We are splitting the pizza into equal pieces. We are dividing into thirds.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 How did you divide the pizzas? We divided the pizzas into thirds.

DOK-1 How many pieces of pizza did you have when you split the four pizzas into thirds? We had 12 thirds.

Intervention

Acceleration

e. DOK-1 How many friends could share the pizza if they each get one piece? Twelve people could share the pizza. 5.

Discuss the following questions: a. b.

DOK-2 Can anyone think of an expression that would describe the math 1 you did in your model? We divided four pizzas by thirds, or 4 ÷ __3. 1 __

DOK-2 What happens when four pizzas are divided by 3? When four is 1

divided by __3, we end up with 12 slices. 1 __

c. d.

So, 4 ÷ 3 = 12. Tell students to write that equation on their Student Journals. DOK-1 Let’s compare thirds and fourths. Which is greater than the 1 1 other? __3 > __4

DOK-2 Next, you are going to cut the four pizzas into fourths; how will the size of the pizza pieces change from when we cut thirds? The size of the pieces will be smaller when we cut fourths.

e. DOK-1 Do you think we will have more or fewer slices of pizza when we cut fourths? I think we are going to have more pieces of pizza because each pizza is being cut into more pieces. 6.

Give each group the second set of four pizzas. They are asked to split the pizzas into fourths. Students should draw lines ﬁrst and then physically cut the pizzas into fourths. Students will then draw the cut pizzas on their Student Journals and label the number of pieces in each of the pizzas. Some students may realize this number is being repeated for each pizza. Allow them to share this with the groups as the foundation of using the reciprocal to multiply. It is not necessary to use the word reciprocal, but students should recognize that each pizza (whole) is being divided into the same number of parts, as shown by the denominator, and they are ﬁnding how many parts are being made. Ask the following questions: a. DOK-1 What expression does your model represent? The model represents 1 _

b. 8.

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4 ÷ 4.

DOK-1 How many pieces of pizzas did you have when you split the four pizzas into fourths? We had 16 pieces.

FACILITATION TIP One way to help some students visualize dividing by a fraction is to say, “How many ______ are in _____?” For example, “How many one-thirds are in four wholes?”.

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.

FACILITATION TIP Consider saying, “The model represents how many one-fourths are in four wholes.”

Connect the answer, 16 pieces, to the expression. Ask the following question: a.

DOK-2 What happens when four pizzas are divided by __4? When four is 1

divided by __4, we end up with 16 slices.So, 4 ÷ __4 = 16. Tell students to write that equation on their Student Journals.

Discuss with students what will happen as they divide the last set of four pizzas 1 __

FACILITATION TIP

by 8. Ask the following questions: a. b.

Continue to clarify that you are looking for how many one-eighths are in four wholes. DOK-1 Will the size of the pieces be larger or smaller than the thirds and When students begin dividing fractions fourths? It will be smaller. by fractions, this phrasing will help them DOK-1 Will we have more or fewer pieces? We will have more pieces, but comprehend the reasonableness of their answers. they will be smaller.

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Divide Fractions Explore 1 — Divide a Whole Number by a Unit Fraction 10.

Give each group the third set of four pizzas. They are asked to split the pizzas into eighths. Students should draw lines ﬁrst and then physically cut the pizzas into eighths. Students should then draw the cut pizzas on their Student Journals and label the number of pieces in each pizza to help them see they have repeated numbers of pizza or groups even though they are dividing. Ask the following questions: a.

DOK-1 OK-1 What expression does your model represent? The expression 1 represented is 4 ÷ __8.

DOK-2 How many friends could share the pizza if they each got one piece? The pizza could be shared by 32 friends.

Connect the answer, 32 pieces, to the expression. Ask the following question: 1

i. DOK-2 What happens when four pizzas are divided by __8? When 4 is 1 divided by __8, we end up with 32 slices. So, 4 ÷ 18 = 32. Tell students to write that equation on their Student Journals. 11.

FACILITATION TIP The difference to these two expressions can be described as, “How many one-thirds are in four wholes?” vs “How many four wholes are in one-third?”.

Discuss the following questions: a.

DOK-2 Let’s talk about what we were showing with our models. Describe to me what was happening in each step. We were taking four pizzas and dividing them into different fractional parts to see how much could be shared.

DOK-1 So were we dividing with a fraction? Yes

DOK-1 If I were to ask you whether you divided a fraction or a whole number, what would you say? Why? We had to divide the whole number because we were dividing the pizzas, and they started out as whole pizzas.

DOK-2 Would it matter if I changed the order of our expression from 4 1 1 ÷ __3 to __3 ÷ 4? Yes. The order of the expression matters when you divide. The ﬁrst number in a division problem is the total amount you are splitting up. 1

e. DOK-1 Let’s break the expression into parts. If I give you 4 ÷ __3 = 12, 1 which part is the divisor? The divisor is __3.

FACILITATION TIP Take time to reinforce and review these math terms before moving on to the following steps: divisor, dividend, and quotient. Use some whole number equations to begin with ﬁrst. Consider using Picture Vocabulary.

DOK-1 What is its role? Its role is to divide, or to make the number of groups or divisions.

DOK-1 What is the dividend? The dividend is 4.

h. DOK-1 What is the dividend’s role? Its role is to be divided. i. DOK-1 What is the quotient? The quotient is 12. j. DOK-1 What is the quotient’s role? It is the answer to a division problem. For example, it is the number of pieces of pizza. k.

DOK-1 Now, let’s talk about the quotients we got for each step. Did anyone notice anything strange about them? They are each greater than 4 (the dividend).

l. DOK-1 Is that normal for division? Explain. We used to always have quotients that were less than the dividend, but when we started dividing by fractions, the quotients were greater than the dividend. m.

1 1

DOK-1 Look at all the fractions we have used: __3, __4, and __8. Are they less than one? Yes

n. DOK-1 So do our answers make sense? Why? Yes. We are dividing the pizzas into smaller pieces, so we are making more pieces. 12. 282

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2. 3.

5. 6.

Review what students have done in Part I. Students have taken whole pizzas and divided them into equal fractions. By doing so, they made more parts. Tell students they are going to use what they have learned to help a child named Mack. Give each student a set of fraction tiles. Read the following scenario to the class: Mack visited the Wonderful World of Candy last weekend and bought three of the same kind of candy bars. The problem is that these candy bars are bigger than Mack’s head, and his mom said that he has to share the candy bars with friends! Help Mack ﬁgure out how many friends he can share his candy bars with as he divides them into different fractional parts. Students will use the fraction tiles to model each scenario. Guide students as needed when making the ﬁrst model. a.

Pull out the whole piece to show that the whole represents one whole candy bar before being divided.

DOK-1 Work with your group to show three candy bars being divided into halves. When you divide each candy bar into halves, how many parts do you make out of each candy bar? We make two parts for each candy bar.

DOK-2 If you divide the he three candy bars by __2, do you only make two equal parts? Why or why not? No, you make more than two parts because each of the three candy bars is being divided into two parts.

DOK-1 How many parts do you have after dividing three by __2? We have six parts.

DOK-1 What are we splitting equally? We are splitting the whole candy bars.

DOK-1 How many parts are we dividing each candy bar into? We are dividing each into two parts.

DOK-1 What numbers were labeled on your number line? The labels were the whole number increments 0,1, 2, and 3.

DOK-1 Do you need to label anything else else on your number line? We probably need to label the halves. DOK-2 Why? Because that is how we 1 are dividing the candy bars. Each piece will be __2.

e. DOK-2 How can we show the dividing of the three candy bars on the number line? We can use jumps to show the dividing, or the number of pieces.

7. 8.

Depending on time and your students, consider doing page 1 and 2 of the Student Journal in one class session and then page 3 and 4 on the next.

Have students draw their model on their Student Journals. Lead students into using the number line to represent the division. Remind them that they are dividing, which involves splitting equally.

Acceleration

FACILITATION TIP

Part II: Sharing a Candy Bar 1.

Intervention

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DOK-2 How big should the jumps be? Each should be __2. How many are there? Explain what you notice. There are six, just as before. This is just a different way of modeling the division.

Allow each student group time to complete the rest of the problems, and check for understanding. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP To support student visualization, consider saying, “How many one-halves in three wholes?” FACILITATION TIP Locating and labeling fractions in between is a critical skill for students. They will need to be able to use this when working with decimals and percents as they progress through further math standards.

STEMscopes Tip Career Connections is found in the Elaborate section of Grades 3–5. This element features a STEM career video or slideshow to showcase how the math concepts students are learning are applied in real-world work settings and what 21st century skills are needed to be successful. A followup activity related to the career that highlights the math concepts from the scope is also included.

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Divide Fractions Explore 1 — Divide a Whole Number by a Unit Fraction Math Chat DOK-2 What similarities did you find in these problems? We were dividing a whole number by a fraction. A whole number was being divided into fractional parts. We were finding the number of parts. The quotient was larger than the dividend. Our answer was a whole number. • DOK-1 When we divided the whole into fractional parts, what happened? We had more pieces that were smaller than the whole. • DOK-1 All the fractions we used were unit fractions. Looking at the fractions on your Student Journal, can you define unit fraction in your own words? The numerator is 1. It is one equal part of a certain size. • FACILITATION TIP Before this Math Chat, take time to find some additional real-world visual examples of dividing a whole number by a unit fraction.

Post-Explore FACILITATION TIP When previewing this Exit Ticket with students, clarify your criteria for success. Students may not be as willing to draw a model when they can intuit the solution. Continue to encourage them to draw models as it will help them to quickly and accurately visualize solutions later in life.

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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Divide Fractions Explore 2 — Divide a Unit Fraction by a Whole Number ACTIVITY PREPARATION Students explore dividing a unit fraction by a whole number by using objects and pictorial models.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Preparation

Materials Printed • • • •

• • • •

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

Reusable • • • •

1 Pair of scissors (per student) 1 Ruler (per student) 1 Set of fraction circles (per group, optional) 1 Set of fraction tiles (per group, optional)

• •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Fractions Cards for each student. Print a set of Scenario Cards for the class, and place scenario 2 and scenario 3 in stations around the room. Because of the number of groups, it is recommended that half of the class works on scenario 2 while the other half of the class works on scenario 3, and then they switch. Depending on the number of groups in the class, print two or three sets of Scenario Cards so all students can see the scenario. Place a set of fraction circles at scenario 2 and a set of fraction tiles at scenario 3 for support, if desired. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS FACILITATION TIP

Be prepared with some concrete examples to show students what it means to have a fraction of something. Show your bowl of treats, prize tickets, or some other high interest item to engage students in questions 1 and 2.

2. 3. 4.

DOK-1 Before students begin, ask them what it means to have a fraction of something. Answers will vary. To have a fraction of something means you do not have all of it (you do not have the whole thing). There was more of something, but you don’t have it all; you just have part of the whole. DOK-2 What are some examples of things you might have a fraction of? You could have a fraction of a pizza, pie, piece of paper, ribbon, candy, etc. Give each student a Student Journal, a pair of scissors, a ruler, and a set of Fraction Cards. Provide groups a set of fraction tiles for support, if desired. Project and read scenario 1. Discuss the following questions: a.

DOK-1 What does Kristen own? She owns a piece of land.

DOK-1 How much land does Kristen own? It is __4 of a square mile.

c. 286

DOK-1 Does that mean she owns less than 1 square mile? Yes.

6. 7.

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Each student will cut out one of his or her Fraction Cards. This will represent offer 1. Discuss the following questions: a.

DOK-1 What does it mean for the land to be divided? It is being split equally.

DOK-1 How can we show we only have one piece? We have to cut it apart.

Suggest to students that they use the ruler to draw a line (horizontally) before cutting. After students cut their Fraction Cards, have them place them together with the shaded part to the left. Tell students that a store will be built in one of the pieces of land Kristen is selling. Have students draw a star in one of the shaded pieces. Ask the following questions: a.

DOK-1 How much of the square mile does the space with the star 1 occupy? It occupies __8.

DOK-1 Is that more or less than __4? It is less than __4.

DOK-1 So what did we do to the __4 piece of land? We divided it.

STEMscopes Tip

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DOK-1 How much did we divide the square mile by? We cut it in two, or in half.

e. DOK-2 What happens when we cut something in half? It becomes smaller. It is split into two equal groups. 9. 10. 11.

12.

Allow students time to draw and answer the questions under Offer 1. Review students’ answers. Challenge students to work with their groups to use their Fraction Cards to complete offers 2–4 and show their thinking on their Student Journals. Assign student groups to work on either scenario 2 or scenario 3. As students complete the scenario they have been assigned, have them move to the other scenario. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 In scenario 2, how can you show that the brownie is being divided into equal pieces? We can draw lines through the brownie to show that it is being divided.

DOK-1 How many lines will you need to draw if you are dividing it into six parts? You will draw ﬁve lines.

DOK-1 Should your lines go all the way through the whole? Yes.

DOK-1 What is the dividend? The dividend is __2.

FACILITATION TIP After completing Offer 1 with students, consider whether students need whole class instruction or are ready to collaborate or work independently on Offers 2–4.

e. DOK-1 Are we dividing the fraction or the whole number? We’re dividing the fraction. f.

DOK-1 What is the divisor? The divisor is 6.

DOK-1 What does the divisor do? It tells us how many parts to divide something by.

h. DOK-1 What is the expression you can use to show this relationship? 1 The expression is one-half divided by six, or __2 ÷ 6. i. DOK-2 In scenario 3, how can you show the fabric being divided into equal pieces? We can divide up the number line into equal pieces.

FACILITATION TIP This expression can be spoken as, “How many six wholes are in one-half?” FACILITATION TIP Before this scope’s Exit Ticket, take time to focus on Scenario 3. The Exit Ticket requires number line models.

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Divide Fractions Explore 2 — Divide a Unit Fraction by a Whole Number j. DOK-2 How many lines will you need to draw if you are dividing into ﬁve parts? You will draw four lines. k.

DOK-1 What does the divisor do? It tells us how many parts to divide something by.

l. DOK-1 Do you need to just divide the shaded area, or should you divide the whole number line? We should divide the whole number line because it is part of the whole piece of fabric. 13. FACILITATION TIP Before this Math Chat, take time to share real-world visual examples of dividing a unit fraction by a whole number. Consider using a high interest item to show students (use the examples from Step 1 and 2 from the procedure).

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

Math Chat DOK-1 How would you describe what you did in this Explore activity with a classmate who was not here today? We looked at fractions of whole objects. We had to split the fractions evenly. • DOK-1 What similarities did you ﬁnd in these problems? A fraction was being divided. We were ﬁnding the number of parts. The quotient was less than the dividend. Our answer was a fraction. • DOK-2 When we split up the fraction, what happened to the size and number of pieces? The greater the divisor was, the smaller the size of each piece became, but there were more pieces. •

Post-Explore FACILITATION TIP

When previewing this Exit Ticket, consider whether some students will need support making tick marks to separate the number lines into equal parts.

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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Divide Fractions Explore 3 — Develop Models to Solve Problems ACTIVITY PREPARATION Students develop pictorial models to represent division of a whole by a unit fraction and division of a unit fraction by a whole.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Preparation

Materials Printed • • • •

• • •

1 Student Journal (per student) 1 School Expansion Scenario (per group, optional) 1 Set of Scenario Cards (per class) 1 Exit Ticket (per student)

•

Reusable • • •

•

4 Sets of fraction tiles (per class, optional) 2 Sets of fraction circles (per class, optional) 1 Pair of scissors (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 School Expansion Scenario, on card stock for durability, for each group of students. Optionally, you can project the scenario for the class. Print and cut apart a set of Scenario Cards, on card stock for durability, for the class. Place the six scenarios around the room as stations. Place a set of fraction tiles at stations 1, 2, 3, and 5 and a set of fraction circles at stations 4 and 6 for support, if desired. For students who need more support in recalling information, please see our Fraction Circles, Fraction Strips, and Open Number Line Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Fraction Circles, Fraction Tiles, and Number Lines)

PROCEDURE AND FACILITATION POINTS 1. 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.

290

2. 3.

Begin the discussion with a review of division with fractions. Ask the following questions: a.

DOK-2 When we divide a whole number by a fraction, what is our quotient? Explain. It is a whole number. We break up each whole into a certain number of pieces, and our quotient tells how many pieces we have. The quotient is greater than the dividend.

DOK-2 When we divide a unit fraction by a whole number, what is our quotient? Explain. It is a fraction. We are breaking up each piece of the whole into smaller pieces, and our quotient tells the fractional value of one of those pieces. The quotient is less than the dividend.

Project or provide the School Expansion Scenario to each group. Read the following scenario to the class: Your school is expanding! The school board has purchased 4 acres of land adjacent to your school to build an addition onto your school. They have already hired designers to ﬁgure out the best use for the land. The designers have decided to start by dividing the land into fourths. How many parts of land will they have to work with? © Accelerate Learning Inc. - All Rights Reserved

9. 10.

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a.

DOK-1 How many acres did the school board purchase? They purchased 4 acres.

DOK-1 How do the designers want to divide the land? They want to divide it into fourths.

DOK-1 What is the expression for this problem? The expression is four 1 divided by one-fourth, or 4 ÷ __4.

d. 5.

Engage

FACILITATION TIP Take time to establish that students know what an acre looks like.

DIVIDE FRACTIONS

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DOK-1 What model could we use to determine the quotient? We could use a rectangular area model or a number line.

Draw either four adjacent rectangles or a number line numbered from 0 to 4. Select students to divide the model into fourths. a.

DOK-1 How many parts do we get when we divide the model into fourths? We get 16 parts.

DOK-1 How many parts of land will the designers have to work with? There will be 16 parts.

Explain to students that they will be helping the designers design some of the areas for the new addition. The designers have combined some parts to make a larger space for larger rooms. Sometimes the designers will be dividing a whole number by a unit fraction, like in the example, and sometimes they will be dividing a unit fraction by a whole number. Tell students they should read the scenario and draw a model to represent what is being divided. Sometimes, students will be drawing a rectangular area model, a circle area model, or a number line. Students should draw the model speciﬁed in each scenario. Finally, students should write and solve the equation that represents the scenario. Give each student a Student Journal. Assign student groups to a speciﬁc station. Remind students that they should make sure the station they are at and the scenario number on the Student Journal match. Tell students they may use the fraction tiles or the fraction circles if needed. When students have completed the model and equation for the scenario, they should move to another scenario until they have completed all six scenarios. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 In this scenario, what are the designers dividing? They are dividing a whole number by a unit fraction and a unit fraction by a whole number.

DOK-2 How did you ﬁgure out how to draw the model in scenario 1? We drew the number of rectangles needed. Then, we shaded in half, because half of the gym is going to be used for basketball. Then, we divided up the rectangles into three parts because the other half of the gym is going to have three areas. We put a star in one of the shaded parts because the question asked how much of the gym area the balltoss area will take up.

DOK-2 In scenario 4, how did you figure out the equation? We drew a circle area model and shaded one part for the fiction section. Then, we divided each piece of the circle into five equal sections. We counted the 1 sections. One bookcase in the fiction section was ___ of the library. 25

FACILITATION TIP These scenarios provide good experience for students to carefully read math stories. The values are written in word form. Students may need coaching to locate the relevant values.

DOK-1 (Scenarios 1, 2, and 4) Are you dividing a whole number by a unit fraction or a unit fraction by a whole number? We are dividing a unit fraction by a whole number.

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Divide Fractions Explore 3 — Develop Models to Solve Problems f.

DOK-1 Is your quotient a fraction or a whole number? Why? It is a fraction because we are ﬁnding just one part of the whole.

DOK-1 (Scenarios 3, 5, and 6) Are you dividing a whole number by a unit fraction or a unit fraction by a whole number? We are dividing a whole number by a unit fraction.

h. DOK-1 How do you know? We are dividing wholes into parts and counting the total number of parts. i. DOK-1 Is your quotient a fraction or a whole number? Why? It is a whole number because we are counting the total number of parts. FACILITATION TIP

11.

Consider pulling the class back together for step 11. Complete page 3 (Reﬂection Questions) together as a class, review answers for the scenarios, and clarify discrepancies.

12.

When students have ﬁnished all six scenarios, they should complete the reﬂection questions. You may wish to pair up student groups and review their answers for the scenarios. If there are discrepancies between their answers, have them return to the scenario station and rework the problem until they agree on the solution. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-1 What did you notice about the relationship between the dividend and the divisor compared to the quotient when whole units were divided by a fraction unit? If I multiply the dividend by the denominator in the divisor, I get the quotient. This works because each whole is being broken apart into the number of pieces shown by the denominator. Each whole is now a group of the number shown by the denominator. • DOK-2 What did you notice about the relationship between the dividend and the divisor compared to the quotient when a fraction unit was divided by whole units? If I multiply the denominator in the dividend by the divisor, I get the denominator in the quotient. This works because the fractional part is being broken apart into the number of pieces shown by the divisor. Each piece of the original whole is now a group of the number of pieces shown by the divisor. • DOK-2 How is division with fractions similar to and different from division with whole numbers? You can use the same strategies to divide whole numbers and to divide fractions, such as using area models and number lines. In both cases, you are dividing numbers. They are different because when dividing with fractions, you are dividing whole amounts into equal parts and counting the total number of parts or you are dividing parts into a certain number of equal groups and counting just one of the parts. When dividing with whole numbers, you are grouping an amount into equal groups and not breaking apart any whole numbers. • 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.

Post-Explore FACILITATION TIP When previewing this Exit Ticket with students, clarify your criteria for success. Consider requiring students to label their models with numbers and words. Be prepared to provide some reading support for students as needed or read the scenario aloud all together.

1. 2. 3. 4.

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Divide 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

Divide a Whole Number by a Unit Fraction 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

Divide a Unit Fraction by a Whole Number 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

Develop Models to Solve 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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ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

A Trip to the Circus

Jaime Escalante

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

Save the Yard!

Divide Unit Fractions – 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

Fluency Builder

Fruity Jars

Problem Solve with the Division of Unit Fractions

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

DIVIDE FRACTIONS

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Divide 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?

DIVIDE FRACTIONS

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What does mastery look like?

I can model and solve problems involving division of a unit fraction by a whole number.

I can model and solve problems involving division of a whole number by a unit fraction.

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SCOPE 1

Classify Two-Dimensional Figures Scope Introduction SCOPE SUMMARY

Student Expectations

Fifth-grade students use the geometric properties of sides, angles, and symmetry to classify polygons, quadrilaterals, and triangles in categories and subcategories. For example, they conclude that squares are parallelograms because they are quadrilaterals with opposite sets of parallel and congruent sides. Students use deductive reasoning to justify their thinking about the categories into which shapes are sorted while gaining a deeper understanding of “if …, then …” relationships. For example, if a shape is a parallelogram, then it must also be a quadrilateral.

5.GSR.8.1 Classify, compare, and contrast polygons based on properties. 5.GSR.8.2 Determine, through exploration and investigation, that attributes belonging to a category of twodimensional ﬁgures also belong to all subcategories of that category.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students make generalizations about properties that are shared between categories of shapes, such as parallel line segments, perpendicular line segments, right angles, and lines of symmetry. Third-grade students mainly focus on identifying quadrilaterals and subcategories of quadrilaterals, but they also classify, compare, and contrast various polygons and 3-dimensional ﬁgures. In fourth grade, students more precisely name 2-D shapes by classifying them based on line types, angle types, and side lengths.

In sixth grade, students use the coordinate system to plot polygons and reason about their attributes. Sixth-grade students identify the bases and heights of triangles and parallelograms, and they apply shape composition and decomposition to derive and understand the formulas for area and volume. Sixth graders also investigate 3-D figures,find the volumes of rectangular prisms, analyze nets of 3-D figures, and use nets to solve problems involving surface area.

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

classify two-dimensional ﬁgures based on the presence or absence of parallel or perpendicular lines.

•

draw a triangle with speciﬁed angles.

•

understand ﬁgure classiﬁcation and triangle drawing.

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: •

classify shapes seen, drawn, and based on attributes into a hierarchy of sets and subsets using a graphic organizer.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 298

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Classify Polygons In this exploration, students will explore classifying polygons. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

classify the polygon cards with how many pairs of parallel, perpendicular, congruent, and symmetric sides they have.

•

determine if two or more angles on a ﬁgure are congruent or symmetric.

•

classify different polygon cards based on the number of sides and the type of angles as acute, obtuse, or right.

Classify Quadrilaterals In this exploration, groups of students will solve a scenario about sorting shapes based on attributes to assign each shape appropriately in a video game. Students will: •

classify quadrilaterals using attributes to create subcategories in a category.

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

CLASSIFY TWO-DIMENSIONAL FIGURES

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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. Classify Triangles In this exploration, students will explore and investigate the angle size and side lengths of triangles to classify them into various categories and subcategories. Students will: •

classify different types of triangles to organize the shelves.

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

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Classify Two-Dimensional Figures Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students answer two questions in which they must analyze the attributes of two-dimensional ﬁgures. This activity is intended to assess mastery of the following standard(s): 4.GSR.8.2 Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicular line segments, or the presence or absence of angles of a speciﬁed size and based on side lengths.

Materials

Preparation

Printed •

•

1 Slideshow (per class or group)

Reusable •

•

Prepare to project the Slideshow for the class, or print one Slideshow for each group. Plan to have students work in groups to complete this activity.

CLASSIFY TWO-DIMENSIONAL FIGURES

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1 Projector or document camera (per class, optional)

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

7. 8. 9.

Project the Slideshow for students, or give one Slideshow to each group. Direct students’ attention to the ﬁrst task box. Challenge students to ﬁnd as many similarities and differences as possible independently. Invite students to share their thinking with their group. Facilitate a class discussion about the similarities and differences students agreed on. 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. While students share their thinking aloud, record their responses in a Venn diagram for the class. a.

Similarities: two sets of parallel sides, four sides, opposite sides are equal.

Differences: rectangle–four right angles, sides are perpendicular, and all four angles are congruent; parallelogram–two acute angles, two obtuse angles, and opposite angles are congruent.

Read the second task box, and give students time to draw the given triangle. Students should compare the triangles they have drawn with other students. Draw your own example on the board, and ask students to list the properties that a right isosceles triangle must have. a.

10. 11.

12.

One right angle, two acute angles, two congruent sides

Read the last question of the second task box, and give students think time. Facilitate a class discussion about students’ explanations. 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 triangle can be both isosceles and equilateral because isosceles triangles have at least two congruent sides, so they can have three congruent sides, too. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP Challenge students to help you name each category (rectangle and parallelogram). Emphasize that a rectangle is a speciﬁc type of parallelogram with 4 right angles.

FACILITATION TIP Challenge students to name these types of quadrilaterals. Emphasize that a rhombus is a speciﬁc type of trapezoid with 4 congruent sides. If students can state that a trapezoid has at least 1 set of opposite congruent sides, ask them whether rectangles, squares, or parallelograms are also speciﬁc types of trapezoids. (They are)

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Classify Two-Dimensional Figures Hook – Shape Sort ACTIVITY PREPARATION Students classify two-dimensional ﬁgures in categories and subcategories, by using a graphic organizer, based on their attributes and properties.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Part II

Reusable • •

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

•

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

Plan to have students work in pairs to complete this activity.

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

2. FACILITATION TIP

Allow students to share their experiences of visiting museums. Ask them to share about the different shapes they saw during their visits. FACILITATION TIP

Create anchor charts as you discuss each type of shape.

DOK-1 What is a two-dimensional shape? A closed ﬁgure that has two dimensions—length and width

FACILITATION TIP

Break this term into its preﬁx and root word to help students better understand it: quad = four; lateral = sides.

DOK-1 What is a quadrilateral? A two-dimensional shape with four straight sides

DOK-1 What is a parallelogram? A quadrilateral in which opposite sides are parallel

DOK-1 What is a rectangle? A parallelogram with four straight sides and four right angles

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e. DOK-1 What is a rhombus? A parallelogram with four equal sides and opposite angles that are equal f. 5.

DOK-1 What is a trapezoid? A quadrilateral with one pair of parallel sides

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

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

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What is a quadrilateral? A two-dimensional shape with four straight sides

DOK-1 What is a parallelogram? A quadrilateral in which opposite sides are parallel

DOK-1 What is a rectangle? A parallelogram with four straight sides and four right angles

Intervention

Acceleration

e. DOK-1 What is a rhombus? A parallelogram with four equal sides and opposite angles that are equal f. 3. 4.

5. 6. 7. 8.

DOK-1 What is a trapezoid? A quadrilateral with one pair of parallel sides

Give the Student Handout to each student. Tell students they should look at each ﬁgure and their attributes and think about how they relate to various categories of two-dimensional shapes and discuss the following questions with their partners: a.

Is it a quadrilateral?

Is it a parallelogram, a trapezoid, or an irregular quadrilateral?

Is it a rectangle and/or a rhombus?

After evaluating each shape, have students record the number of each shape in the most specific category where it fits on the graphic organizer. Give students about 5–10 minutes to identify the properties of each shape and classify where it belongs on the graphic organizer. When students are finished, have each pair meet with another pair and compare and discuss the results. Discuss the following questions: a.

DOK-2 Can a shape be classiﬁed in more than one category? Yes

DOK-2 What categories does a square belong to? Quadrilateral, parallelogram, rectangle, and rhombus

DOK-2 What are some examples of shapes that are not quadrilaterals? Triangles, pentagons, hexagons, etc.

DOK-1 What is the most general category on the graphic organizer? Quadrilateral

FACILITATION TIP As an alternative, enlarge the graphic organizer and ask the students to cut out the shapes. They should physically sort the shapes into the organizer.

CLASSIFY TWO-DIMENSIONAL FIGURES

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FACILITATION TIP Give students the opportunity to evaluate other groups’ sorting. Provide sticky notes for them to leave constructive guiding questions.

e. DOK-3 What are the similarities and differences between a rectangle and a rhombus? Both are quadrilaterals and parallelograms and both have straight sides. Both have opposite angles that are equal. Rectangles have four right angles. A rhombus has to have four equal sides. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________

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Classify Two-Dimensional Figures Explore 1 – Classify Polygons ACTIVITY PREPARATION Students classify polygons based on their number of sides, lines of symmetry, and whether their sides are parallel, perpendicular, or congruent. In addition, they will classify each polygon’s angles by their type, measurement, and whether they are congruent.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of Table Shapes (per group) 1 Exit Ticket (per student)

• •

Consumable •

•

1 Resealable bag (per group) •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Table Shapes, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag. For students who need more support in recalling information, please see our Angles and Geoboard Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Geoboard)

PROCEDURE AND FACILITATION POINTS 1.

Read the following scenario to the class: The employees at a party-supply rental company are reorganizing their warehouse. They need some help organizing all their different tables. Can you help them classify the tables? Give a bag of table shapes to each group, and tell them these represent models of the tables stored in the warehouse. a.

Tell students the employees cannot ﬁgure out the best way to organize the tables, so they have come up with three ways to try. Instruct students to remove the shapes from their bags and to observe them.

Give them a few minutes to classify the shapes however they choose. Ask the following guiding questions, and allow time for students to share their thinking: i. What are some of the ways you have learned to classify shapes in the past? ii. How can we classify these shapes? iii. Is there more than one way to classify these shapes? Explain. iv.

What are some of the attributes that make these shapes similar or different?

Make a list on the board of the following ways these shapes can be classiﬁed as students mention them during the discussion: i. Number of sides ii. Size of angles iii. Type of lines

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Give a Student Journal to each student, and explain how they will be classifying the Table Shapes. a.

Part I: By number of sides and lines of symmetry

Part II: By the size of the angles (acute, obtuse, or right)

Part III: By the type of lines (how many pairs of parallel or perpendicular lines)

Explain that they are also responsible for labeling each set of tables once they are classiﬁed using the correct mathematical terms. Sample labels include the following: a.

Tables with four sides would be labeled “Quadrilaterals.”

Tables with corners larger than 90 degrees would be labeled “Obtuse Angles.”

Tables with one pair of sides that are the same distance apart and never meet would be labeled “One Pair of Parallel Sides.”

FACILITATION TIP For Part I, students can write the number of sides and the name on sticky notes. Students can then organize the cards by each title. This can be repeated for Part II with the size of angles and Part III with the types of lines.

CLASSIFY TWO-DIMENSIONAL FIGURES

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Part I: Number of Sides and Lines of Symmetry 1.

2. 3.

Explain that the employees want to try sorting the tables by the number of sides and their lines of symmetry. Some customers want tables with more or less sides, while some customers want symmetrical or non-symmetrical tables. Challenge students to discuss and determine how to use the number of sides and the presence or absence of symmetrical lines to classify the tables. In their Student Journals, students have four tasks to do in this part: a.

They should help the employees correctly label each group. They should be sure to use the correct term for shapes with that number of sides, such as hexagons. Students will sort the polygon tables into groups based on the number of sides they have. Ask students to write the number from the top-right corner of each card in the correct group. Every table belongs in one of the groups.

Students will then take each polygon table group (triangles, quadrilaterals, etc.) and sort them based on how many lines of symmetry they have. Ask students to write the number from the topright corner of each card in the correct group. Every table belongs in one of the groups.

Encourage students to discuss and answer the reﬂection questions using their observations.

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

DOK-1 What is the name of shapes that have three sides? Triangles

DOK-1 What is the name of shapes that have four sides? Quadrilaterals

DOK-1 What is the name of shapes that have ﬁve sides? Pentagons

DOK-1 What is the name of shapes that have six sides? Hexagons

e. DOK-1 What is the name of shapes that have eight sides? Octagons f.

DOK-2 Do all the shapes in each of these groups look the same? Explain their differences. Answers will vary. Even though they have the same number of sides, the length of their sides might be different, and the orientation looks different.

DOK-1 What is a line of symmetry? A line of symmetry is an imaginary line we can use to divide a shape into two identical halves.

FACILITATION TIP In the Explain section, the Picture Vocabulary can be used or printed as a reference for students. 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.

FACILITATION TIP Students should discuss with a partner how the shapes are similar and different. You can write down their ideas on chart paper.

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Classify Two-Dimensional Figures Explore 1 – Classify Polygons h. DOK-2 How can you determine how many lines of symmetry a shape can have? To ﬁnd a line of symmetry, you can look for two halves of the shape that are identical to each other. A shape may have more than one line of symmetry. Part II: Angle Size 1.

Now, the employees want to try sorting the tables by the size of the angles. a.

Students will need to look at the angles of each shape and decide if they are acute, obtuse, or right. They will also determine if two or more angles on a shape are congruent.

Ask the following guiding questions to review the types of angles, and allow time for students to share their thinking:

FACILITATION TIP

i. Which table shapes have an acute angle? How do you know?

To review angles, have students make an example of each type of angle using their hands and ﬁngers.

ii. Which table shapes have an obtuse angle? How do you know? iii. Which table shapes have a right angle? How do you know? iv.

Can you show me a way to determine if an angle is a right angle Note: Students might suggest using the corner of a piece of paper. If they do not, show them this method. In addition, show students how a shape has a right angle if you see a little square drawn in the angles.

Do any of these table shapes have more than one type of angle? Which ones?

vi.

How can you tell the difference between an acute and obtuse angle?

vii. How is a right angle different from acute and obtuse angles? FACILITATION TIP Congruent refers to having the same shape and size. You can demonstrate with two objects that are the same but different colors.

FACILITATION TIP As you are monitoring groups, listen for misunderstandings about angles and address individually or as a whole class. 306

viii. What are congruent angles? Which shapes have at least two congruent angles? Note: Discuss the term congruent if students do not already know what this means. 2. 3.

Once students have had an opportunity to review types of angles, they should sort the table shapes into piles by the size of the angles of each table. Invite students to brainstorm the different ways to classify the shapes by their angle types, and then share in a whole group discussion. As students share their thinking, make a list of the suggested ways to classify angles on the board. These could include the following: a.

Tables with all acute angles

Tables with all right angles

Tables with all obtuse angles

Tables with some right angles

e. Tables with some acute and some obtuse angles 4.

On their Student Journals, students should do the following: a.

They should help the employees correctly label each group. They should use the correct terms for the sizes of angles, such as acute.

They should write the number from the top-right corner of each card in the correct group. Every table belongs in at least one of the groups.

Encourage students to discuss and answer the reﬂection questions using their observations.

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

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

opposite angles. I know this because congruent means equal or the same and all the angles on a square or rectangle are the same, so the opposite angles are going to be congruent. Parallelograms can have right angles or opposite and congruent acute or obtuse angles. b.

DOK-1 Are there tables that could ﬁt in more than one category? How do you know? Answers may vary. Yes, the hexagon and octagon tables have obtuse angles, but they also have pairs of congruent angles.

DOK-1 Which Table Shapes have more than one type of angle? Answers may vary. Triangles, trapezoids, and parallelograms have more than one type of angle.

DOK-1 Which Table Shapes have only one type of angle? Squares and rectangles have only one type of angle.

Part III: Parallel Sides 1. 2.

Finally, the employees want to sort the tables based on how many pairs of parallel, perpendicular, and/or congruent sides they have. Give students time to talk within their groups as you ask the following guiding questions to review the types of lines: a.

What are parallel lines?

Which shapes have at least one pair of parallel lines?

Which shapes have more than one pair of parallel lines?

What are perpendicular lines?

e. Which shapes have at least one pair of perpendicular lines? f.

Which shapes have more than one pair of perpendicular lines?

What are congruent lines?

h. Which shapes have at least one pair of congruent lines?

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FACILITATION TIP Students can draw the different types of lines and the terms on sticky notes to help them in their classiﬁcation.

FACILITATION TIP Have students use total physical responses to review parallel, perpendicular, acute, obtuse, and right angles. Students can use their arms, hands, ﬁngers, legs, and/or knees to show understanding.

i. Which shapes have more than one pair of congruent lines? j. Which shapes do not have any parallel or perpendicular lines? 3.

Once students have had an opportunity to review types of angles, they should sort the table shapes into piles by how many pairs of parallel, perpendicular, and/or congruent sides they have. Students should brainstorm the different ways to classify the shapes by their line types and then share in a whole group discussion. As students share their thinking, make a list of the suggested ways to classify on the board. These could include the following: a.

Tables with no parallel sides

Tables with one pair of parallel sides

Tables with two pairs of parallel sides

Tables with more than two pairs of parallel sides

On their Student Journals, students should do the following: a.

They should write the number from the top-right corner of each card in the correct group. Every table belongs in at least one of the groups.

Encourage students to discuss and answer the reﬂection questions using their observations.

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

DOK-2 Which shapes have congruent sides? How do you know? Answers may vary. Squares, regular hexagons, regular octagons, regular pentagons, and equilateral triangles have congruent sides. I know this because of the congruency symbols on the shapes.

FACILITATION TIP You can check for understanding by asking individual students to model with their hands a congruent side, parallel lines, and perpendicular sides.

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Classify Two-Dimensional Figures Explore 1 – Classify Polygons

6. FACILITATION TIP

•

FACILITATION TIP

•

Take time to be sure these preﬁxes are posted where students can read and refer to them. Use choral response and physical responses to engage students and reinforce comprehension.

•

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.

DOK-1 Which shapes have a pair of parallel sides? Squares, regular hexagons, regular octagons, trapezoids, and parallelograms have a pair of parallel sides.

DOK-1 Which shapes have a pair of perpendicular sides? What do you notice about the angle made by perpendicular sides? Right triangles, squares, rectangles, and right trapezoids all have a pair of perpendicular sides. Shapes that have perpendicular sides will always have a right angle.

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

Math Chat

Before this Math Chat, take time to ﬁnd some real-world examples of patterns, use of shapes, lines, and angles to show students. Consider carpentry, sports, and engineering.

STEMscopes Tip

•

• •

•

DOK-2 What patterns do you notice in the names of the shapes? The names each begin with a preﬁx that tells how many sides those shapes have. TRIangles have 3 sides, QUADrilaterals have 4 sides, PENTagons have 5 sides, HEXagons have 6 sides, and OCTagons have 8 sides. DOK-2 What is the relationship between a polygon’s number of sides, angles, and vertices? A polygon will always have the same number of sides, angles, and vertices. DOK-1 If you look at the pictures on the cards, what do all the symbols mean? The tick marks on the sides can tell you which sides are congruent. The squares in the corners of some shapes mean those are right angles. The curved lines in the corners of some shapes mean those angles are congruent. DOK-1 What is the name for a polygon that has all equal sides? It is a regular polygon. DOK-1 What is special about the angles of a regular polygon? They are also all congruent. So if one angle in a regular polygon is obtuse, all the angles in that polygon are obtuse. DOK-1 Why isn’t it possible to draw a triangle with all obtuse angles? The triangle wouldn’t be able to close because the angles would be too big. DOK-2 Why is it impossible to have a triangle with parallel sides? If you have two sides that are parallel, you need at least two more sides to close the shape. This would make it a quadrilateral. You cannot make a triangle with parallel sides. DOK-2 What can you use the knowledge of parallel sides for? You can use it for classifying shapes into narrow categories, such as classifying quadrilaterals into trapezoids (one pair of parallel sides) or parallelograms (two pairs of parallel sides). DOK-2 Why don’t all regular shapes have pairs of parallel sides? If the shape has an odd number of sides, it will not have pairs of parallel sides. For example, the regular pentagon does not have any parallel sides.

Post-Explore FACILITATION TIP

When you preview this Exit Ticket with students, clarify your criteria for success. Consider having students label the details (right angle, parallel lines, perpendicular lines etc).

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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Classify Two-Dimensional Figures Explore 2 – Classify Quadrilaterals ACTIVITY PREPARATION Students explore and investigate attributes belonging to a category and subcategories of quadrilaterals, including kites, rectangles, squares, rhombuses, and other parallelograms, in order to classify those attributes.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • • •

•

1 Student Journal (per student) 1 Set of Quadrilateral Shapes (per group) 1 Set of Category Headings (per group) 1 Quadrilateral Classiﬁcation (per teacher) 1 Exit Ticket (per student)

• •

Reusable • •

•

1 Pair of scissors (per group) 1 Marker (per group)

•

Consumable • • • •

1 Glue stick (per group) 1 Resealable bag (per group) 1 Large sheet of adhesive chart paper or butcher paper (per group) 1 Roll of tape (per class)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print one set of Quadrilateral Shapes, on card stock for durability, for each group of students. Cut them out, remove shape 6 (square) from each set, and place them in a resealable bag. Shape 6 will be given to the students after the other shapes have been organized. Print one set of Category Headings, on card stock for durability, for each group of students. For students who need more support in recalling information, please see our Angles and Geoboard Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Geoboard)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Provide each group with a copy of the Picture Vocabulary Cards (accessed in the Explain section of this scope). Students who are unsure of speciﬁc shape names or who need support with spelling, can reference the Vocabulary Cards.

Read the following scenario to the class: You are a team of video game designers. A brand new game called Quadrilateral Quest is in the beginning stages of development. Your team has been tasked with forming the parameters of the game. You will work through the shapes and sort them based on their attributes so the correct attributes can be assigned to each shape in the game. Distribute the materials to the class. Each group should have a bag of Quadrilateral Shapes, a set of Category Headings, a large sheet of chart paper, a marker, a glue stick, and a pair of scissors. Each student should have a Student Journal. As a whole group, discuss students’ prior knowledge about attributes as potential classiﬁcation groups. Ask the following guiding questions while students observe and think about the quadrilaterals with their groups: a.

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Engage

Explore

Explain

Elaborate

Evaluate

b. DOK-2 Give an example of a shape that shares an attribute with another shape. Answers will vary. Rectangles and trapezoids each have at least one set of parallel lines. Rectangles and squares have two sets of parallel lines and four right angles. c. DOK-2 How can shapes look different but share similar attributes? Answers will vary. Shapes may have the same number of sides but different types of angles. For example, squares and rhombuses each have four sides, but squares have four right angles and rhombuses do not. 4.

5. 6. 7.

8. 9. 10. 11. 12.

13. 14.

15. 16. 17.

Explain that they will now work with their groups to create and investigate quadrilateral categories and subcategories to classify figures based on their attributes. Explain that they will not glue any of the shapes on their chart paper until they are instructed. Students will cut out their Category Headings. Have students glue the heading for “Four-sided polygon” at the top of the chart paper. Refer to the Quadrilateral Classification handout to help you guide the students through the different classifications. Note that the handout is not meant for students. Invite student groups to look at their shapes and collaborate to determine which shapes fit the attribute “Four-sided polygon.” DOK-1 Challenge the students to classify the shapes by naming the group they have made. Quadrilateral Have them write down the numbers of all shapes that can fit in that classification category. Invite students to analyze the quadrilaterals. Challenge them to discuss and create groups according to their sides. Students should classify by the following attributes: a.

No sets of parallel sides (2, 8)

Exactly one set of parallel sides (3, 7, 10)

Two pairs of parallel sides with two opposite sets of congruent sides (1, 4, 5, 9, 11, 12)

Ask students to ﬁnd the category headings that match these attributes, and challenge them to name the shapes. DOK-1 Invite groups to write the classiﬁcation names on the blanks of the category headings. a.

Trapezoid – exactly one pair of parallel sides (3, 7, 10)

Parallelogram – two pairs of parallel sides and two opposite sets of congruent sides (1, 4, 5, 9, 11, 12)

Acceleration

FACILITATION TIP Students may not be familiar with the symbols used to mark attributes. For example, ask students to observe the rectangle diagram. Ask, “Why do you think the two shorter sides have different markings than the 2 longer sides?” (They show that the 2 shorter sides are the same length and that the 2 longer sides are the same length.) Ask, “Why do you think the corners are marked?” (They show right angle symbols to represent that this type of ﬁgure has 4 right angles.) FACILITATION TIP Depending on your students, consider guiding some of them through part or all of this investigation. Struggling students may need some step-by-step supports.

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.

Have students write down the number of all the shapes that fit in that classification category. Have the students draw arrows from “Quadrilateral” to each of the three new category headings. Encourage the groups to discuss how a quadrilateral can fit into more than one category based on attributes. a.

18.

Intervention

CLASSIFY TWO-DIMENSIONAL FIGURES

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As a quadrilateral moves from one category to another, encourage them to list the number of the quadrilateral under the classiﬁcation heading so they are able to see which quadrilaterals can be classiﬁed in more than one way based on their attributes.

Challenge them to analyze and discuss the parallelograms.

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Classify Two-Dimensional Figures Explore 2 – Classify Quadrilaterals 19.

Ask the students how they could put these into two groups based on congruent sides. a.

20.

Have students ﬁnd this category heading and write the name on the blank.

21.

Have students write down the number of all the shapes that ﬁt in that classiﬁcation category. Remind the students to draw the arrow and mark where the shapes came from. Challenge them to analyze and discuss the rectangles. Ask them how they could put these into two groups according to their sides. side

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.

DOK-1 Exactly four congruent sides (5, 12)

22. 23.

a. 24.

26. 27.

28.

DOK-1 At least two sets of perpendicular sides (1, 11)

Have students ﬁnd this category heading and write the name on the blank a.

25.

Rhombus – Exactly four congruent sides (5, 12)

Rectangle – At least two sets of perpendicular sides (1, 11)

Have students write down the number of all the shapes that ﬁt in that classiﬁcation category. Have students glue the category headings and quadrilateral shapes to the chart paper. Give each group quadrilateral shape 6 (square). Challenge them to discuss the following in their groups: a.

Attributes of the shape

Name of the quadrilateral

Category or categories in which it can be sorted and why

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

What attribute(s) are you using to classify this shape?

What shapes have this speciﬁed attribute?

Why did you place shape 6 under (category heading)?

Why didn’t you place shape 6 under (category heading)?

e. All the shapes you placed on this category heading share a common attribute—what attributes does shape 6 have that makes it different from the others? 29. 30. 31. 32. 33.

34.

Have students write “6” under each category heading that it falls under. Add the name Square to the Rectangle and Rhombus titles. Glue the square under the last category heading it falls under. Allow each group time to answer the reﬂection questions on their Student Journals. Instruct groups to work together to draw how they categorized their quadrilaterals on their chart paper model on the last page of their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP Before this Math Chat, take time to ﬁnd some real world uses of quadrilaterals to show students. Architecture, design engineering, technology, and high interest games will provide engaging examples. 312

• •

DOK-1 What did you notice about all the shapes? They are all quadrilaterals. They all have four sides. DOK-1 What can you determine about a square? It can also be considered a rhombus, rectangle, parallelogram, and quadrilateral.

• •

• • •

•

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What shapes are also classiﬁed as special parallelograms? Rectangles, rhombuses, and squares are also classiﬁed as special parallelograms. DOK-2 If a square is always a rectangle, is a rectangle always a square? Why or why not? No. Not all rectangles have four equal sides. A square is a special type of rectangle that must have four equal sides. DOK-2 Why aren’t all parallelograms considered rectangles? They are not all rectangles because not all parallelograms have four right angles. DOK-1 What quadrilaterals have perpendicular sides? Squares, rectangles, and some trapezoids. DOK-1 Is a trapezoid a type of parallelogram? No. A parallelogram is a type of trapezoid. A parallelogram has two pairs of parallel sides, and a trapezoid has at least one pair of parallel sides. DOK-1 Could a rectangle be considered a type of trapezoid? Yes, a rectangle is a type of parallelogram and has two pairs of parallel sides. A trapezoid has at least one pair of parallel sides.

Intervention

Acceleration

CLASSIFY TWO-DIMENSIONAL FIGURES

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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, clarify the shapes, boxes where Complete the Anchor Chart as a class. the answers are to be written. Some Have each student complete their Interactive Notebook. students may see those rectangles as part of the quadrilateral sorting.

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Classify Two-Dimensional Figures Explore 3 – Classify Triangles ACTIVITY PREPARATION Students explore and investigate the angle size and side lengths of triangles to classify them into various categories and subcategories.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

•

1 Student Journal (per student) 1 Set of Triangle Shapes (per group) 1 Set of Category Headings (per group) 1 Exit Ticket (per student)

• •

Reusable • •

•

1 Pair of scissors (per group) 1 Marker (per group)

•

Consumable • • • •

1 Glue stick (per group) 1 Resealable bag (per group) 1 Large sheet of adhesive chart paper or butcher paper (per group) 1 Roll of tape (per class)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print one set of Triangle Shapes, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag. Print one set of Category Headings, on card stock for durability, for each group of students. For students who need more support in recalling information, please see our Angles and Geoboard Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Geoboard)

PROCEDURE AND FACILITATION POINTS Part I: Classify Types of Triangles Based on Side Lengths and Angles FACILITATION TIP

Print and project this sailboat scenario for students. Provide some visual images of sailboats and sails for students who may have limited exposure to sailboats.

FACILITATION TIP If students are going to complete this activity in small collaborative groups, post and project the steps for them to refer to as they work. For example, #1 Cut out headings #2 Write the heading #3 Examine triangles #4 Name the shapes ...

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3. 4.

Read the following scenario to the class: A local outdoor store just got a shipment of boxes containing sails for various types of sailboats. These sails are in the shape of a triangle; however, the side lengths and angles of these sails vary in size. Depending on the kind of sailboat someone owns, they may need a certain type of triangle for that sailboat. The store needs your help classifying the different types of triangles so they can organize the shelves correctly and it is easier for sailboat owners to purchase the correct type of sail for their sailboat. Distribute the following materials to the class. Each group should have a bag of Triangle Shapes, a set of Category Headings, a large sheet of chart paper, a marker, a glue stick, and scissors. Each student should have a Student Journal. Instruct each group to cut out their Category Headings. Have students write the heading “Three-sided polygon” at the top of the chart paper. Students will then remove the triangle shapes from the resealable bag and examine their attributes. Explain to the class that these triangle shapes represent the different sails the local outdoor store received and will be selling to customers. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

As a whole group, discuss students’ prior knowledge about shapes and their attributes as potential classiﬁcation groups. Ask the following guiding questions while students observe and think about the triangles with their groups: a.

Intervention

Acceleration

FACILITATION TIP Consider leading this discussion before students get into collaborative groups.

DOK-1 What attributes can help us classify shapes? Number of sides, type of angles, and differing side lengths

b. DOK-2 Give an example of a shape that shares an attribute with another shape. Answers will vary. A triangle with two sides that are the same length can contain a right angle (isosceles right triangle) just like a triangle with three different side lengths can also have a right angle (scalene right triangle). c. DOK-2 How can shapes look different but share similar attributes? Answers will vary. Shapes may have the same number of sides but different types of angles. 6. 7. 8.

10. 11. 12.

13.

Invite student groups to look at their shapes and collaborate to determine which shapes fit the attribute “Three-sided polygon”. DOK-1 Challenge the students to classify the shapes by naming the group they have made. Triangle Have the students write “Triangle” under the “Three-sided polygon” at the top of their chart paper and then write down the numbers of all shapes that can fit in that classification category on their Student Journals. Students should notice that all the shapes they received are triangles. Explain to the students that the local outdoor store has printed off the following labels to be placed on the shelves to help with organizing the sails: “Equilateral,” “Isosceles,” or “Scalene.” Ask students to find the category headings that match these attributes and place them in a row under the “Triangle” on their chart paper. Have students draw arrows from “Triangle” to each of the three category headings. Challenge student groups to discuss and create groups according to the side lengths of each triangle. Students should classify by the following attributes: a.

Equilateral – all three sides are the same length (1, 8)

Isosceles – two sides are the same length (3, 4, 6)

Scalene – each side is a different length (2, 5, 7)

Encourage students to analyze and discuss the descriptions given for an equilateral, isosceles, and scalene triangle to classify each triangle correctly. Ask the following guiding questions after students have shared their observations with their groups: a.

CLASSIFY TWO-DIMENSIONAL FIGURES

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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.

DOK-1 What are some of the attributes of a triangle? 3 sides, 3 angles

b. DOK-1 What do you notice about the sides of the triangles you were given? Some triangles have side lengths that are all congruent or equal in length, while other triangles have two side lengths that are congruent or no side lengths that are congruent. c. DOK-3 Why is it important to notice the differences between the given triangles? Answers may vary. It is important to notice differences between triangles because it shows us that even though all triangles have 3 sides and 3 angles, those 3 sides and 3 angles can have various side lengths and angles. d. DOK-2 How did you determine which triangles are equilateral, isosceles, or scalene? I analyzed each image of the triangle and examined their side lengths and the symbols on each side length to determine how many of the triangle side lengths were congruent.

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Classify Two-Dimensional Figures Explore 3 – Classify Triangles 14.

FACILITATION TIP

15.

Bring the class back together for Step 15 to discuss this new direction of classifying sails.

16. 17.

Have students write down the number of all the shapes that fit in that related classification subcategory on their Student Journals. Students will also represent and label how they classified the triangles from their chart paper into the correct categories on their Student Journals. Explain the following to the class: The local outdoor store would like you to organize the sails even further by classifying the angles of the sails. The store manager has printed off more labels that say “Acute,” “Right,” or “Obtuse.” Ask students to find the category headings that match these attributes and place each heading under “Equilateral,” “Isosceles,” and “Scalene” on their chart paper. Encourage the groups to discuss how a triangle can fit into more than one category based on attributes. a.

18.

As a triangle moves from one category to another, encourage them to list the number of the triangle under the classiﬁcation heading so they are able to see which triangles can be classiﬁed in more than one way based on their side lengths or their angles.

Challenge them to analyze and discuss the equilateral triangles. a.

DOK-1 What types of angles are represented in triangle 1? Acute

b. DOK-1 What types of angles are represented in triangle 8? Acute c. DOK-2 Is it possible to have an equilateral triangle with a right or obtuse angle? Explain. No, it is not possible because in order for a triangle to have a right or obtuse angle it would lengthen or shorten a side, which would make the sides no longer congruent. 19.

Challenge students to analyze and discuss the isosceles triangles. a.

DOK-1 What types of angles are represented in triangle 3? It has 1 obtuse angle and 2 acute angles. The obtuse angle makes this an obtuse isosceles triangle.

b. DOK-1 What types of angles are represented in triangle 4? It has 1 right angle and 2 acute angles. The right angle makes this a right isosceles triangle. c. DOK-1 What types of angles are represented in triangle 6? All the angles are acute, which makes this an acute isosceles triangle. 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.

20.

DOK-1 What types of angles are represented in triangle 2? It has 1 right angle and 2 acute angles. The right angle makes this a right scalene triangle.

b. DOK-1 What types of angles are represented in triangle 5? It has 1 obtuse angle and 2 acute angles. The obtuse angle makes this an obtuse scalene triangle. c. DOK-1 What types of angles are represented in triangle 7? All the angles are acute, which makes this an acute scalene triangle. 21. 22.

23. 24.

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Challenge students to analyze and discuss the scalene triangles.

Students should discuss with their groups and help each other as they are working. Students’ work should be recorded on their Student Journals. Have the students glue each triangle into its correct classiﬁcation and draw arrows to mark where each triangle came from so students can notice that each triangle can be named by its side lengths as well as its angles. Students may tape up their chart paper around the classroom to display how they classiﬁed their triangles. Allow each group time to answer the questions on their Student Journals.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Choosing the Best Triangle 1.

Read the following scenario to the class: Now that you have organized all the boxes of sails, it is time to complete customer orders. Three sailboat owners have requested particular requirements for the sails they need to get their sailboat up and running. Students will look at the three requests on their Student Journals. They will read each request and use their ﬁndings from Part I to draw a triangular sail for each sailboat. They will identify each sail type by right, acute, or obtuse and equilateral, isosceles, or scalene. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How can you determine whether a triangle is equilateral, isosceles, or scalene? You can determine whether a triangle is equilateral , isosceles, or scalene by identifying how many congruent sides the triangle contains. • DOK-2 How can you determine whether a triangle is right, acute, or obtuse? You can determine whether a triangle is right, acute, or obtuse by examining all three of the angle types within a triangle. If the triangle contains only acute angles, it is an acute triangle. However, if the triangle contains one right angle but two acute angles, it is considered a right triangle. If the triangle contains one obtuse angle and two acute angles, it is considered an obtuse triangle. • DOK-3 Explain how a triangle can be named after two different classiﬁcations. A triangle can be classiﬁed by its side lengths and by its angles. When we name a triangle, its name could be “equilateral,” “isosceles,” or “scalene” based on the side lengths. It can also be named “right,” “acute,” or “obtuse” based on the angles. •

Post-Explore 1. 2. 3. 4.

FACILITATION TIP Before this Math Chat, take time to ﬁnd some real-world uses of different triangles to show students. Roofs, trusses, pyramids, triangulation mapping, and the Bermuda Triangle may provide engaging examples.

CLASSIFY TWO-DIMENSIONAL FIGURES

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FACILITATION TIP On this Exit Ticket, struggling students may need to draw a line from/to the correct answer rather than drawing a detailed answer.

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Classify Two-Dimensional Figures Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

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

Classify Polygons 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

Classify 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

Classify Triangles 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

318

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

Scout’s Motto

Fashion 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

Do You Have a Pencil?

Match Attributes to Triangles and Quadrilaterals

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

CLASSIFY TWO-DIMENSIONAL FIGURES

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

319

Students who are still acquiring the concept and need remediation

CLASSIFY TWO-DIMENSIONAL FIGURES

Classify Two-Dimensional Figures

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Career Connections

320

 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 explore and investigate through the use of a variety of tools to classify, compare, and contrast the properties of polygons.

What prompts will be used?

What does mastery look like?

CLASSIFY TWO-DIMENSIONAL FIGURES

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I can make sense of the relationships between the attributes of two-dimensional ﬁgures within a category and subcategory.

I can use graphic organizers to classify, compare, and contrast the attributes of shapes.

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SCOPE 1

Unit Conversions Scope Introduction SCOPE SUMMARY

Student Expectations

5.MDR.7.1 Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time. 5.MDR.7.3 Convert among units within the metric system and then apply these conversions to solve multi-step, practical problems. 5.MDR.7.4 Convert among units within relative sizes of measurement units within the customary measurement system.

Students use their knowledge of place value and the relationship between units to convert different-sized units of measure within both the customary and metric systems. They reason that changing the form of a measurement does not change the size or amount of the quantity being measured. Students decide and explain if a converted amount would be more or less than the original unit before making the actual conversion. Visual models, such as a table or diagram, are tools used to reason about the conversion of units. Once students understand the relationships between units and how to convert between units, they solve multistep problems that involve the conversion and renaming of units.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

Fourth-grade students recognize and express relative benchmark sizes within the metric system of measurement, and they record equivalent measures in a two-column table. Fourth graders solve measurement problems that involve all four arithmetic operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with the same denominator. Students also solve problems that require expressing measurements given in a larger unit in terms of a smaller unit as well as expressing a smaller unit in terms of a larger unit based on the idea of equivalence.

In sixth grade, students are introduced to ratios and work on explaining the concept of a ratio, representing a ratio, and using ratio language to describe a relationship between two quantities. Sixth graders are using this knowledge of ratios and their prior knowledge of unit conversions to solve problems that exist in everyday life to convert ratios within the customary and metric measurement systems. Students will be working to solve one-step conversions, two-step conversions, and multistep conversions between systems of measurement.

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

determine if different conversions are correct or incorrect.

•

determine if they agree or disagree with each conversion.

•

support explanations and identify the mistake in a class discussion.

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

Hook

Accessing Prior Knowledge

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

solve problems by calculating conversions within a measurement system.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 322

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Convert Units of Length In this exploration, students will learn from participating in solving a scenario where they help an urban planner design small-town improvements. Students will: •

solve problems by calculating single-step and multistep real-world problems related to customary and metric length conversions that contain whole numbers, decimals, and fractions.

•

use measurement materials.

Explore 2

Explore 1

EXPLORE ACTIVITIES

Convert Units of Liquid Volume In this exploration, groups of students will be presented with a scenario about helping determine the amounts of different liquids needed for a town’s celebration party and for the baking. Students will: •

In this exploration, students will be tasked with using conversion tables to determine the correct amount of food needed for zoo animals. Students will: •

rotate to different stations to convert unit conversions of weight and mass for both the metric system and customary system.

•

complete a standard conversion table for mass and weight using a scale or balance.

•

complete a table, write an equation, show the work and write a solution statement for task cards.

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

Explore 4

Explore 3

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

Convert Units of Weight and Mass

UNIT CONVERSIONS

Home

determine the liquid volume by calculating multistep problems using customary and metric units of liquid volume conversions involving whole numbers, fractions, and decimals.

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

Convert Units of Time In the last exploration, learning occurs through solving scenarios where students help ensure that everything for the town party is done on time and that there is plenty of time to complete several activities so that the party is successful. Students will: •

solve problems by calculating multistep conversions of time.

•

use task cards, clocks, timers, and exploration resources.

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

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UNIT CONVERSIONS

Unit Conversions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

324

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students analyze multiple conversion equations and decide whether they agree that the equation is true or disagree and believe that the equation is not true. This activity is intended to assess mastery of the following standard(s):

UNIT CONVERSIONS

Home

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. 4.MDR.6.1 Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with like denominators, and also problems that require expressing measurements given in a larger unit in terms of a smaller unit, and expressing a smaller unit in terms of a larger unit based on the idea of equivalence.

Materials Printed • •

1 Set of Opinion Cards (per group) 1 Set of Conversion Cards (per group)

Reusable • •

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

Preparation • • • •

Plan to have students work in groups of 2 or 3 to complete this activity. Prepare to project the Slideshow for the class. Print a set of Opinion Cards on card stock for durability for each group. Print a set of Conversion Cards on card stock for durability for each group. Cut the cards apart, and place them in a resealable bag.

Procedure and Facilitation Points 1. 2. 3.

4. 5. 6.

7. 8. 9.

Project the Conversion Cards for the class. Distribute the bags of Conversion Cards and a set of Opinion Cards to each group. Starting at Conversion 1, read the conversion equation aloud with the class. Explain to students that some of the conversion equations are correctly converted, and some are not. Instruct students to work out the conversion to decide whether they agree or disagree with the equation. Ask each group to display either the agree opinion card or the disagree opinion card after their work time. Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Have students continue to work out the conversions to decide whether they agree or disagree with the equations. For the conversions that are incorrect, have students solve the conversion correctly and identify the mistake. If students are struggling to complete this task, do the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP The sample anchor chart within this scope could be projected as a reference tool. It shows customary and metric conversions for length, liquid volume, and time. FACILITATION TIP Have pairs of students discuss the mistakes with the conversions that are incorrect.

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UNIT CONVERSIONS

Unit Conversions Hook – Rain, Rain, Go Away! ACTIVITY PREPARATION Students solve problems by calculating conversions within a measurement system.

Materials

Preparation

Reusable • •

•

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

Part II • •

Consumable •

Plan to show the Phenomena Video.

Plan to have students work in pairs to complete this activity. Gather enough scratch paper for each student to have a sheet.

1 Sheet of scratch paper (per student)

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

FACILITATION TIP

Write students’ ideas on the board or on a poster board to refer back to following the completion of the Explore activities.

FACILITATION TIP Print and project this scenario. First, have students read it alone silently and jot down notes. Next, have them read it together with a shoulder partner. Finally, read it all together as a class and guide students to note the math phrases and values.

FACILITATION TIP Provide students a visual, such as a ruler, if needed.

DOK-1 What is a measurement system? A collection of units of measurement and the set of rules that relate the units to each other

DOK-1 Which system of measurement uses inches and feet? The customary measurement system

DOK-2 How do you convert a larger unit to a smaller unit? You have to ﬁnd the conversion factor and multiply.

DOK-2 How do you convert a smaller unit to a larger unit? You have to ﬁnd the conversion factor and divide.

e. DOK-1 How many inches are in a foot? 12 inches 5.

Move on to complete the Explore activities.

326

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1.

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

DOK-1 What is a measurement system? A collection of units of measurement and the set of rules that relate the units to each other

DOK-1 Which system of measurement uses inches and feet? The customary measurement system

DOK-1 How do you convert a larger unit to a smaller unit? You have to ﬁnd the conversion factor and multiply.

DOK-1 How do you convert a smaller unit to a larger unit? You have to ﬁnd the conversion factor and divide.

FACILITATION TIP Revisit students’ ideas from the Pre-Explore.

UNIT CONVERSIONS

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e. DOK-1 How many inches are in a foot? 12 inches 2. 3. 4. 5.

Divide students into pairs, and distribute scratch paper to students. Remind students that they are converting from a larger unit (feet) to a smaller unit (inches). Give students a couple minutes to convert feet to inches and determine whether Josie’s go-kart is safe. Using a show of hands to take a yes/no vote, ﬁnd out how many groups determined that Josie’s go-kart was safe and how many determined that it was ﬂooded. Discuss the following questions: a.

DOK-2 How did you ﬁgure out whether the go-kart was safe? It was a two-step problem. First, we used the conversion factor of 12 (since there are 12 inches per foot) and multiplied (since we are converting from a larger to a smaller unit). 3 × 12 = 36 Then, we compared how many inches above the river the go-kart was to how many inches the water had risen. 40 > 36, so it is safe.

DOK-2 How many more inches could the water rise before it will ﬂood her go-kart? 40 – 36 = 4 When it rises 4 more inches, it will ﬂood her go-kart.

DOK-3 Do you think you would use the same process to convert between units in different measurement systems? Explain. Yes, you would, but you would have more diﬃcult conversion factors.

FACILITATION TIP Provide manipulatives for students who are struggling.

FACILITATION TIP While this is the optimal method to solve the problem, allow students to describe other methods they used; then, compare and contrast the eﬃciency of the methods.

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Unit Conversions Explore 1 — Convert Units of Length ACTIVITY PREPARATION Students solve problems by calculating multistep real-world problems related to both customary and metric length conversions.

Standards for Mathematical Practice • • • •

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

Materials

Preparation

Printed • • •

• • •

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

• •

Reusable • • •

6 Rulers (per class) 6 Yardsticks (per class) 6 Metersticks (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 and cut out a set of Task Cards, on card stock for durability, for the class. Place one Task Card at each station. Place one ruler, one yardstick, and one meterstick at each station for reference. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS FACILITATION TIP Project the scenario and guide students through a read aloud. This scenario is an excellent real-world example of constraints that many engineers and planners must work around.

FACILITATION TIP Also reference a yardstick. Have the students observe that a yardstick is slightly shorter than a meter stick. Some measuring tools have standard units (inches, feet, and yards) on one side and metric units (millimeters, centimeters, and meters) on the other. If this is the case in your classroom, have the students observe that the standard units are spaced farther apart and the metric units are spaced closer together. This will help students determine which side of the tool to use when measuring. 328

3. 4. 5.

Read the following scenario to the class: An urban planner begins to create a design for improvements to a small town that is quickly growing. The planner will use existing buildings and add new places and structures to prepare for the growing population. There are many limitations and regulations she must follow. You will help the urban planner follow these regulations by answering 6 tasks for her. You will use the tools you were given to help you answer these tasks. Review length measurement tools with students. Ask the following types of questions: a.

DOK-1 What are the units we commonly use to measure length? Inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers are commonly used.

DOK-1 Using your ruler, describe the relationship between 1 foot and inches. I see that in 1 foot, there are 12 inches.

DOK-1 Using your meterstick, ﬁnd 100 centimeters. What is another name for or way to describe 100 centimeters? I see that 100 centimeters is also the same as 1 meter. The meterstick is exactly 1 meter, which is also the same as 100 centimeters.

Give each student a Student Journal, and assign each group to one of the six stations. Explain that their job is to use the measurement tools and given information to answer each question and make sure the planner’s measurements are accurate. When students have completed the tasks at their stations, have them move to the next station and complete the task. Students should continue to move to each station until they have completed the tasks in all six stations. © Accelerate Learning Inc. - All Rights Reserved

8. 9.

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

Engage

DOK-1 How did you convert meters to centimeters? I multiplied the number of meters by 100 because I found that there are 100 centimeters in each meter.

DOK-1 How did you convert inches to yards? I divided the number of inches by 12 to convert to feet, and then I divided that quotient by 3 to ﬁnd the number of yards.

DOK-1 Do you notice a pattern when you need to convert a measurement unit to the next-smallest measurement unit? Yes, I need to multiply to ﬁnd the smaller unit.

DOK-1 Do you notice a pattern when you need to convert a measurement unit to the next-largest measurement unit? Yes, I need to divide to ﬁnd the larger unit.

FACILITATION TIP

UNIT CONVERSIONS

Home

Record units in a T-chart using the categories of Metric System and Standard System. Discuss their differences. (The metric system is used worldwide and in the ﬁeld of science, and it is organized using multiples of 10. The standard system is used mainly in the US and UK, and it does not follow a predictable pattern when units are converted.) FACILITATION TIP Take time to lead students through some physical responses to review common measurements. For example: the width of a pinky is about a cm, a meter is about doorknob height, an inch is about the top of your bent knuckle of your thumb.

Math Chat DOK-2 What do you notice about the solution when converting smaller measurement units to larger measurement units? The solution becomes a smaller number than the smaller measurement-unit numbers. You also have to use division because you are trying to ﬁnd out how many larger units you have by creating equal groups of smaller units. • DOK-2 What do you notice about the solution when converting larger measurement units to smaller measurement units? The solution becomes a greater number than the larger measurement-unit numbers. You also have to use multiplication because you are ﬁnding the total number of smaller units when each larger unit is a group of smaller units. • DOK-2 Even though the numbers change when converting units of measurement, what can you say about the distance they represent? Both numbers represent the same distance. The distance stays the same, but the numbers are based on the different measurement units that are used, so they are different. • DOK-3 Why do some conversions require only one step while other conversions require two steps? When converting measurement units to the next-largest or next-smallest unit, only one step is needed because the units are next to each other. When converting measurement units to units that are not next to each other, more steps are needed. •

Post-Explore 1. 2. 3.

FACILITATION TIP Connect students with some relevant realworld examples for when older students or adults will need to convert measurements. Consider using some visuals from metric countries (non-US), sports, science experiments, and any popular hobbies in your 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.

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UNIT CONVERSIONS

Unit Conversions Explore 2 — Convert Units of Weight and Mass ACTIVITY PREPARATION Students solve problems by calculating multistep weight and mass conversions.

Standards for Mathematical Practice • • • •

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

Materials

Preparation

Printed • • •

• • •

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

•

Reusable • • • •

•

1 Digital scale or balance (per group) 1 Set of metric weights (per group) 1 Set of customary weights (per group) 1 Resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Task Cards, on card stock for durability, for each group of students. Cut the cards apart, and place them in a resealable bag. Prepare a digital scale or balance and a set of metric and customary weights for each group. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION POINTS 1.

Read the following scenario to the class: Your class is going on a ﬁeld trip to the zoo! In addition to seeing all the animals, you are going to get a behind-the-scenes guided tour of the feeding stations of 6 different animals in the zoo. It is extremely important that the animals’ food is measured precisely to keep them healthy and thriving. You can hardly wait to see how much the animals eat during feeding time!

Part I 1.

Distribute weights to each group. a.

FACILITATION TIP You can create a T-chart on the board sequencing the types of units from smallest to largest for each type of unit based on students’ responses. FACILITATION TIP Provide visual and real-world tactile references for ounces, pounds, and tons.

330

Please note that although students are converting both customary and metric units, they are not required to distinguish them scientiﬁcally.

Discuss the following questions: a.

DOK-1 How are ounces related to pounds? Ounces are smaller than pounds. Ounces ﬁt within pounds.

DOK-1 How are tons related to pounds? Tons are much larger than pounds; 1 ton has many pounds in it.

DOK-1 What does that mean about the relationship between ounces and tons? Since ounces are smaller than pounds and pounds are smaller than tons, there are very many ounces within a ton.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

e. DOK-1 How are milligrams and grams related? Milligrams are smaller than grams. Milligrams ﬁt within grams. f.

3. 4. 5.

DOK-1 What does that mean about the relationship between milligrams and kilograms? Since milligrams are smaller than grams and grams are smaller than kilograms, there are very many milligrams within a kilogram.

Give a Student Journal to each student. Explain that their job is to solve the problems by converting weight or mass measurements. Give a digital scale or balance to each group. Explain that precise measurements are very important when feeding animals to keep them healthy and strong. Students will be expected to use the scale or balance to determine precise measurements. Challenge groups to ﬁrst determine the precise relationship between the units. a.

DOK-1 Remind students that they have determined that ounces ﬁt within a pound. They will use the balance to determine the precise number of ounces within a pound. Students will record this amount on their Student Journals. There are 16 ounces in a pound.

DOK-1 Students have also determined that grams ﬁt within a kilogram. Students will use the digital scale to measure the precise amount of grams in 1 kilogram. There are 1,000 grams in 1 kilogram.

DOK-1 Students have also determined that milligrams fit within a gram. Tell students the weight of the tip of a pencil lead is a milligram. Ask if it is reasonable to measure how many milligrams fit in a gram. No, it would be too hard to find a lot of something that small to measure in the class.

DOK-1 Give students the precise amount of milligrams in 1 gram. There are 1,000 milligrams in 1 gram.

e. DOK-1 Students have also determined that pounds ﬁt within tons. Ask students if it is reasonable to measure a ton in the classroom to ﬁnd the precise amount of pounds. No, a ton is too large to measure in the class. f. 7.

DOK-1 Give students the precise amount of pounds in 1 ton. There are 2,000 pounds in a ton.

Students will record the measurements on their Student Journals.

UNIT CONVERSIONS

Home

FACILITATION TIP You will need to model how to use the scale or balance to create their conversions. Include in the modeling how to make precise measurements. Provide practice time for each student to practice before beginning the collection of data.

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.

Part II 1.

After students have used the tools to determine precise measurements, distribute the bags of Task Cards to each group. The students will solve the Task Cards 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 did you convert ounces to pounds? I divided the number of ounces by 16.

DOK-1 What would you have to do to convert a measurement unit to the next-smallest measurement unit? I would multiply.

DOK-1 What would you have to do to convert a measurement unit to the next-largest measurement unit? I would divide.

When students have completed the conversions in all the scenarios, allow the groups to work together 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.

FACILITATION TIP In Part II, students will need to convert to similar units ﬁrst and then answer the question on the Task Card. Have students circle the units in each Task Card. FACILITATION TIP Students should share in the Math Chat the strategies and operations they used to convert for each Task Card.

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UNIT CONVERSIONS

Unit Conversions Explore 2 — Divide a Unit Fraction by a Whole Number Math Chat DOK-2 What do you notice about the numbers when converting measurement units? When going from larger measurement units to smaller measurement units, the numbers become greater than the larger measurement numbers. When going from smaller measurement units to larger measurement units, the numbers become smaller than the smaller measurement numbers. • DOK-2 Even though the numbers change when converting units of measurement, what can you say about the weight they represent? Both numbers represent the same weight. The weight stays the same, but the numbers themselves are based on the different measurement units that are used, so they are different. • DOK-3 Why do some conversions require only one step while other conversions require two steps? When converting measurement units to the next-largest or next-smallest unit, only one step is needed because the units are next to each other. When converting measurement units to units that are not next to each other, more steps are needed. • 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.

Post-Explore FACILITATION TIP

Before having students complete this Exit Ticket, clarify your expectations for the written explanations and methods for students to show their thinking.

2. 3.

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

332

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

UNIT CONVERSIONS

Home

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UNIT CONVERSIONS

Unit Conversions Explore 3 — Convert Units of Liquid Volume ACTIVITY PREPARATION Students solve problems by calculating multistep liquid volume conversions using customary and metric units.

Standards for Mathematical Practice • • • •

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

Materials

Preparation

Printed • • •

• • •

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

• •

Reusable •

1 Liquid-volume container set (gallon, quart, pint, cup, mL, and L, per group)

•

Consumable •

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Task Cards, on card stock for durability, for the class. Place one Task Card at each station. Gather the liquid-volume container set and gallon of water in a gallon container for each group. For students who need more support in recalling information, please see our G and Gallon Display Supplemental Aids elements in the Intervention section.

1 Gallon of water in a gallon container (per group)

PROCEDURE AND FACILITATION POINTS 1.

Read the following scenario to the class: Your town is having a Centennial Celebration! It’s the town’s 100th birthday, and the community wants to celebrate it in style with a huge party in the park. Everyone’s invited! Your family signed up to help with the food. Your parents are in charge of making and baking the food, and your sister is in charge of ﬁguring out the dry-ingredient amounts needed to make food for so many people. It will be your job to determine the amounts of different liquids needed for the party as well as for baking.

Part I FACILITATION TIP Cover student workspaces with large tubs, trash bags, shower liners, or waterproof tablecloths. Provide access to paper towels and a funnel (to return the water to the gallon jug between station rotations). Discuss the importance of cleaning up spills, especially if water falls onto the ﬂoor. 334

1. 2. 3.

Give a Student Journal to each student. Assign each group to one of six stations. Have them take their liquid-volume container set and gallon of water to their assigned station. Invite students to discuss how the units relate to one another as they explore with the water: a.

Ask students to use the 1-gallon container to ﬁnd equivalent measures. i. DOK-1 What other measurements can you ﬁnd that are equal to one gallon of water? 4 quarts © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Ask students to ﬁnd the number of pints that are equivalent to one quart using their tools. i. DOK-1 How many pints are equivalent to one quart? 2 pints equal 1 quart.

UNIT CONVERSIONS

Home

ii. DOK-1 Can you use the relationship between pints and quarts to ﬁnd the number of pints that are equivalent to one gallon? Yes. How? If 1 quart has 2 pints, then 4 quarts has 8 pints, which is equal to 1 gallon. c.

Ask students to continue to use the liquid-volume container sets to ﬁnd equivalent measures for gallons, quarts, pints, cups, and ﬂuid ounces.

Students will record their measurements on their Student Journals.

e. Students will then use the metric liquid-volume container for 1 L. f.

Invite students to pour 1 mL into the container, and ask them to share their observations and predict how many times they’d have to refill the milliliter dropper or container to fill the liter. i. DOK-1 What do you notice? It hardly fills anything—it’s almost like a drop. ii. DOK-1 How many times do you think you will need to refill the milliliter dropper or container to fill the liter? You’d need a lot of milliliters to fill the liter.

Explain that it would take 1,000 mL to ﬁll the liter and that the preﬁx milli- indicates 1,000.

h. Explain that a kiloliter holds a thousand liters. Ask them to predict how many times they’d have to refill the milliliter dropper or container to fill a kiloliter. i. DOK-1 How many times do you think you will need to refill the milliliter dropper or container to fill a kiloliter? If it takes 1,000 mL to fill a liter, then it would take 1,000,000 milliliters to fill a kiloliter. i. Ask students to find an example of converting from one unit to another in which they would need to multiply to find the equivalent measure and explain why. i. DOK-2 Can you think of an example of converting from unit to another in which you would need to multiply to find the equivalent measure? Explain. Answers will vary. I would need to multiply to find the number of pints in gallons because pints are smaller than gallons, so more pints fit in a gallon. j. Ask students to find an example of converting from one unit to another in which they would need to divide to find the equivalent measure and explain why. i. DOK-2 Can you think of an example of converting from unit to another in which you would need to divide to find the equivalent measure? Explain. Answers will vary. I would need to divide to find the number of liters in milliliters because liters are larger than milliliters, so it takes fewer liters to equal a large number of milliliters.

FACILITATION TIP Model the process of taking a liquid volume measurement after the water settles and at eye level. Show students that the water needs to settle so that the top surface is evenly distributed. When you look directly down at a liquid-volume measuring tool, the reading is not as precise as when you view it from the water level.

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

FACILITATION TIP Connect this reasoning to the previous Explore activity on length. Have students observe that the same principles hold true. (When converting from a smaller unit to a larger unit, divide. When converting from a larger unit to a smaller unit, multiply.)

335

UNIT CONVERSIONS

Unit Conversions Explore 3 — Convert Units of Liquid Volume Part II FACILITATION TIP Before switching stations, make sure the water is returned to the gallon jug and that all spills are cleaned. This will enable the next group to work through the process of measuring and to record their work on a dry work surface.

1. 2. 3. 4.

Assign each group to one of the six stations. Explain that their job is to help create several drinks and recipes using precise measurements so the town’s Centennial Celebration will be successful. Encourage students to use the conversion guide they made in Part I to help solve the problems at each station. Have students begin to work at the station to which they were assigned. When students have solved the problems at their stations, have them move to the next station and solve the next problem. Students should continue to move to each station until they have completed all six stations. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP Pause to discuss eﬃcient strategies for multiplying and dividing by powers of 10. It may help to make a table of converted values with a calculator ﬁrst. As students repeat the process, they will notice structure in the products or quotients. (To multiply by a power of 10, move the decimal point to the right for each zero. To divide by a power of 10, move the decimal point to the left for each zero.)

DOK-1 How did you convert milliliters to liters? Why? I divided the number of milliliters by 1,000 to ﬁnd the number of liters. I did this because liters are much larger than milliliters, so the number of liters is actually a smaller value than the number of milliliters.

DOK-1 Look at task 2. What operations did you need to do? I needed to multiply by 8 to ﬁnd the number of ﬂuid ounces. DOK-1 How were 1

1 3 × 8 = 24, and then to get __2, I found half of 8 = 4. Then, I added 24 + 4 to

get 28. I added 28 oz. for the brownies and 9 oz. for the cake batter to get 37 oz. total. c.

6. 7. FACILITATION TIP Explain that many adults use conversion reference resources, especially for the standard system. For example, ask a question to your cell phone or use a Google search to answer the question “How many inches are in one foot?” Have the class help generate a conversion reference sheet to post, copy, and distribute for future reference. Many notebooks (such as composition notebooks) have a conversion reference table printed on the cover.

DOK-1 In Task 3, there are several ways to solve for the leftover milk. Explain how you chose to solve it. I chose to change the cups to pints and add the pints together. I know that 16 pints is equal to 2 gallons because each gallon has 8 pints. Then, I subtracted 4 gallons – 2 gallons = 2 gallons left over.

Math Chat •

•

336

you able to solve for the 3 __2 cups of oil? I broke 3 __2 into 2 parts. I found

DOK-3 If someone asked you how it is possible that you found 16 pints to be equal to 2 gallons, how would you explain this is true using what you learned from your measurement tools? I would explain that each gallon, which is larger than 1 pint, can hold 4 quarts because I saw this using my measurement tools. 1 gallon is the same as 4 quarts. I also know that each quart can hold 2 pints because the pints are smaller than the quart. This means that since 4 × 2 equals 8, there are 8 pints in a gallon. If there are 8 pints in 1 gallon, then there are 16 pints in two gallons. DOK-2 How do you know when more than one step is needed to convert units? Some units of measure are bigger or smaller than others, and they increase or decrease in size gradually. If we need to convert to a unit that is not immediately the next size up or down, more than one step will be needed. For example, if we are converting cups to quarts, we’ll ﬁrst need to ﬁgure out the number of cups in a pint and then the number of pints in a quart.

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. Before having students complete this Exit Ticket, consider allowing students to use a Complete the Anchor Chart as a class. standard US conversion chart. Have each student complete their Interactive Notebook.

UNIT CONVERSIONS

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

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UNIT CONVERSIONS

Unit Conversions Explore 4 — Convert Units of Time ACTIVITY PREPARATION Students solve problems by calculating multistep conversions of time.

Standards for Mathematical Practice • • • •

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

Materials

Preparation

Printed • • •

• • •

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

• • •

Reusable • •

1 Geared practice clock (per group) 1 Timer (per group)

•

Plan to divide the class into six groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out a set of Task Cards, on card stock for durability, for the class. Place one Task Card at each station. Prepare a geared practice clock and a timer for each group. 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. (Clock)

PROCEDURE AND FACILITATION POINTS Part I 1.

FACILITATION TIP Pause to observe the multiples of 60. Generate them using an online calculator. (Enter “60 + 60 =” Then, continue to press = after each multiple is displayed.) Students may notice that the multiples of 60 are just like the multiples of 6, only they have an extra zero at the end. This observation will lead to eﬃciency with the calculation of converted units.

338

Read the following scenario to the class: It is the day of the Centennial Celebration, and you have a very busy schedule to keep so that you and your family will have everything ready for the party. You will use your knowledge of units of time to make sure all of the tasks you are in charge of helping with are done in time. Give each student a Student Journal, and distribute geared practice clocks and timers to each group. Discuss the following questions: a.

DOK-1 What are the units commonly used to measure time? Seconds, minutes, hours, days, weeks, months, and years

DOK-1 Ask students to explain the relationship between seconds and minutes. Seconds are part of a minute. There are 60 seconds in each minute.

DOK-2 Ask each student group to use the timer to prove that the relationship they established between seconds and minutes is true. Have students discuss how the timer shows this relationship. As the timer counts up by seconds, it reaches 59 seconds and then switches to 1 minute the next second. This shows that 60 seconds is equal to 1 minute.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

e. DOK-2 Ask each student group to use the practice clock to prove that the relationship they established between minutes and hours is true. Have students discuss how the practice clock shows this relationship. Each mark in the hour represents 1 minute. Each number represents 5 minutes. There are 12 numbers times 5 minutes, so there are 60 minutes. This shows that 60 minutes is equal to 1 hour. f.

DOK-2 Ask students to use their knowledge of seconds, minutes, and hours to ﬁnd the relationship between seconds and hours. There are 60 seconds in 1 minute, and there are 60 minutes in 1 hour. So, 60 × 60 is equal to 3,600. That means there are 3,600 seconds in 1 hour.

After students have established the relationships between seconds, minutes, and hours, they will record them on the table and answer the questions on their Student Journals.

Part II 1. 2.

3. 4. 5.

UNIT CONVERSIONS

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FACILITATION TIP Students may ask about leap years. (Approximately every four years, February has 29 days instead of 28, so there are 366 days in a leap year.)

Assign each group to one of the six stations. Explain that their job is to prepare for the town’s Centennial Celebration by making sure there is plenty of time to complete several activities so the party will be successful. Encourage students to use Part I to help solve the problems at each station. Have students begin to work at the station to which they were assigned. When students have solved the problems at their stations, have them move to the next station and solve the next problem. Students should continue to move to each station until they have completed all six stations. FACILITATION TIP As students are working, monitor and check for understanding. Ask the following types of questions: Connect conversion reasoning to the previous length and liquid-volume Explore a. DOK-1 How did you convert minutes to hours? Why? I divided the activities. (When converting from a smaller number of minutes by 60 to find the number of hours. I did this because unit to a larger unit, divide. When converting hours are larger than minutes, so the number of hours is actually a from a larger unit to a smaller unit, multiply.) smaller value than the number of minutes. FACILITATION TIP b. DOK-1 Look at the Task Card “Setting up Chairs.” What operations did you need to do? I needed to divide to find the number of hours and then Discuss that unlike length and liquid volume, units of time are universal add the amount of time to get the total. (worldwide); however, there are different c. DOK-1 What does the remainder represent when you divide the number time zones. Discuss how sunlight plays a of minutes to find the hours? The remainder is the number of minutes. factor in the structure of time zones and The quotient is the complete number of hours, and the remainder is units of time measurement. extra time in minutes. d.

DOK-1 Look at the Task Card “Icing Cookies.” What operations do you need to do to solve? I need to multiply to ﬁnd the total seconds and then divide by 60 to get the number of minutes.

e. DOK-1 What does the remainder represent when you divide the number of seconds by 60? The quotient is the number of minutes, and the remainder is the number of seconds. 7. 8. 9.

FACILITATION TIP Challenge students to explain why a broken clock is always right twice a day.

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UNIT CONVERSIONS

Unit Conversions Explore 4 — Convert Units of Time Math Chat • 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.

•

DOK-2 Explain how you can use your knowledge of fractions to eﬃciently solve problems related to a fraction of an hour or minute. I have already learned that an hour can be broken into half-hour and quarter-hour time periods. A half hour is equal to 30 minutes, which is half of 60. A quarter hour is equal to 15 minutes, which is the same as one-fourth of an hour. DOK-2 In which task did you need to convert twice? Why? On the Task Card titled “Party Events,” I had to convert twice because I had to convert from hours to minutes, and then I had to convert to seconds. I knew there are 60 minutes in an hour, and each minute has 60 seconds, so I really multiplied by 60 twice. DOK-2 If you were given seconds, minutes, and hours and told to convert each time to the same unit, which unit of time would you choose? Why? I would choose to convert each time to seconds. I could easily convert the minutes to seconds by multiplying by 60. I could convert the hours to seconds by multiplying by 60 and then 60 again or multiplying by 3,600.

Post-Explore FACILITATION TIP

Before having students complete this Exit Ticket, determine your criteria for student success when showing their methods for solving.

2. 3. 4.

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Unit Conversions 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

Convert Units of Length Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

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

Convert Units of Weight and Mass Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

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

Convert Units of Liquid Volume

Interactive Notebook

Show What You Know, Part 4

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

Convert Units of Time

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

The Candy Counter

Veterinarian

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

Mysteries of Our Moon

Equivalent Measurements – 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

UNIT CONVERSIONS

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Problem-Based Task Time for a Vacation! Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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UNIT CONVERSIONS

Unit Conversions 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?

UNIT CONVERSIONS

Home

What does mastery look like?

I can use my knowledge of place value and the connection between decimals and fractions to express measurements of larger or smaller units within a measurement system.

I can reason that changing the form of a measurement by using different units does not change the size or amount of the quantity being measured.

I can use strategies and tools, such as a two-column table and a conversion chart, to reason about the conversion of units.

I can use unit conversions to discuss and solve multistep problems.

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SCOPE 1

Volume Scope Introduction SCOPE SUMMARY Students learn what volume is, what a cubic unit is, and how a cubic unit is used to determine volume. They use familiar concrete objects and pictorial models to understand and develop formulas used to calculate volume in a rectangular prism, (l × w × h) and (Bh), and also a cube (s × s × s), which is a special kind of rectangular prism.

Student Expectations

5.GSR.8.3 Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems. 5.GSR.8.4 Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In third grade, students measure the lengths of objects and the volumes of liquids. They also use models and formulas to ﬁnd the areas of rectangles. Fourth-grade students solve measurement problems involving the areas and perimeters of composite rectangles.

In sixth grade, students will continue to solve for the volumes of rectangular prisms. However, in sixth grade, the rectangular prisms will now have fractional side lengths. Students will apply the formula for volume, V = B × h or V = l × w × h, to solve.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

choose the picture that correctly represents the perimeter and area of a rectangular garden.

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

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

use concrete models in the form of unit cubes to measure the volume of an object in the shape of a rectangular prism.

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

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Cubic Units In this exploration, students will recognize a cube with a side length of one as a unit cube. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

understand that the volume of a three-dimensional ﬁgure is the number of unit cubes needed to ﬁll it.

In this exploration, students will determine the volume of a rectangular prism with whole-number side lengths. 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

Discover Volume

create two buildings (rectangular prisms) with the same volume.

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

Volume of Rectangular Prisms In this exploration, students will use concrete objects and algorithms to apply the formula for the volume of a rectangular prism. Students will: •

ﬁgure out which pet crates a store owner can put on the top shelf of a display.

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

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Volume Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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ACCESSING PRIOR KNOWLEDGE Students choose the picture that correctly represents the perimeter and area of a rectangular garden. This activity is intended to assess mastery of the following standard(s): 4.GSR.8.3 Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths.

Materials

Preparation

Printed •

•

1 Garden Cards (per class)

•

Consumable •

Print the Garden Cards on cardstock for durability for the class. Cut the cards apart. Make four columns on the board. At the top of each column, place one of the Garden Cards.

1 Sticky note (per student)

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

Ask students to think about the following question: What is the perimeter and area of a rectangular garden in which one side is 18 feet and another side is 24 feet? Instruct students to write their names on their sticky notes and place them under the Garden Card they agree with. Inform them that they should be ready to defend the reason why they chose that card. Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

I think the perimeter is 42 feet and the area is 432 square feet because you add the sides together to find the perimeter. 24 + 18 = 42. You multiply the sides together to find the area. 24 × 18 = 432. I think the perimeter is 84 feet and the area is 432 square feet because you add all the sides together to find the perimeter. 24 + 24 + 18 + 18 = 84. To find the area, you multiply the length by the width.24 × 18 = 432.

FACILITATION TIP Project this scenario so that students can see the text. Consider gathering some information about what prior vocabulary knowledge: perimeter and area. Students commonly get the two concepts mixed up even if they have had past experience with the concepts. FACILITATION TIP If space and time is an issue, consider projecting the Garden Cards one at a time. Allow students to make silent observations and notes and then discuss with partners. FACILITATION TIP To simplify, students can vote using hand signals (on their chest to keep them private) for their choices rather than move around with sticky notes.

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

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VOLUME

Volume Hook – Turtle Tank ACTIVITY PREPARATION Students use concrete models in the form of unit cubes to measure the volume of an object in the shape of a rectangular prism.

Materials

Preparation

Printed •

• •

1 Turtle Conservation Tank (per group)

Part II

Reusable • • • •

Plan to show the Phenomena Video. Print the Turtle Conservation Tank for each group.

• •

1 Phenomena Video (per class) 1 Projector (per class) 100 Unit cubes (per group) 1 Resealable bag (per group)

Plan to have students work in groups of 3-4 to complete this activity. Prepare the 100 unit cubes for each group by counting them out and putting them in a resealable bag.

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

FACILITATION TIP Print and project this scenario. Encourage students to read it silently and make some notes about the essential math phrases and values. Have students turn and talk to a partner and be prepared to contribute to a class discussion.

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Show students the image of the turtle tank. Discuss the following questions: a.

DOK-1 What is volume? The amount of space an object occupies

DOK-2 How can you use a model to determine volume? You can ﬁll an object full of unit cubes and count up the cubes to determine the volume of a rectangular prism.

DOK-1 How do you use the unit cubes to ﬁgure out volume in cubic feet? Each unit cube is equal to one cubic foot.

DOK-1 What is a rectangular prism? It is a three-dimensional ﬁgure made from six rectangular or square sides.

Move on to complete the Explore activities.

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 scenario. Discuss the following questions: a.

DOK-1 What is volume? The amount of space an object occupies.

DOK-2 How can you use a model to determine volume? You can ﬁll an object full of unit cubes and count up the cubes to determine the volume of a rectangular prism.

DOK-1 How do you use the unit cubes to ﬁgure out volume in cubic feet? Each unit cube is equal to one cubic foot.

DOK-1 What is a rectangular prism? It is a three-dimensional ﬁgure made from six rectangular or square sides.

Give the Turtle Conservation Tank to each group. Distribute the resealable bags with the cubes. Remind students that the tank will be a rectangular prism that is 10 feet long, 5 feet wide, and 2 feet deep. Also remind students that each unit cube represents 1 cubic foot. Give students about 5–10 minutes to build the model of the turtle tank and determine how many cubic feet it contains. Using a show of hands to take a yes/no vote, ﬁnd out how many groups found the turtle tank to meet the requirement of 100 cubic feet of volume. Discuss the following questions: a.

DOK-2 How did you ﬁnd the volume of your pool? Answers will vary. We counted the cubes. (There were 100 cubes.) We added the total number of cubes in each layer together (repeated addition → 50 + 50 = 100). We could have also chosen to multiply the cubes in each layer by the number of layers (50 × 2 = 100).

DOK-2 If you couldn’t count the cubes in your model and only had a pictorial model labeled with the dimensions of length (10 feet), width (5 feet), and height (2 feet), what strategy could you use to ﬁnd the volume? We could multiply the dimensions to solve the problem (length × width × height).

DOK-1 Is there a formula for ﬁnding the volume of a rectangular prism? Yes, the formula is l × w × h (length × width × height).

DOK-3 Why might someone need to know the volume of a turtle tank? Answers will vary. They may want to ﬁgure out how many baby turtles can ﬁt comfortably in the tank.

Intervention

Acceleration

VOLUME

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FACILITATION TIP Project these questions to help facilitate your discussion. 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.

FACILITATION TIP Take time to check for understanding about the mathematical/scientiﬁc deﬁnition of volume.

FACILITATION TIP Monitor and assess visually as groups build their models.

FACILITATION TIP Before asking this yes or no question, ask some open-ended questions about geometric formulas. FACILITATION TIP In addition to this question about turtle tanks, guide students to come up with some other real-world volume applications (room occupancy, gas tanks, amount of concrete needed for construction projects). 351

VOLUME

Volume Explore 1 — Cubic Units ACTIVITY PREPARATION Students recognize a cube with a side length of one as a unit cube and understand that the volume of a three-dimensional ﬁgure is the number of unit cubes needed to ﬁll it.

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 Shipping Boxes (per group) 1 Exit Ticket (per student)

Reusable • • • •

120 Centimeter cubes (per group) 1 Ruler with centimeters (per group) 12 Rulers (per class) 8 Metersticks or yardsticks (per class)

Preparation • • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Shipping Boxes for each group. When printing the Shipping Boxes, ensure the printer is set to Print Scale 100% (not Scale to Fit Page) so measurements will be correct. Cut out each box on the outline, and fold on the dotted lines. Use tape to secure the edges. You should now have open-top boxes to ﬁll with centimeter cubes. Assemble a cube, using rulers and tape, to represent 1 cubic foot. Create another cube, using the metersticks or yardsticks and tape. Use a wall as one side to make it more stable (see example below).

Consumable •

1 Roll of tape (per class)

•

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PROCEDURE AND FACILITATION POINTS Part I: Boxing Hats 1.

Read the following scenario to the class: The Jolly Elf Hat Factory just got a big order for elf hats at the North Pole, and they have hired you to pack shipping boxes with the elf hats! It is your job to ﬁt as many elf hats into each shipping box as you can. Each centimeter cube contains one elf hat. The boxes will have lids so the elfhat boxes cannot go over the top of the shipping box. Give each student a Student Journal. Give each group Shipping Box 1, a centimeter ruler, and centimeter cubes. Discuss the following question: a.

3. 4. 5.

Explain that students should record how many elf hats ﬁt the length, width, and height of Shipping Box 1 on their Student Journals. Allow students to pack the boxes and write their cube totals. After they have packed their boxes with cubes, students should measure the length, width, and height of the shipping box and the elf-hat boxes using the centimeter ruler. Students should record these measurements in their Student Journals. Discuss the following question: a.

11. 12.

FACILITATION TIP Project this scenario for students to view as you read aloud together. Be prepared to answer questions about the constraints. (Will the cm cubes take up space? How can there be elves that small?) FACILITATION TIP If possible, have the Shipping Boxes printed on card stock. Consider having adult volunteers or older students build the boxes ahead of time.

DOK-1 What are the dimensions of the elf-hat boxes that you measured? 1 cm × 1 cm × 1 cm

DOK-1 How many elf hats could you ﬁt into a shipping box with dimensions of 5 cm long, 4 cm wide, and 3 cm tall? 60 elf hats

Explain that the word for the amount of space objects or substances take up is volume. Explain that because the cubes ﬁt together side by side, we use cubic units to measure the space, or volume, inside an object like the shipping box. Discuss the following question: a.

9. 10.

To engage students, create a tiny elf hat that matches the Student Journal scenario; it must ﬁt in a 1 cm cube. If time allows, create a hat for the Exit Ticket (1 cubic inch).

Explain that this is called a cubic centimeter. Have students refer to the cubic FACILITATION TIP foot and cubic yard or meter that were built. Discuss with students how each of Some students may be interested to know these are called cubic units because their length, width, and height are each 1 how a cubic centimeter of water relates to a unit of measure. For this activity, students will be working with cubic centimeters. milliliter of water. a.

DOK-2 How can you pack the boxes so that you can ﬁt as many elf hats into Shipping Box 1 as possible? I can make neat rows of elf-hat boxes so the centimeter cubes are side by side.

FACILITATION TIP

DOK-1 What is the volume of Shipping Box 1? 60 cubic cm

Students should write the volume of Shipping Box 1 in their Student Journals. Give students Shipping Box 2. Discuss the following questions: a.

DOK-2 Compare box 1 and box 2. Which box do you think will hold more elf hats? Answers will vary. I think the second box will hold more elf hats because it is longer.

DOK-2 How will you ﬁnd the volume of this box? I will make neat rows of elf-hat boxes inside Shipping Box 2 until it is full.

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

Have students complete the information for Shipping Box 2 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 many elf-hat boxes could you ﬁt into Shipping Box 2? 48

DOK-1 What is the volume of Shipping Box 2? 48 cubic centimeters

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VOLUME

Volume Explore 1 — Cubic Units Part II: Missing Boxes 1.

6. 7.

Read the following scenario to the class: The Jolly Elf Hat Factory didn’t get their shipment of new boxes in yet, but they still need to figure out how many elf-hat boxes will fit into each shipping box when they do arrive. The factory knows how many elf-hat boxes will fit in the length, the width, and the height of each box. Tell students that even though they don’t have the Shipping Boxes, they can still use the centimeter cubes to build the box shape and determine the volume of the shipping box. Have students work on building the boxes using the information on their Student Journals and centimeter cubes. Students should complete the information on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How did you know how many centimeters the length of Shipping Box 3 was? Three elf-hat boxes will ﬁt in the length of the box. Since each elf-hat box is 1 centimeter, that means the length of the box is 3 centimeters.

DOK-1 What are the dimensions of the bottom, or base, of Shipping Box 4? It is 6 centimeters long by 5 centimeters wide.

After students have found the volume of Shipping Boxes 3 and 4, have them meet with another group and review their answers. If there are discrepancies with the answers, have them rebuild the boxes using the centimeter cubes and reach an agreement on the volume of the boxes. Students should complete the reﬂection question on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP During this Math Chat, ﬁnd time to list relevant real-world applications for calculating cubic volume. (Garden mulch, sea level, foundations made out of cinder block)

DOK-2 What conclusion can you draw about the volume of a container and the number of cubic units that fit into it? The volume of a box is equal to the number of cubic units that fit into it. • DOK-2 Why can’t you have any gaps or overlaps of centimeter cubes when finding the volume of an object? If there were gaps between centimeter cubes or overlapping cubes, the measurements wouldn’t be accurate. If there were gaps, there would be a greater number of centimeters, and if the cubes overlapped, there would be fewer centimeters. •

Post-Explore FACILITATION TIP

When previewing this Exit Ticket with students, have them read the units of the cube carefully. The Student Journal used centimeters and the Exit Ticket uses inches.

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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Volume Explore 2 — Discover Volume ACTIVITY PREPARATION Students determine the volume of a rectangular prism with whole-number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base.

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.

Preparation

Materials Printed • • •

• • •

1 Student Journal (per student) 1 Set of Building Bases (per group) 1 Exit Ticket (per student)

• •

Reusable • • •

120 Linking cubes (per group) 1 Resealable bag or small bin (per group) 1 Sheet protector (per group, optional)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Building Bases for each group. Laminate or place it in a sheet protector for future use. Place 120 linking cubes in a bag or bin for easy distribution to groups. For students who need more support in recalling information, please see our 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 POINTS Part I: Skyscraper Design FACILITATION TIP

Project this scenario and read it along with students. Provide them time to read it independently, then with a partner, and ﬁnally read it all together as a class. FACILITATION TIP

Only give students page one of the Student Journal to begin. Discuss Question 2a and Step 3 before distributing Student Journals and the Building Bases to groups.

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Read the following scenario to the class: You have been asked to design skyscrapers for a new college campus in your area. The college has given you the floor plan information. To begin, you will need to create two buildings (rectangular prisms) with the same volume. The length and width of each of the two buildings are given. You may use the floor plans on the Building Bases sheet to help lay out the buildings. Give each student a Student Journal. Give each group a set of Building Bases and linking cubes. Discuss the following question: DOK-2 How can you find the volume of each floor of the building? We can build the building using linking cubes. We know the length and width of each building, and the number of floors is the height of the building.

Tell students that another way they can find the volume of a rectangular prism such as a building is to first find the number of cubes that make up the base of the building. The base of a rectangular prism is the number of unit cubes it takes to form the bottom layer. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Have students use the linking cubes to build building 1’s base using the Building Bases. Discuss the following questions: a.

DOK-1 How many linking cubes are in building 1’s base? There are 12 linking cubes.

DOK-2 What do you notice about building 1’s length and width in relation to the number of linking cubes in its base? If we multiply the length by the width, we get the number of linking cubes in its base.

DOK-1 What is the equation you could use to ﬁnd the base of building 1? I could use 4 × 3 = 12.

DOK-1 What is the area of the base of building 2? It is 10 square units.

DOK-1 How did you ﬁnd the base? I multiplied the length of 5 units by the width of 2 units.

DOK-2 When you are ﬁnding the volume of an object, what else do you need to include? I need to know the height, or how many layers of cubes there will be. I need to know how many unit cubes make up the height.

DOK-1 What is the height of the ﬁrst ﬂoor of both buildings? It is 1 unit.

9. 10.

11.

12.

13.

Acceleration

FACILITATION TIP Encourage students to carefully build the buildings even if they can already calculate the volume. Creating the visual physical model will help them eﬃciently solve volume problems without cubes later in life.

Explain that besides actually building the base of a three-dimensional object, we can first find the area of the base of the object. The product of the length times the width of the object is called the area of the base. Just like finding the area of a rectangle, the area of the base is called units squared and is written as square units. Have students write the area of the base for building 1 (12 square units) and work together to find the area of the base of building 2 (10 square units). Discuss the following questions:

e. DOK-1 How many total units make up the first floor of building 1? The first floor is made up of 12 units.

Intervention

VOLUME

Home

DOK-1 What is the equation you used to ﬁnd the area of building 1? I used 12 × 1 = 12.

Have students find the volume of the first floor of building 2 and write the information on their Student Journals. Tell students that this is just the first floor of each building. Each new layer above the base will be a multiple of the base area. Students should list the multiples of each base area until they find a common multiple since they are trying to find the dimensions of both buildings that result in the same volume. Students may use the linking cubes to construct their buildings. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you find the volume of building 1 with four floors? I multiplied the base of 12 times the number of floors, which was four: 12 × 4 = 48 cubic units.

DOK-1 What expression could you use to ﬁnd the volume of a rectangular prism if you knew the area of the base of the prism? I could multiply the area of the base times the height.

Once the students have constructed or algebraically found heights that will produce the same volume, they should record the heights and write an equation for the volumes in their Student Journals. Show students how the process they are using can be written as a formula. The formula for ﬁnding the volume of a rectangular prism that they used is written as B × h, in which B is the area of the base and h is the height. After Part I, invite the class to a Math Chat to share their observations and learning.

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Volume Explore 2 — Discover Volume Math Chat DOK-2 How did you find the volume that would be the same for both buildings? The area of the base of the first prism is 12, so I counted by 12s: 12, 24, 36, 48, 60. The area of the base of the second prism is 10, so I counted by 10s: 10, 20, 30, 40, 50, 60. Each number I skip counted was another layer added to the height of the prisms. • DOK-2 How did you know what the height of each building was once you found the correct volume? The number of times I skip counted was the height. For the first prism, I skip counted five times, so the height was 5 units. For the second prism, I skip counted six times, so the height was 6 units. • DOK-2 How could you find another possible volume that both buildings could have? If you keep skip counting, you would find that a volume of 120 cubic units is possible (heights of 10 and 12). Any multiple of 60 cubic units would be a correct answer. • FACILITATION TIP During this Math Chat, find time to list relevant real-world applications for calculating cubic volume. (Garden mulch, sea level, foundations made out of cinder block)

Part II: Buildings in All Shapes FACILITATION TIP

Before giving students page 2 of the Student Journal, project this scenario and read it aloud with students. 2. FACILITATION TIP If you can, use the packing boxes from Explore 1 to show how rotating a prism doesn’t alter its volume.

FACILITATION TIP If this geometric formula is not already posted in the classroom, take time to explain, label, and post it. Use Picture Vocabulary and have students record the formula on their Student Journals.

3. 4. 5.

6. 7. 8.

Read the following scenario to the class: The college design board really liked what you did with the ﬁrst two buildings, and they have allowed you to use your creativity to make different building designs, as long as they have a speciﬁc volume. They would like you to come up with as many different building designs as possible. Tell students they will be given the volume and will have to build different rectangular prisms. Discuss the following questions: a.

DOK-2 If you turn a rectangular prism on its side, what happens to the dimensions and volume of the prism? The dimensions are the same if it is turned on its side. The dimensions stay the same; therefore, the volume is the same.

DOK-2 In Part I, we learned that we could take the area of the base and multiply it by the height to get the volume. Is there another formula that could be used to ﬁnd the volume of a rectangular prism? We can multiply length by width (which is the same as ﬁnding the area of the base) and multiply that by height.

Tell students that this formula for finding the volume of a rectangular prism is written as l × w × h, h, in which l is the length, w is the width, and h is the height. Explain that to find as many different building designs as possible, students will need to find various combinations of a building’s length, width, and height. Remind students that they need to make sure they do not repeat the dimensions. For example, the volume of 3 × 4 × 5 is the same as the volume of 5 × 3 × 4. If students seem to struggle with this concept, take a moment to have them build two buildings with these dimensions so they can see that the total number of unit cubes, or volume, stays the same. Monitor students as they build. Make sure they don’t use the same set of dimensions twice. When students have finished constructing all possible building combinations with the two volumes, have them complete the reflection questions. After Part II, invite the class to a Math Chat to share their observations and learning. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Math Chat

Intervention

Acceleration

VOLUME

Home

STEMscopes Tip

DOK-1 What are the areas of the bases when the rectangular prism has a volume of 36? Answers will include products of two of the three dimensions: 18, 12, 9, 4, etc. • DOK-2 How can there be two formulas for finding the volume of a rectangular prism? To find the area of the base of a rectangular prism, you have to multiply length by width. The formula for finding volume can be written as either B × h or l × w × h because B = l × w. • DOK-2 What did you notice about the relationship between the area of the base and the height of the skyscraper when you had two skyscrapers with the same volume? The smaller the area of the base was, the taller the tower was. The building with the bigger base area was not very tall. •

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.

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, clarify any Complete the Anchor Chart as a class. constraints for the dimensions of the other skyscraper. Consider that some students Have each student complete their Interactive Notebook. may create a base area of 1. Notes

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VOLUME

Volume Explore 3 — Volume of Rectangular Prisms ACTIVITY PREPARATION Students use concrete objects and algorithms to apply the formula for the volume of a rectangular prism, including the special form for a cube.

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.8 Look for and express regularity in repeated reasoning.

Preparation

Materials Printed • • •

• • •

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

•

Reusable • •

70 linking cubes (per group) 1 Resealable bag or small bin (per group)

• •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Place 70 linking cubes in a resealable bag or small bin for easy distribution to groups. Print the Station Signs. Cut them apart, and place them at various locations around the room. You may want to print two copies to make six stations rather than three. Laminate them for future use, if desired. For students who need more support in recalling information, please see our 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 POINTS Part I: Small Pet Crates FACILITATION TIP

Project the scenario and conduct a structured read aloud with students. Guide them to locate the essential math phrases, words, and values. 2.

3. 360

Read the following scenario to the class: MeWOW’s Pet Store is setting up a new display for their small pet crates. They would like to put the crates that have a volume of at least 10 cubic feet but have a base area of 7 square feet or less on the top shelf of the display. They have three crates that are similar, but they aren’t sure which crates would fit these dimensions. They have asked you to help them figure out which pet crates they can put on the top shelf of their display. Review finding volume of a rectangular prism. Discuss the following questions: a.

DOK-1 How can you ﬁnd the volume of a rectangular prism, such as a pet crate? We can make a model; we can multiply the area of the base times the height; and we can multiply the length, width, and height of the prism.

DOK-1 How do you write the volume of a rectangular prism? Units cubed or cubic units

DOK-1 How can you ﬁnd the area of the base of a rectangular prism like a pet crate? We can multiply the length by the width.

DOK-1 How do you write the area of the base? Square units or units squared

5. 6.

10.

Engage

Explore

Explain

Elaborate

Evaluate

Explain that students should construct a model of the pet crates using the linking cubes. Then, students should write the equations of the base area of the crates and use the two volume formulas to write equations for the volumes of the crates. Students will select the small pet crate or crates that meet the criteria and explain why. Give each student a Student Journal. Give each group 70 linking cubes in a resealable bag. Assign students either crate A, B, or C to begin. Have students take their linking cubes and move to their assigned stations. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you ﬁnd the area of the base for crate A? I multiplied the length of three by the width of two. The area of the base is 6 square feet.

DOK-1 How did you determine the volume of crate B? I multiplied the area of the base, which was eight, by the height, which was two. Eight times two is 16 cubic feet.

DOK-2 What did you notice about the formulas to ﬁnd volume? They both result in the same product.

When students are finished with the first crate, have them move through the other two stations and find the dimensions of the other crates. Remind them to take their linking cubes with them. When students are finished finding the dimensions of all three crates and have answered the question at the end of Part I, have them meet with another group and review their answers. If there are discrepancies, have them rework the problems and come to an agreement. After Part I, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

VOLUME

Home

FACILITATION TIP Consider giving students only one page of the Student Journal at a time as needed. Color code page 1, 2, and 3. FACILITATION TIP To simplify use of space and classroom movement, have students complete each station at their table groups. The linking cubes can stay a the table. As students complete a crate, they can have one student go get the next Station Sign and then build the next one.

FACILITATION TIP After students have had enough time to complete the three crates, gather the class together to review answers and clear up discrepancies. Groups that ﬁnish Crates A, B, and C early can design another crate.

Math Chat DOK-1 How did you figure out which small pet crate or crates would fit on the top shelf of the display? Crates A and C have volumes of at least 10 cubic feet and bases less than 7 square feet. Crate B’s base is too big. • DOK-2 Why does the formula V = B × h also work to find the volume of a rectangular prism? The area of the base, B, is equal to length times width. Just replace l × w in the volume formula with B. • DOK-3 When might you need to use the formula B × h? h You might know the area of the base of a rectangular prism but not the specific length and width. As long as you know the area of the base and the height, you can figure out the volume of a rectangular prism. •

Part II: Cat Toy Display 1.

Read the following scenario to the class: MeWOW’s has an area in their store to place cube-shaped bins for cat toys. Because their space is limited, they must make sure the bin is big enough to hold all the cat toys and tall enough so that customers can easily look through the sides of the bin to see the toys. The bin must have a volume of at least 25 cubic feet and a height of 3–5 feet. Your job is to ﬁnd which bin or bins will work in MeWOW’s Pet Store. Review the attributes of a cube. Discuss the following questions: a.

DOK-1 What makes a cube special? It is a rectangular prism with all sides the same length.

DOK-1 What is special about all the faces of a cube? All the faces of a cube are squares.

DOK-1 What is the formula for the area of a square? A = s × s

FACILITATION TIP Print and project the scenario and read it aloud along with students. Pause for them to record any relevant values or constraints.

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Volume Explore 3 — Volume of Rectangular Prisms 3. 4.

5. 6. 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.

Tell students that each linking cube represents 1 cubic foot. It is 1 foot wide, 1 foot long, and 1 foot tall. Students should construct a model of the cat toy bins using the linking cubes. Then, students should write the equations of the base area of the bins and use the two volume formulas to write equations for the volumes of the bins. Students will select which bin or bins meet the criteria and explain why. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 Why do you only need to know one side length to ﬁnd the volume and base of these bins? The bins are cube shaped. That means all the sides are the same length.

DOK-1 How would you find the volume of a cube-shaped bin that has a side that is five feet? I would multiply five by five by five.

DOK-2 What did you notice about the formulas to ﬁnd volume? The products are the same.

When students are ﬁnished ﬁnding the dimensions of all three bins and have answered the question at the end of Part II, have them meet with another group and review their answers. If there are discrepancies, have them rework the problems and come to an agreement. After Part II, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

DOK-2 Why can you use the formula V = s × s × s to ﬁnd the volume of a cube? Because all the sides are the same length. Length = s, width = s, and height = s. DOK-2 Why does the formula V = B × h also work to ﬁnd the volume of a cube? The area of the base, B, is equal to length times width, or side length times side length. Just replace s × s in the volume formula with B.

Part III: Cat Food Display FACILITATION TIP

Depending on your students, consider having them work on Part III individually or with partners at their desks. 2.

362

Read the following scenario to the class: MeWOW’s Pet Store’s specialty is their variety of cat food. The cat food containers come in all shapes and sizes. While customers love the different cat foods, it is diﬃcult for MeWOW’s to determine how much shelf space the containers will take. Unfortunately, they don’t always get all the dimensions from the cat food companies. MeWOW’s needs your help determining dimensions for the cat food containers. Discuss the following questions: a.

DOK-1 What are the formulas you can use to ﬁnd volume? B × h or l×w×h

DOK-2 If you know the volume and the area of the base of a rectangular prism, how can you ﬁnd the height? We can multiply different numbers for the height with the area of the base until we get the correct volume. Or we can divide the volume by the area of the base to get the height.

DOK-2 If you know the volume and the height of a rectangular prism, how can you ﬁnd the area of the base? We can multiply different numbers for the area of the base with the height until we get the correct volume. Or we can divide the volume by the height to get the area of the base.

DOK-2 If you know the volume of a cube but don’t know any of the dimensions, what can you do? Since the sides of a cube are all the same, we can multiply a number by itself three times to see if we get the correct volume. If not, we can keep choosing numbers and try again until we get the correct volume.

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

Have students attempt to work on Part III mathematically rather than by making models. (Allow students who need extra support to build each cat food container with linking cubes. Students will need an additional 55 linking cubes to model the Fish Stew Cat Food container.) Students should use the space to the right of the dimensions to show their work. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How did you determine the height of the ﬁrst cat food container? I found the area of the base of the container by multiplying length by width. The product is six. Since the volume of the container is 6 cubic feet, the height has to be 1 foot because 1 × 6 = 6.

DOK-1 How did you determine the side dimensions of the Fish Stew Cat Food container? I started with the number two and multiplied it by itself three times. The product was eight, which was a lot less than the volume of the container. I tried multiplying four by four by four. The product was 64, which was still less than the volume of the container. I finally multiplied five by five by five, and that equaled 125, which is the volume of the cat food container.

When students are finished finding the missing dimensions of all three cat food containers, have them complete the reflection questions. After Part III, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 What can you do if you need to ﬁnd missing dimensions of a rectangular prism? If you know the volume, you can divide it by the dimensions you know to get the unknown dimensions. You can guess and check until you get the correct volume. • DOK-2 When might it be useful to use both volume formulas on the same problem? You can ﬁnd the volume using one of the formulas and then check your answer with the other formula. •

Intervention

Acceleration

VOLUME

Home

FACILITATION TIP Struggling students may need times tables or calculators to solve Part III mathematically. Even so, students should show their thinking.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP When you preview this Exit Ticket with students, make time to answer questions. Some students may need clariﬁcation about the shape of the image as it relates to rectangular prisms.

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Volume 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

Cubic Units 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

Discover Volume 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

Volume of Rectangular Prisms 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

364

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

VOLUME

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Career Connections

Polly’s Pie Emporium

Fireﬁghter

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

You Have 4 Seconds

Problem Solving with Volume

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

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Volume 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

366

 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

VOLUME

Home

What prompts will be used?

What does mastery look like?

I can use a cube with a side length of one unit, called a unit cube, to measure volume.

I can describe the volume of a ﬁgure in terms of cubic units.

I can investigate the volume of right rectangular prisms by packing them with unit cubes to solve problems.

I can discover and explain how the volume of a rectangular prism can be found by multiplying the area of the base times the height to solve problems.

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SCOPE 1

Graph in the First Quadrant Scope Introduction SCOPE SUMMARY

Student Expectations

5.PAR.6.2 Represent problems by plotting ordered pairs and explain coordinate values of points in the ﬁrst quadrant of the coordinate plane.

Students first become acquainted with the coordinate plane in fifth grade. They identify the origin and axes in the coordinate system, and they plot and label ordered pairs in the first quadrant. Students connect their understanding of the number line to the x- and y-axes. Once they learn to navigate along the coordinate plane, they apply this knowledge by representing mathematical and real-world problems involving plotted points, and they interpret their values within the context of the situation. Instruction includes the connection between two-column tables and coordinates on a coordinate plane. In fifth grade, coordinate planes and corresponding ordered pairs should only include whole numbers.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

By third grade, students are expanding their knowledge of numerical patterns to multiplication and representing and solving problems related to data by using frequency tables, line plots, pictographs, and bar graphs. In fourth grade, students represent problems by using an inputoutput table and numerical expressions to generate a number pattern that follows a given rule. Fourth graders use tables and line plots to solve real-world problems in relation to collected data. It is not until ﬁfth grade that students encounter the coordinate plane.

In sixth grade, students extend their understanding of the coordinate plane to plot, interpret, locate, and graph rational-number ordered pairs in all four quadrants and on both axes. Sixth-grade students use the signs of integers within an ordered pair to determine which quadrant a point is located in, and they recognize that when two ordered pairs differ only by signs, the locations of the points are related by a reﬂection across an axis.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

choose the way data is represented on the input-output table they agree with the most.

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: •

create perfect squares in the ﬁrst quadrant of a coordinate plane.

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

368

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

The Coordinate Plane In this exploration, students will describe key attributes of the coordinate plane, including axes and origin. Students will: •

learn about ordered pairs.

•

describe the process for graphing ordered pairs.

•

graph ordered pairs in the ﬁrst quadrant.

Explore 2

Explore 1

EXPLORE ACTIVITIES Plot Shapes In this exploration, students will plot shapes on a coordinate plane in the ﬁrst quadrant. Students will: •

decide how to arrange the furniture in a living room.

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

GRAPH IN THE FIRST QUADRANT

Home

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. Graph Real-World Problems In this exploration, students will generate and represent ordered pairs on a coordinate plane and analyze the graph to solve real-world problems. Students will: •

collect and document data on a coordinate plane.

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

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GRAPH IN THE FIRST QUADRANT

Graph in the First Quadrant Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students choose the way data is represented on the input-output table they agree with the most. This activity is intended to assess mastery of the following standard(s): 4.PAR.3.2 Use input-output rules, tables, and charts to represent and describe patterns, ﬁnd relationships, and solve problems.

Materials Printed • •

GRAPH IN THE FIRST QUADRANT

Home

1 Student Handout (per group or student) 1 Set of Choice Signs (per class)

Reusable •

1 Projector or document camera (per class)

Preparation • • • •

Plan to have students work in groups of 3 or 4 to complete this activity. Prepare to project the Student Handout for the class. Print a Student Handout for each group or each student. Print a set of Choice Signs, and place each sign at a different location in the classroom.

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

Project the Student Handout for the class, and give a printed Student Handout to each group or student. Instruct students to think about how data would be represented in an inputoutput table. Tell students they need to decide whose input-output table is correct–Raj’s or Tariq’s. Have students stand by the sign that they agree with the most. Inform students that they should be ready to justify their choices. Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. a.

I think Raj’s input-output table is correct. The number of bags of apples has to be multiplied by the cost of $5 because each bag costs $5. As the number of bags increases, each bag still has to cost $5.

I think Tariq’s input-output table is correct. Five dollars has to be added to the number of bags of apples because bags of apples cost $5.

FACILITATION TIP Student experience with input-output tables may be very limited. Reassure them that it is understandable if they can only guess about their choice. After this scope, they should feel much more conﬁdent.

FACILITATION TIP Consider allowing students some quiet time to make observations about the table, then chat with a partner, and then vote for their choice from their seats.

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

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GRAPH IN THE FIRST QUADRANT

Graph in the First Quadrant Hook – Perfect Square ACTIVITY PREPARATION Students create perfect squares in the ﬁrst quadrant of a coordinate plane. They accomplish this by plotting 3 given points, determining what the fourth point should be, marking the fourth point, and connecting the points to construct the square.

Materials

Preparation

Printed •

•

1 Coordinate Plane (per pair)

Part II

Reusable • • • •

Plan to show the Phenomena Video.

• • •

1 Phenomena Video (per class) 1 Projector (per class) 1 Set of colored pencils (per pair) 1 Ruler (per pair)

Plan to have students work in pairs to complete this activity. Print the Coordinate Plane for each pair of students. Gather enough sets of colored pencils and rulers for each pair of students to have one of each.

PROCEDURE AND FACILITATION POINTS Part I: Pre-Explore 1. FACILITATION TIP Students can share their ideas ﬁrst in small groups and then with the whole class. FACILITATION TIP

Explain that the girls wanted their shapes to be drawn accurately (e.g., a square to be drawn with four equal straight sides and four right angles). 4. FACILITATION TIP Remind students of the directionality of horizontal and vertical. Use physical responses and have students draw horizontal lines and vertical lines in the air with their arms, ﬁngers, eyes, or pencils.

DOK-1 When reading a graph, what do we call the horizontal axis? The x-axis

DOK-1 When reading a graph, what do we call the vertical axis? The y-axis

DOK-2 When writing or reading coordinates for a graph in the ﬁrst quadrant, how do we plot a point? We look at the ﬁrst coordinate (the x-coordinate) and count over the correct number of spaces horizontally. Then, we look at the second coordinate (the y-coordinate) and count up the correct number of spots vertically.

Move on to complete the Explore activities.

Part II: Post-Explore 1. 2. 372

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: © Accelerate Learning Inc. - All Rights Reserved

3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 When reading a graph, what do we call the horizontal axis? The x-axis.

DOK-1 When reading a graph, what do we call the vertical axis? The y-axis.

Give a Coordinate Plane, a set of colored pencils, and ruler to each pair of students. Tell students they will utilize their knowledge of coordinate planes and graphing to construct a perfect square in the ﬁrst quadrant. They should accomplish this by carrying out the following steps: a.

Plotting the following points: (1, 2) (1, 8) (7, 2)

Figuring out and plotting the ﬁnal point to complete the square (7, 8)

Intervention

Acceleration

FACILITATION TIP Although students may have had previous experience with graphing on a coordinate plane, provide careful explicit review of these vocabulary words and concepts: coordinates, x and y coordinates, origin, and point.

GRAPH IN THE FIRST QUADRANT

Home

FACILITATION TIP Depending on your students’ experience, they may not know about “ﬁrst quadrant.” FACILITATION TIP

Write or display these steps for students to Using the ruler to carefully connect the points to form the perfect square follow.

Decorating the square with their choice of colored pencils

e. NOTE: If students ﬁnish early, they may construct other shapes on the coordinate plane. They should record the coordinates for the vertices of each shape. 5.

7. 8.

Give students about 5–10 minutes to construct/decorate their perfect squares. Walk around during this time, and observe groups. Offer assistance, and ask guiding questions to help groups that might be struggling. You may want to ask, “What do we know about the length of each side of a square?” Group two pairs together, and have them show the squares they plotted and decorated. They should point out what they noticed while constructing their squares. Allow a few students to show their perfect square art projects to the class. Discuss the following questions: a.

FACILITATION TIP Remind students to use relevant vocabulary words as they share their graphs. FACILITATION TIP

Rather than allowing just a few students to share, consider holding a gallery walk, DOK-3 How did you figure out the final coordinate pair to complete where students walk around and look at all the square? Answers may vary slightly regarding the method students the perfect-square art projects. used to figure out the coordinates. I know that all squares have sides that are the same length, so I counted how many squares were in each of the other 3 sides and found it was always a length of 6 squares. I counted over 6 squares horizontally to the right from coordinate (1, 8) and I counted up 6 squares vertically from coordinate (7, 2). Both times I ended on coordinate (7, 8). DOK-2 What was the most challenging part of this activity for you? Answers will vary. Plotting the first point of the square was most difficult for me because at first I was confused about whether the first coordinate meant I should count horizontally or vertically. Notes

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Graph in the First Quadrant Explore 1 – The Coordinate Plane ACTIVITY PREPARATION Students describe key attributes of the coordinate plane, including axes and origin; learn about ordered pairs; describe the process for graphing ordered pairs; and graph ordered pairs in the ﬁrst quadrant.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

Materials

Preparation

Printed • • • •

• •

1 Student Journal (per student) 1 Set of Directional and Ordered Pair Cards (per class) 1 Set of Ordered Pair Cards (per group) 1 Exit Ticket (per student)

• •

Reusable •

• •

•

1 Privacy board (for example, ﬁle folder, cardboard carrel, large hardcover book; per student) 1 Resealable bag (per group) 1 Projector or document camera (optional)

•

Consumable • •

Masking tape or chalk 1 Colored pencil (per student, optional)

•

Plan to divide the class into 2 groups to complete the activity in Part I. Plan to have students work in groups of 3 or 4 to complete the activity in Part II. Print a Student Journal and an Exit Ticket for each student. Print a set of Directional and Ordered Pair Cards for Part I, on card stock for durability, for the class. Cut the cards apart, and put them in two separate piles. Half the class will get Directional Cards, and half will get Ordered Pair Cards. Print a set of Ordered Pair Cards for Part II, on card stock for durability, for each group. Cut the cards apart, and place them in a resealable bag. Make a giant coordinate grid outside, in the gym, in the classroom, or somewhere else. A suggested size would be 10 × 10. Make sure it’s large enough for several students to stand on different points at the same time. Put an x and a y at the end of the appropriate axes. Label the origin as “Dock Origin.” For students who need more support in recalling information, please see our Grid Paper and Coordinate Plane 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. (XY Coordinate Board)

PROCEDURE AND FACILITATION POINTS 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.

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Part I: Plotting Points 1.

First, have students look at the coordinate plane you made. a.

DOK-1 What do you notice? It has a lot of little squares. There are vertical and horizontal lines that cross over each other. Each line is labeled. One is labeled x, and one is labeled y.

Explain that this is called a “coordinate plane.” A coordinate plane is a two-dimensional surface that has two intersecting, perpendicular number lines. The labeled lines are the x-axis -axis and y-axis. y

Read the following scenario to the class: We are going to visit the ocean! Many ships get lost at sea, but we have the coast guard to help ﬁnd them. The real coast guard ﬁnds lost boats by using longitude, latitude, and coordinates. When you are © Accelerate Learning Inc. - All Rights Reserved

3. 4.

5. 6.

7. 8. 9. 10.

11. 12. 13. 14. 15. 16. 17. 18.

19. 20. 21.

Engage

Explore

Explain

Elaborate

Evaluate

describing the location of something, you can use cardinal directions, such as north, south, east, and west, to help others know where it is. Some of you will be the ships that are going to get lost, and some will be the coast guard who ﬁnds them. Now, divide the class into two groups: the ships and the coast guard. Explain to the ships that they are going to be given a set of directions to follow. Everyone starts at the same dock (the origin). Explain that the origin on a coordinate plane is the point at which the perpendicular axis lines intersect. The word origin means “beginning,” so that’s where they will begin! Show students where the origin (dock) is on the class’s coordinate plane. Explain to the other half of the students that they are the coast guard and will have to ﬁnd the lost ships. The pair of numbers on their cards must stay together and must stay in the exact order. Those numbers will tell the location of a ship that needs to be rescued. This pair of numbers is called an “ordered pair.” Distribute the Directional Cards to the students acting as ships. Distribute the Ordered Pair Cards to the students acting as the coast guard. All ships will need to line up in a line behind the dock (origin). One at a time, release them to follow the directions on their cards. Discuss what is happening with the coast guard students. a.

DOK-1 What do you notice about each ship that leaves the dock? Everyone is going to the right ﬁrst.

DOK-1 What are they all doing next? They are going up from where they stopped walking.

Once all the ships have found their points, explain that they are to stay where they are and are not permitted to move yet. Have the coast guard students line up behind the dock (origin). Show students how the ordered pairs on their cards show them where to find the distressed ships. Explain that the first number shows how far across to travel. It is called the x-coordinate -coordinate because it shows where to go on the x-axis. Explain that the second number tells how far up to travel. It is called the yy-coordinate -coordinate because it shows where to go on the y-axis. y Once the coast guard students find their ships, have them compare cards and decide if they are in the correct locations. Allow students to share their reasoning for why they found the correct places. Give a Student Journal to each student. Have students leave the coordinate plane ocean and fill out Part I of their Student Journals. Students will need 3 ordered pairs from the activity to complete. Students can swap ordered pairs with each other, or ordered pairs can be projected for the class. Check each pair in the same manner as above, asking what came first, second, etc. If time allows, redistribute cards so students can do this activity again and switch roles. Discuss the following questions: a.

DOK-1 How did the ordered pairs help you ﬁnd the lost ships? I could ﬁnd the exact locations of the lost ships using the ordered pairs.

DOK-2 What did you notice about the x-axis -axis and yy-axis -axis as you traveled to your destination? Answers may vary. I noticed that the x-axis and y-axis looked like a number line. I noticed that each axis counted by ones.

DOK-1 Why do we need to start from the origin? This is where the x-axis and y-axis intersect. It is the location we start from when moving right on the x-axis and vertically on the y-axis.

Intervention

Acceleration

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FACILITATION TIP Before starting this simulation, have students locate various parts of the coordinate plane. For example, ask “Who can hop 3 times on the origin? Who can tiptoe along the x-axis?” FACILITATION TIP Write this information on the board for students to reference. Write (x, y) with an arrow pointing right above the x and an arrow pointing above the y. Be sure to discuss the exception of zero. If zero is the x-coordinate, you don’t travel forward at all, and if zero is the y-coordinate, you don’t travel up at all.

FACILITATION TIP Ask students to consider where points are located when one of the coordinates is zero. (They are located directly on the x- or y-axis.)

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Graph in the First Quadrant Explore 1 – The Coordinate Plane d.

e. DOK-2 Is it possible to switch the coordinate pair numbers around and still get the same location? Why or why not? It is possible only if the coordinate pair has the same coordinate numbers, such as (4, 4). If the x- or y-coordinate numbers were different, the location would change on the coordinate plane.

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.

Part II: Missing Ships 1. 2. 3.

4. 5. FACILITATION TIP

If there is a discrepancy, have the students discuss how each of them located the point(s) and assist as needed.

8. FACILITATION TIP In addition to the Math Chat questions, provide some relevant real-world examples of uses for coordinate planes.

DOK-1 How did you know which coordinate to plot ﬁrst? I knew the ﬁrst coordinate number was a location on the x-axis. This number told me how far right to move from the origin on the x-axis.

Place students in groups of three or four. Have students choose who will go first, second, third, etc. Give each student a privacy board. Have them set up the boards around their Student Journals. Read the following scenario to the class: You have just received word from coast guard dispatch that some more ships have been reported missing! You have been assigned the task of creating coordinate grid maps that show where all the missing ships are located. Your job will be to plot the coordinates on the grid so the coast guard can quickly find the missing ships. Students will take turns drawing an Ordered Pair Card and reading it aloud. All students will plot the coordinates on Part II of their Student Journals. Have students write the ordered pair beside the plotted point on the coordinate plane. Invite students to compare their coordinate grids when all the cards have been drawn to make sure they have plotted all the points correctly. If desired, students can then take a colored pencil and draw the most efficient route the coast guard could take to find all the missing ships if the coast guard was starting from the origin. (Note: Students do not have to agree on the most efficient route, but the route they choose must be logical.) After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

•

• •

•

DOK-2 What is the purpose of ordered pairs? Ordered pairs allow you to locate points on coordinate planes. They can show relationships between numbers. DOK-1 What process did you use to graph ordered pairs? I looked at the first coordinate number, which showed me where to go on the x-axis. The second coordinate number showed me where to go on the y-axis. I placed my point where the x and y lines intersected. DOK-2 How can your prior knowledge of number lines help you navigate a coordinate plane? The x-axis and y-axis resemble number lines, so if I know what my number lines are counting by, that will help me travel across each axis to graph my ordered pairs. DOK-1 What would happen if the xx-coordinate -coordinate were zero? The x-coordinate would be on the origin, so the points would be plotted on the y-axis. DOK-2 What would happen if the coordinates were reversed? If the coordinates were not the same numbers, the reversed coordinates would be a reflection of the original coordinates; they would be flipped. They would be in a different location. DOK-3 Where else might coordinates be used? They might be used for finding the location of anything, making a drawing, making a map, designing a park, choosing locations for buildings in a town, etc.

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FACILITATION TIP

When previewing this Exit Ticket, consider requiring students to label the points that they graph themselves.

2. 3.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Graph in the First Quadrant Explore 2 – Plot Shapes ACTIVITY PREPARATION Students plot shapes on a coordinate plane in the ﬁrst quadrant.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

•

1 Student Journal (per student) 1 Blueprint (per pair) 1 Set of Furniture Shapes (per pair) 1 Exit Ticket (per student)

• • •

Reusable • •

1 Pair of scissors (per pair) 3 Markers (per student)

•

Plan to have students work in pairs to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a Blueprint and a set of Furniture Shapes, on card stock for durability, for each pair. For students who need more support in recalling information, please see our Grid Paper and Coordinate Plane 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. (XY Coordinate Board)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP Model for students how to use a straight edge to guide their pencils to the correct point. Take time to ensure that students are plotting points at the intersections of the lines. Reassure students that they may make errors even as they focus closely. Encourage students to lightly record points at ﬁrst and then double check before moving on to the next one. A lighter pencil mark is easier to ﬁx.

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2. 3. 4.

Read the following scenario to the class: Michaela is deciding how to arrange the furniture in her living room. She decides to use graphing paper to create a blueprint of the room. She then cuts out shapes to represent the furniture in her room. This way she can experiment with different layouts without having to actually move the furniture. With your partner, cut out the shapes, and help Michaela ﬁnd an arrangement for her furniture. Give a Student Journal to each student. Give a Blueprint and a set of Furniture Shapes to each pair. Invite students to discuss the following with their partners before sharing with the class: a.

DOK-1 How can Michaela use a grid to help her determine the arrangements of her furniture? If she creates a grid or coordinate plane out of her living room space, Michaela can precisely plot the position of her furniture.

b. DOK-1 How can ordered pairs relate to the furniture position? These can tell her exactly where she can position certain furniture items as she creates an x- and y-axis for her living room space. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

c. DOK-2 What are some things Michaela needs to take into consideration as she is plotting her furniture position? She needs to be careful about the order of the coordinate pairs. The ﬁrst coordinate indicates the position on the x-axis and is always placed ﬁrst; the second coordinate indicates the position on the y-axis and is always placed second. 5.

6. 7. 8.

Have students work with their partners to cut out the shapes, use the coordinates on their Student Journals to place them on the Blueprint, and then record the furniture corner coordinates. As students collaborate, walk around to monitor student understanding. Have students complete the activity on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-2 How did the given vertices help you determine the missing vertex for the shapes? We plotted the given points and then used what we knew about how the shape was supposed to look to plot the missing point. Then, we could determine the x- and y-coordinates for this point. • DOK-2 How would your Blueprint change if the given points had their x- and y-coordinates switched? Answers should include something about how the location for the furniture would change. •

Intervention

Acceleration

FACILITATION TIP If time and supplies are limited, consider having students plot and label the furniture shapes rather than cut and glue. (Glued pieces would be very diﬃcult to ﬁx is errors are made).

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FACILITATION TIP Provide access to rulers so that students can connect vertices using the straight edges.

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 with Complete the Anchor Chart as a class. students, encourage them to lightly cross out each ordered pair as they plot them. Have each student complete their Interactive Notebook.

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Graph in the First Quadrant Explore 3 – Graph Real-World Problems ACTIVITY PREPARATION Students generate and represent ordered pairs on a coordinate plane and analyze the graph to solve real-world problems.

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 Coordinate Plane Anchor Chart (per class) 1 Set of Business Scenario Cards (per class) 1 Who Marked the Spot Card (per station) 1 Exit Ticket (per student)

Reusable • •

• • • • • •

2 Sheet protectors (per station) 2 Dry-erase markers (per station)

•

Plan to divide the class into 5 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print the Coordinate Plane Anchor Chart, on card stock for durability, and display it at the front of the classroom. Print a Who Marked the Spot Card, on card stock for durability, for each station. Place the cards inside sheet protectors so they can be written on. Print a set of Business Scenario Cards, on card stock for durability, and place them inside sheet protectors so the cards can be written on. Place the Business Scenario Cards around the room as station cards, with 2 dry-erase markers and a Who Marked the Spot Card. For students who need more support in recalling information, please see our Grid Paper and Coordinate Plane 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. (XY Coordinate Board)

PROCEDURE AND FACILITATION POINTS 1.

2. 3. 4.

Read the following scenario to the class: You and your business partners own a company that sells shirts. As with any business, there are many tasks that need to be completed for the business to run smoothly and make money. Today, you and your business partners will be collecting and documenting data on a coordinate plane. It is important that your group works together to help your company run a successful business. Give a Student Journal to each student. Display the Coordinate Plane Anchor Chart to review important vocabulary from past Explore activities. Invite students to discuss the following questions with their groups before sharing with the class: a.

FACILITATION TIP A coordinate plane is used to plot and locate speciﬁc points in a two-dimensional space. 380

DOK-1 What does the picture on the anchor chart represent? A coordinate plane (Write this label at the top of the Coordinate Plane Anchor Chart.)

b. DOK-1 What is a coordinate plane? A coordinate plane is a type of graph that has two intersecting perpendicular number lines. The horizontal line is known as the x-axis, and the vertical line is the y-axis. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

c. DOK-2 How do you think a coordinate plane can help us document our business data? I think a coordinate plane can help us document our business data by showing a relationship between two variables, such as how much money we can earn by selling each shirt. d. DOK-1 What does the vertical number line represent? It represents the y-axis. (Write the label for the y-axis on the Coordinate Plane Anchor Chart.)

Intervention

Acceleration

FACILITATION TIP This is a new, abstract, yet important concept. Students may not be able to describe this relationship until after they represent the business scenarios. Revisit this point as needed later in the activity.

e. DOK-1 What does the horizontal number line represent? It represents the x-axis. (Write the label for the x-axis on the Coordinate Plane Anchor Chart.) f. DOK-1 What do the numbers (3, 4) represent when using a coordinate plane? They represent an ordered pair. (Write the label “Ordered pair” underneath the numbers on the Coordinate Plane Anchor Chart.) g. DOK-1 What is an ordered pair? An ordered pair is two numbers that go together to show how you are moving on a coordinate plane to represent your data. h. DOK-1 What does the ﬁrst number represent in an ordered pair? The ﬁrst number represents the x-coordinate and how we will be moving on the x-axis. i. DOK-1 What does the second number represent in an ordered pair? The second number represents the y-coordinate and how we will be moving on the y-axis. j. DOK-1 What does the point where the x-axis and y-axis meet represent? It represents the origin and the point (0, 0). (Write the label “Origin” in the speech bubble on the Coordinate Plane Anchor Chart.)

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k. DOK-1 What is the origin? The origin is the point on the coordinate plane where the two perpendicular number lines intersect. Origin means “beginning,” so this is where we begin when we get ready to graph our ordered pairs. l. DOK-1 How would we plot the ordered pair (3, 4) on our coordinate plane? First, we need to see what our number lines are counting by. This one is counting by 1s, so we would begin at the origin, move right on the x-axis 3 lines, and then move up on the y-axis 4 lines. Then, we would draw our point on the spot where we ended. 5. 6.

8. 9. 10.

Explain to the class that they will be using their knowledge of coordinate planes to represent their business scenarios. They will read each Business Scenario Card as a group and then use the coordinate plane and dry-erase markers to represent the data from each scenario. Explain to students that they will need to rotate the job of placing ordered pairs on their coordinate plane. After each student has placed a point on the coordinate plane, they must write the ordered pair and their name on the Who Marked the Spot card. After the group has agreed that the points are representing the ordered pairs correctly, they will then record their data on their Student Journals. Place each group at a station. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

FACILITATION TIP To support student success, consider guiding the whole class through the ﬁrst scenario together: T-Shirt Titan. Model how to correctly write an ordered pair (on page 1) with parentheses and commas, and model again how to carefully plot points (on the corresponding business scenario card).

DOK-2 After reading the scenario, what do you think the x-coordinate represents? Answers will vary based on the Business Scenario Card. The x-coordinate represents the number of shirts and materials/each hour/each full box/each trip to the supplier.

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Graph in the First Quadrant Explore 3 – Graph Real-World Problems b. DOK-2 After reading the scenario, what do you think the y-coordinate represents? Answers will vary based on the Business Scenario Card. The y-coordinate represents the money earned/money left in budget/ shirts made/total shirts in the boxes/total miles traveled. c. DOK-2 What information in the scenario can help you ﬁgure out the relationship for the ordered pairs that are being represented on the coordinate plane? Answers may vary based on the scenario. The information that will help me ﬁgure out the ordered pairs is where it talks about the relationship between my numbers. The relationship for these scenarios can have me adding, subtracting, or multiplying for each ordered pair.

FACILITATION TIP Ask students to consider why scaled intervals vary from graph to graph. (It depends on the values of the data.) Let them know that it is okay for each axis to use a different scaled interval, as long as all values are shown. Relate this to a ruler. (When marking a measurement, you can't just skip ahead to the desired length; you need to pass through each increment leading up to that distance.) FACILITATION TIP Alternatively, most of this Explore activity could be completed at student table groups in partners or small groups rather than rotating stations.

d. DOK-1 Is each number line on the coordinate plane counting by the same amount? No, some number lines are counting by 1s, 2s, 5s, or 10s. e. DOK-1 What should you do if your ordered pair doesn’t fall exactly on a line? I should use my best judgment to place the ordered pair near the number it belongs to. 11.

12. 13.

Math Chat •

• •

•

FACILITATION TIP When previewing this Exit Ticket with students, consider helping struggling students label the table (x-axis is jackets and y-axis is proﬁt). Additionally, provide multiplication charts or tables if students don't have their 12s memorized.

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Before groups rotate, check each group’s Who Marked the Spot Card to ensure that each student participated in placing ordered pairs on the coordinate plane. Once each group has been quickly checked, make sure students clean up each station and erase their points and ordered pairs from their Business Scenario Cards and Who Marked the Spot Cards before groups are allowed to rotate. Once the station is cleaned up, allow students to rotate from station to station after an allotted amount of time. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-1 What process did you use to create your ordered pairs? I first figured out each x-coordinate based on the scenario. Then, I applied the rule or relationship to the x-coordinate value, which then gave me the number for the y-coordinate. DOK-2 What is the purpose of ordered pairs? Ordered pairs allow you to locate points on coordinate planes. They can show a relationship between numbers. DOK-2 Why is the order of numbers in an ordered pair important? The order of numbers in an ordered pair is important because if you were to switch the numbers, your point would be in a different location, therefore representing a different value. DOK-1 What process did you use to graph the ordered pairs? I looked at the first coordinate number, which showed me where to go on the x-axis. The second coordinate number showed me where to go on the y-axis. I placed my point where the x and y lines intersected. DOK-2 Why do you think the values on the number lines changed on the coordinate plane? I think the values on the coordinate plane can change based on how large or small the numbers are that you are dealing with. DOK-3 Are ordered pairs always created using a rule, or can ordered pairs be used to simply represent data? Explain. Ordered pairs can be created to simply represent data. For example, in other Explore activities, we used ordered pairs to find a location and to represent the placement of furniture.

Post-Explore 1. 2. 3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Graph in the First Quadrant 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 Coordinate Plane 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

Plot Shapes 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

Graph Real-World 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

Abuela’s Storage Closet

René Descartes

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

Water: One of Earth’s Most Powerful Forces

Match Ordered Pairs to Coordinate Directions

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 Can I Take Your Order? Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

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

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Students who are still acquiring the concept and need remediation

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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 describe the coordinate system and identify the origin.

What prompts will be used?

What does mastery look like?

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I can identify the x-axis and y-axis.

I can plot an ordered pair.

I can describe the relationship between ordered pairs and their locations in the ﬁrst quadrant.

I can determine when a mathematical problem has a set of ordered pairs.

I can interpret coordinate values in the context of the situation.

I can solve problems by graphing points in the ﬁrst quadrant of the coordinate plane.

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SCOPE 1

Generate and Graph Numerical Patterns Scope Introduction SCOPE SUMMARY Students generate numerical patterns with the same starting number for two different rules and identify relationships between corresponding terms. They examine these relationships within sequences of ordered pairs graphed on a coordinate plane. The resulting graphs are analyzed to determine the relationship between the two patterns. The graphs show how two quantities vary together. Student Expectations

5.PAR.6.1 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In second grade, students identify, describe, and create growing patterns and shrinking patterns resulting from a repeated operation, such as addition and subtraction, up to 20. In third grade, students identify patterns involving multiplication and explain them using a hundred chart, a multiplication chart, and properties of operations. In fourth grade, students identify, generate, and analyze number and shape patterns and corresponding rules.

Knowledge gained between kindergarten and fifth grade about patterns within base-ten numbers will build an essential foundation in sixth grade that will be used to support algebraic thinking in later grades. In sixth grade, students will make tables of equivalent ratios, compare equivalent ratios, find missing values in the tables, and plot pairs of values on the coordinate plane. Sixth-grade students will use knowledge learned in fifth grade to help them solve problems using a coordinate grid. Seventh-grade students will identify the constant of proportionality and use equations and graphs to represent and analyze proportional relationships. In eighth grade, students will use proportional relationships to solve multistep ratio and percent problems. Students have used tables to represent and compare values since the fourth grade, but in eighth grade, functions will be formally explored as an algorithm for slope. Students in eighth grade will define, evaluate, and compare linear functions.

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

identify patterns and use input/ output charts.

•

analyze the numerical patterns and describe the patterns.

•

match rules to the corresponding numerical patterns.

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: •

complete the input/output chart from the determined pattern.

•

graph each mode of transportation using coordinate points on one graph.

•

explain the relationship between the two modes of transportation.

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

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 388

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Generate and Graph One Numerical Pattern In this exploration, students will work in groups to draw a model, complete an input/output chart, and draw a graph using coordinate pairs for different scenarios. Students will:

Explore 2

Explore 1

EXPLORE ACTIVITIES Generate and Graph Two Numerical Patterns In the last exploration, students will analyze different carnival contest scenarios to create input/output charts and graph the corresponding coordinate pairs. Students will:

•

identify the variables from each scenario and describe the given rule in their own words.

•

determine the variables and the rules from the scenario cards.

•

explain the relationship of the x-axis to the y-axis for different scenarios in their own words.

•

complete the input/output chart based on the rule provided for each comparison.

•

label each graph with the corresponding variables and titles.

•

restate the rule in their own words for each variable.

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

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

GENERATE AND GRAPH NUMERICAL PATTERNS

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Generate and Graph Numerical Patterns Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students match given patterns with the rules that describe them. This activity is intended to assess mastery of the following standard(s): 4.PAR.3.1 Generate both number and shape patterns that follow a provided rule.

Materials

Preparation

Printed •

1 Set of Pattern and Rule Cards (per group)

Reusable •

• • •

Print and cut out the Pattern and Rule Cards. Plan to have students work in groups to complete this activity. Place the cards in a resealable bag or envelope for each student group.

1 Resealable bag or envelope (per group)

Procedure and Facilitation Points 1. 2. 3.

Distribute the sets of Pattern and Rule Cards to groups. Direct students to remove the cards and to separate the purple cards and green cards into two sets. Ask students to set aside the green set and to lay out the purple set. Ask students to analyze the patterns they see on the purple cards and describe them. Ask students to share their observations. a.

5. 6.

I see that in this pattern the numbers are increasing by two. These are all odd/even. Each number ends in zero. These are all multiples of ten.

Challenge student groups to set out the green set of cards and to choose the card that matches each purple card. Explain to students that only four of the eight green cards will be used. After completing the matches, invite students to state the characteristics of each pattern that helped them match it to the correct rule. Facilitate a class discussion about the students’ descriptions of the patterns. 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, move on to the Foundation Builder to ﬁll this gap in prior knowledge before moving on to other parts of the scope.

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FACILITATION TIP Project the pattern, and allow students time to analyze it before showing them the student response choices. Allow students to use concrete objects, such as counters, to generate the pictorial representations of the patterns shown. The act of physically arranging and counting the objects can help students conceptualize how the pattern generates.

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Generate and Graph Numerical Patterns Hook ACTIVITY PREPARATION Students review the rules of travel for two different modes of transportation—a scooter and a bike. They will generate patterns of travel for both modes, using an input-output chart for each, generating coordinate pairs for the scooter and the bike, and then graphing both patterns on a coordinate plane. Based on their graphs, students will identify and explain the relationship between the travel patterns of the scooter and the bike.

Materials

Preparation

Printed •

• • •

1 Student Handout (per student)

Reusable • • •

Plan to show the Phenomena Video. Print a Student Handout for each student. Part II • •

2 Different colored pencils (per pair of students) 1 Phenomena Video (per class) 1 Projector (per class)

Plan to have students work in pairs to complete this activity. Gather enough different colored pencils for each pair of students to have 2 of each.

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

FACILITATION TIP

Print and project this scenario. First, have students read it alone silently and jot down notes. Next, have them read it together with a shoulder partner. Finally, read it all together as a class and guide students to note the math phrases and values.

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DOK-1 What are input-output tables? Input-output tables follow a rule to generate numbers/ordered pairs.

DOK-1 What is the horizontal axis called in a graph? The x-axis

DOK-1 What is the vertical axis called in a graph? The y-axis

DOK-2 How can you tell the relationships between different patterns? We can look at the input-output charts to see the patterns. We can also look at the lines generated on the graph.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

3. 4.

7. 8.

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

DOK-1 What are input-output tables? Input-output tables follow a rule to generate numbers/ordered pairs.

DOK-1 What is the horizontal axis called in a graph? The x-axis

DOK-1 What is the vertical axis called in a graph? The y-axis

DOK-2 How can you tell the relationships between different patterns? We can look at the input-output charts to see the patterns. We can also look at the lines generated on the graph.

FACILITATION TIP Refer back to the scenario and address what students are supposed to ﬁnd out.

Put students in pairs. Give each pair a Student Handout and two different colored pencils. Tell students they should use their knowledge of number patterns and graphing to identify the two patterns, graph them, and explain the relationship between them. They should accomplish this by observing and filling in the input-output chart for the scooter and the bike and looking for patterns. (Hint: ( Is it a pattern of adding on? Is it a pattern of taking away? What is happening?) happening? Then, have them graph each pattern separately and look at the relationship between them. Give students about 5–10 minutes to work with their partners to find the patterns and the relationship between them. Walk around during this time, and observe groups, offering assistance and asking guiding questions to help groups that might be struggling. FACILITATION TIP Group two pairs together, and have them share their graphs and discuss the patterns they noticed for both the scooter and the bike. Then, they should discuss Assist students who are having difficulty the relationship between the patterns of the scooter and the bike. completing the graphs. Use manipulatives as After a couple of minutes, ask for a volunteer to explain their findings to the needed. whole class. Gather students in a whole group, and discuss the following questions: a.

DOK-2 How did you ﬁnd the rule of the scooter table? I looked at what happened every time a minute passed and noticed that the number of blocks traveled went up by 2. It is an adding-on pattern. It could also be called a multiplying pattern because the number of blocks traveled is always double (two times greater than) the minutes.

DOK-2 How did you ﬁnd the rule of the bike table? I looked at what happened every time a minute passed and noticed that the number of blocks traveled went up by 4. It is an adding-on pattern. It could also be called a multiplying pattern because the number of blocks traveled is always quadruple (four times greater than) the minutes.

DOK-2 When plotting the ordered pairs, how did you know which order to put the numbers in? I plotted x ﬁrst on the horizontal axis and then y on the vertical axis to plot the correct point from the ordered pair.

DOK-2 How did ﬁguring out the rule help you generate the pattern for the rest of the table? When I saw that the scooter pattern was adding on 2 every time a second passed or multiplying the seconds by 2, I was able to ﬁnd and check the rest of the numbers by adding on 2 or multiplying the input (or x-value) by 2. The same was true of the bike pattern except it was adding on 4 or multiplying the seconds by 4.

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e. DOK-2 What relationship did you identify between the patterns of travel of the scooter and the bike? The bike traveled twice as fast as the scooter. f.

DOK-2 What was the most challenging part of this activity for you and your partner? Answers may vary. Plotting the points was most diﬃcult because we sometimes mixed up the x- and the y-coordinates and axes.

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Generate and Graph Numerical Patterns Explore 1 — Generate and Graph One Numerical Pattern ACTIVITY PREPARATION Students explore various numerical relationships and express them using tables and graphs.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 2 Sets of Scenario Cards (per class) 1 Exit Ticket (per student)

Reusable • • • • • •

•

2 Sets of counters (per class) 2 Pads of sticky notes (per class) 4 Sets of play money (per class) 1 Pair of scissors (per student) 1 Glue stick (per group) 2 Rulers (per class)

• • • • •

Consumable •

Plan to divide the class into 8 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut out 2 sets of Scenario Cards. You will be running 2 sets of the four stations at the same time, four on one side of the room and four on the other side of the room. Prepare 2 sets of plastic containers with each Scenario Card and the following contents:

2 Balls of string (per class)

•

Scenario 1: Sticky notes and counters Scenario 2: A ball of string, a ruler, and a pair of scissors Scenario 3: Play money Scenario 4: Play money

For students who need more support in recalling information, please see our Grid Paper and Coordinate Plane 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. (XY Coordinate Board)

PROCEDURE AND FACILITATION POINTS

FACILITATION TIP Have group members take turns reading the Scenario Cards, identifying the patterns, and creating a model.

1. 2. 3. 4. 5.

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Distribute a Student Journal to each student. Distribute the plastic container with a Scenario Card and supplies to each group. Challenge students to read the Scenario Card and collaborate to use the supplies to model the scenario using the rule given. Invite students to draw their models on their Student Journals. DOK-1 Ask students to talk to their groups or partners about what they notice is happening to the numbers. It has formed a pattern, with every unit (hour, object, etc.) the result (y) grows by being multiplied by _____ or added _____. They will then use the model to ﬁnd a corresponding term from the x value in their table to the y value. A variable is a symbol that represents a value we don’t know yet. Explain that when they are trying different numbers that represent a change in a scenario or context, that is called a variable and is usually represented by a letter like x or y. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 How does the given rule for the scenario and the model you created help you determine the corresponding term to the x value? I can represent the given x value from the table to model the rule in order to determine the corresponding term of the y value.

DOK-2 Given the scenario, discuss with your group what you think the x value and y value stand for. Answers will vary. The ﬁrst scenario is trying to ﬁnd how many students can play a game based on how many games are available. Since the rule shows that I’m trying to determine the y value, then the y value must represent the number of students playing games. The x value represents the number of games available.

Intervention

Acceleration

FACILITATION TIP DOK-1 How can we represent the numerical pattern of the corresponding terms by continuing with different numbers? On the given Discuss how the numbers in these table, we can record the result of the x value and the y value when the numerical patterns increase as the pattern rule is applied—this creates the coordinate points or ordered pairs. progresses. Increased values in a numerical d. DOK-2 How can we represent the corresponding terms as an ordered pattern are the result of a rule involving pair? The x value will be the ﬁrst number in the ordered pair, and the multiplication and/or addition. In these y value will be the second number in the ordered pair. patterns, multiplication is part of each rule. e. DOK-2 How would the graph compare to the numbers on the table? The Tax is sometimes added on, and a discount is sometimes subtracted, but the resulting coordinate points on the graph would represent the numbers used on values are always greater than the previous the table as well as the result of applying the rule. So if the numbers increase on the table, the graph will show a line increasing on both axes. values in each pattern. c.

7. 8. 9. 10. 11.

12.

Students should record the rule, define what the variables mean, and describe the rule in their own words on their Student Journals. Students should then use the models to create a table showing the numerical pattern. After recording the information for each scenario in the table provided, students should answer the questions below the table on their Student Journals. Discuss each scenario and how the pattern was recorded in the table. Have students look at the graphing templates on the last page of their Student FACILITATION TIP Journals. If needed, model how to graph the values in the table on a coordinate Consider modeling the first graph all together plane using scenario 1. with students. Creating a scale may be a Ensure that students do the following with each graph: difficult step for some students. Consider providing support for deciding and labeling a. Begin by giving the graph a title and labeling each axis. They can the scale on each axis. reference what they said each variable stood for in the top-right cell of FACILITATION TIP the table for each scenario. b.

Students should then look at the values for x and the values for y to decide what scale to use on each axis.

Have students write the number values along each axis.

Guide students in ﬁnding the line that represents x = 0. Zero is found where the xx-axis -axis and yy-axis -axis intersect.

e. DOK-1 What is that called? The origin f.

DOK-1 When x = 0, what is the value of y? The value of y is 0.

Have students draw a point on the lines where x = 0 and y = 0.

h. Have students repeat the same process for each value listed in the table. 13.

GENERATE AND GRAPH NUMERICAL PATTERNS

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

DOK-1 For the x-axis, -axis, should we count by ones, twos, ﬁves, or 10s? We should count by ones, because we only have numbers zero through three.

DOK-1 For the yy-axis, -axis, what should we count by? We should count by twos since our values range from 0 to 12.

DOK-1 What is the ﬁrst value we have for x in our table? The ﬁrst value we have is 0.

Create a checklist for each group to use as they are creating the graphs as a self-check. 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.

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Generate and Graph Numerical Patterns Explore 1 — Generate and Graph One Numerical Pattern 14. 15. 16. FACILITATION TIP Groups can compare their graphs to begin the Math Chat discussion.

Have students cut out the graphs and glue them on the correct page of their Student Journals. Have students rotate bins with scenarios until they have completed them all. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat Brieﬂy discuss how each graph looks and what scale each group used to graph the values in the table. •

• •

DOK-2 Why do you think we should know how to graph something like this? A graph can help you see how changing one number affects another number. In scenario 1, I could see how adding more games allows more students to play. DOK-1 What two operations did you use to create the tables? We used addition and multiplication. DOK-2 How does your graph compare to the table? As the numbers increase on the table, the line on the graph goes up, indicating higher numbers on both axes.

Post-Explore 1. FACILITATION TIP When you preview this Exit Ticket, consider providing struggling students extra support when determining and labeling the scale.

2. 3.

Instructional Strategies 1.

3. 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.

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.

If students are struggling to complete their x-y tables, have them include a process column (such as “×4” or “+1”) in the table in between the xx- and y y-columns. If students are struggling to determine if a rule is additive or multiplicative, have them test to see if the output is a multiple of the input. Encourage students to discuss how this could be done. Students could divide the output by the input and see if each pair of numbers share the same relationship. If not, students can complete the same type of test for an additive relationship. Students could subtract the input from the output and test to see if each pair of numbers share the same relationship. Review graphing in the ﬁrst quadrant. Touch on the following concepts: x-axis, x-axis, yy-axis, -axis, coordinates, and ordered pairs.

Language Acquisition Strategies The following Language Acquisition Strategy is supported in this Explore activity. See the strategies below for ways to support a student’s language development. Students will demonstrate grade-level listening comprehension by following and retelling instructions, responding to questions, and through collaboration with peers. Beginner: After explaining to students what they will do with each graph on the last page of their Student Journals, ask student groups to paraphrase what they understood about the directions and clarify or repeat information as needed. Intermediate: Instruct students to take turns reading the Scenario Cards within their groups. Students who are not reading aloud should follow along. Students will check each other for comprehension after the scenario is read by having the student to the left of the reader restate the given information before the group begins working on the problem. Advanced: Provide additional structure to the Math Chat by having students respond to each other using the following sentence stem: I heard you say ____; I think ____.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

GENERATE AND GRAPH NUMERICAL PATTERNS

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Generate and Graph Numerical Patterns Explore 2 — Generate and Graph Two Numerical Patterns ACTIVITY PREPARATION Students generate coordinate pairs and graph two numerical patterns. They also analyze the relationship between both patterns.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments, and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 2 Sets of Carnival Contests Cards (per class) 1 Exit Ticket (per student)

Reusable • • •

• • •

1 Pair of scissors (per student) 1 Glue stick (per group) 1 Ruler (per group)

•

Plan to have students work in 8 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print and cut 2 sets of the Carnival Contests Cards, which will create two sets of the same stations to keep the number of students in a group low. There will be 8 stations. Prepare each station with a ruler, scissors, and glue stick. Place the stations around the room. For students who need more support in recalling information, please see our Grid Paper and Coordinate Plane 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. (XY Coordinate Board)

PROCEDURE AND FACILITATION POINTS 1. 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.

2. 3. 4.

Read the following scenario to the class: It’s Carnival time! There is always so much to do at a carnival. We can ride the rides, play so many games, and eat a ton of yummy food. Everything is so much fun, but the contests are always the most popular attractions. Each of the stations represents a different contest. Work together to determine how much you can win! Distribute a Student Journal to each student. Assign each group to a station. Explain to the class that they will be working with their group to determine a rule for each part of the scenario, describe what the x and y values stand for, complete each table with the corresponding term for each x value, and complete a graph for each scenario by graphing each numerical pattern. Explain that when they are trying different numbers that represent a change in a scenario or context, that is called a variable and is usually represented by a letter like x or y. a.

DOK-2 How does the scenario help you determine the rule used to ﬁnd the y value? I can read the scenario and determine if I am multiplying or adding onto an unknown variable, the x value, in order to determine the solution or the y value.

b. DOK-2 How does the scenario help you determine the corresponding term to the x value? I can represent the given x value from the table to model the rule in order to determine the corresponding term of the y value. 398

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 Given the scenario, discuss with your group what you think the x value and the y value stand for. Answers will vary. The ﬁrst scenario is trying to ﬁnd the total number of footlongs Sam and Hank ate depending on the time they spent eating. Since the rule shows that I’m trying to determine the y value, then the y value must represent the number of footlongs eaten. The x value represents the number of minutes spent eating.

FACILITATION TIP DOK-1 How can we represent the numerical pattern of the corresponding terms by continuing with different numbers? On the given Help students make this connection for table, we can record the result of the x value and the y value when the rules involving multiplication by forming rule is applied—this creates the coordinate points or ordered pairs. equal-sized groups to find patterns. e. DOK-2 How would the graph compare to the numbers on the table? FACILITATION TIP The coordinate points on the graph would represent the numbers used Analyzing graphs with different types of on the table as well as the result of applying the rule. So if the numbers increase on the table, the graph will show a line increasing on both axes. data is based on the ability to find the pattern. Challenge students to work with their groups to complete the scenarios. As the students are working in groups, monitor discussions, and look for misconceptions. Students should record the rules, define what the variables mean, and describe the rule in their own words on their Student Journals. Students should then use the rules to complete the tables showing the numerical patterns. For each contest there are two rules. Be sure students record both tables on the same graph. Have students look at the graphing templates on the last page of their Student Journals. If needed, model how to graph the values in the table on a coordinate FACILITATION TIP plane, using a separate example. Demonstrate how to graph data that is Ensure that students do the following with each graph: about students’ interests. Label the x-axis, d.

6. 7. 8. 9. 10. 11.

12.

Give the graph a title and label each axis. They can reference what each variable represents.

Students should then look at the values for x and the values for y to decide what scale to use on each axis.

Have students write the number values along each axis.

Guide students in ﬁnding the line that represents x = 0. Zero is found where the x-axis and yy-axis intersect.

e. DOK-1 What is that called? The origin f.

DOK-1 When x = 0, what is the value of y? The value of y is 0.

Have students draw a point on the lines where x = 0 and y = 0.

h. Have students repeat the same process for each value listed in the table. 13.

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

DOK-1 For the x-axis, -axis, should we count by ones, twos, ﬁves, or 10s? We should count by ones, because we only have numbers zero through three.

DOK-1 For the yy-axis, -axis, what should we count by? We should count by twos since our values range from 0 to 12.

DOK-1 What is the ﬁrst value we have for x in our table? The ﬁrst value we have is 0.

DOK-1 Both rules are related to each other. What do you notice about the two tables? They both have the same x values.

GENERATE AND GRAPH NUMERICAL PATTERNS

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y-axis, and the origin. Have students help create the scale to use to make the graph.

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Generate and Graph Numerical Patterns Explore 2 — Divide a Unit Fraction by a Whole Number e. DOK-2 What do you notice about the two lines when you graph them? They stay the same distance apart when it is an adding rule. When it is a multiplying rule, they get further apart. Any ideas why? When you multiply by a bigger number, the product gets bigger. f.

14. 15.

Remind students to put both rules on the same coordinate grid. Have students cut out and glue grids to the correct page in their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP

16.

Have groups compare their graphs and discuss the differences and similarities.

Math Chat •

•

FACILITATION TIP Before having students complete this Exit Ticket, clarify your expectations for the written explanations and methods for students to show their thinking.

• •

DOK-2 How can you discover how the two rules are related to each other? Look at the table or the coordinate grid to see the patterns and how the two rules are related.

DOK-2 Why do you think we should know how to graph something like this? A graph can help you see how changing one number affects another number. When graphing 2 patterns, you can see how they are related. DOK-2 What connections did you make while doing this Explore activity? I was able to see how much I would win and how it will increase when I make a table and a graph. Making a pattern with numbers is similar to making any kind of pattern. I had to multiply and add for these patterns. I saw that when building a table of values, I can see the rule easier. DOK-2 How does your graph compare to the table? As the numbers increase on the table, the line on the graph goes up, indicating higher numbers on both axes. DOK-2 What observations did you make with the two patterns in the same contest? The rules are related in every contest. They are both increasing. The variables stand for the same thing. For every value of x, the same pattern between the two rules stays the same.

Post-Explore FACILITATION TIP

When administering this Exit Ticket, provide supports to struggling students for creating and labeling the scale. In addition, consider encouraging students to use two different colors or shapes for each set of points.

2. 3. 4.

Instructional Strategies 1. 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.

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Students could be confused by the horizontal table and the vertical table. Make sure to show and explain that these are two different ways to organize the same information. If students are struggling to complete their x-y tables, have them include a process column (such as “×15” or “+4”) in the table in between the x- and y-columns. Review properties of zero to help students determine if a relationship is additive or multiplicative. Use the following guiding questions to help students see the relationship: If there is an input of zero into a relationship, what would the output be if the relationship is additive? What would the output be if the relationship were multiplicative? Review graphing in the ﬁrst quadrant, if needed. Remind students which axis represents x, which represents y, and how to read ordered pairs.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Language Acquisition Strategies The following Language Acquisition Strategy is supported in this Explore activity. See the strategies below for ways to support a student’s language development. Students will accurately include newly acquired basic and context-based, grade-level vocabulary in their writing. Beginner: Display and encourage students to utilize an anchor chart or word wall featuring key vocabulary in this scope: rule rule, graph, multiplicative, additive additive, and numerical pattern. Intermediate: Provide sentence frames for students to use during group work: In an additive rule, a value is being ____ to the x value to the y value. In a multiplicative rule, a value is being ____ to the x value to get to the y value. In an additive graph, when the x value is 0, the y value is ____. In a multiplicative graph, when the x value is 0, the y value is ____.

Advanced: During the Math Chat, have students work with a partner to answer the questions ﬁrst verbally and then in writing, highlighting the key vocabulary used.

GENERATE AND GRAPH NUMERICAL PATTERNS

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401

GENERATE AND GRAPH NUMERICAL PATTERNS

Generate and Graph Numerical 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

Generate and Graph One Numerical Pattern 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

Generate and Graph Two Numerical Patterns 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

402

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 Treasure Hunt

Earthquake Kate Hutton

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

Carnival of Colors

Problem Solving with Tables and Graphs

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

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

Problem-Based Task

Interactive Practice

Getting Stronger

Wildﬁre

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

GENERATE AND GRAPH NUMERICAL PATTERNS

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

403

Students who are still acquiring the concept and need remediation

GENERATE AND GRAPH NUMERICAL PATTERNS

Generate and Graph Numerical Patterns

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 generate two numerical patterns with the same starting number for two different given rules.

What prompts will be used?

What does mastery look like?

GENERATE AND GRAPH NUMERICAL PATTERNS

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I can identify apparent relationships between the corresponding terms by completing a table.

I can represent the corresponding terms as ordered pairs.

I can graph ordered pairs on a coordinate plane.

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SCOPE 1

Represent and Interpret Data Scope Introduction SCOPE SUMMARY Students collect, represent, and interpret numerical data by using tables, bar graphs, and line plots. They solve real-world problems in relation to the data collected, and they consider the distribution of data by determining and analyzing measures of mode, median, mean, and range.

Student Expectations

5.MDR.7.2 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 third grade, students collect, organize, and represent numerical data by using tables, line plots, pictographs, and bar graphs. They interpret these types of graphs and use the graphs to solve oneor two-step problems. In fourth grade, students collect, represent, and interpret numerical data with fractional values by using tables and line plots, and they solve real-world problems in relation to the data collected.

Students will continue to represent and interpret numerical data. Sixth graders work with histograms, box plots, line plots, and double bar graphs to qualitatively describe and interpret the spread and distribution of data. In sixth grade, students design simple experiments, collect data, and use the gathered data from realistic scenarios and simulations to determine quantitative measures of center (median and/ or mean) and variability (interquartile range and range). Students then use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions.

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

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

choose the statement that identiﬁes the data in a table and a line plot.

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

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

represent and interpret the mean, mode, median, and range of data by using a line plot.

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.

406

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Line Plots In this exploration, students will collect data from a variety of sources. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

display the data in a line plot.

•

order the data from least to greatest.

•

use centimeter cubes or linking cubes to create a line plot using the two number lines on their desks to represent the data.

analyze bar graphs.

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

Explore 4

Explore 3

In this exploration, students will analyze numerical data in real-world problems and interpret the mean as a balance point, an equal share, or leveling out. Students will:

In this exploration, students will create business ideas and collect data responses from fellow classmates that will be represented on bar graphs. 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.

Interpret Mean

Bar Graphs

REPRESENT AND INTERPRET DATA

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Mean, Mode, Median, and Range In this exploration, students will analyze data tables and line plots and interpret the data in order to determine the mean, mode, median, and range of whole number values. Students will: •

analyze that data using their Data Work Mats.

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.

407

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 Description Students choose the statement that identiﬁes the data in a table and a line plot. This activity is intended to assess mastery of the following standard(s): 4.MDR.6.2 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Materials

Preparation

Printed •

•

1 Student Handout (per group)

• •

Reusable • •

REPRESENT AND INTERPRET DATA

Home

Plan to have students work in groups of 2 or 3 to complete this activity. Print a Student Handout for each group. Prepare to project the Student Handout for the class.

1 Projector or document camera (per class) 1 Pair of scissors (per group)

Procedure and Facilitation Points 1. 2. 3.

4. 5.

Project the Student Handout for the class, and give one printed Student Handout to each group of students. Ask students to look at the table and the line plot and then read the two statements. Have students connect the table and the line plot with the statement that correctly identiﬁes the data. Have them cut and paste the correct statement under the corresponding graph. Tell students to be ready to justify their choices. Facilitate a class discussion about the students’ choices. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. 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 Discuss the key attributes of each data representation. Ask students the beneﬁts of using each type and whether one type reveals more information than the other.

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Hook – Shoe Lengths ACTIVITY PREPARATION Students represent and interpret the mean, mode, median, and range of data by using a line plot.

Materials

Preparation

Printed •

• •

1 Student Handout (per group)

Reusable • • • • •

•

1 Phenomena Video (per class) 1 Projector (per class) 1 Measuring tape or ruler with inches (per group) 1 Set of 100 linking cubes (per group) 1 Resealable bag (per group)

•

Plan to show the Phenomena Video. Plan to have students work in groups of 3 or 4 to complete this activity. Gather enough measuring tapes and/or rulers and index cards for each group to have one of each. Gather sets of 100 linking cubes and place them in resealable bags, one for each group.

Part II •

Print the Student Handout for each group

Consumable •

1 Index card (per group)

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

FACILITATION TIP

Write students’ ideas on the board or on a poster board to refer back to following the completion of the Explore activities.

3. 4. 5.

8. 9. 10. 410

DOK-2 How could we organize the whole class data? We could place the data in a table and then create a line plot.

DOK-2 Once the data is organized, in what ways could we interpret the data? Answers may vary. We could interpret the shape and spread of the data on the graph to see which sizes are most common, and what the largest and smallest shoe lengths in the class are.

Explain that students will learn different ways to organize and interpret data in this scope. Collect the index cards and save them for use in Part II. Move on to complete the Explore activities. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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

4. 5.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Display the index cards with recorded shoe lengths. Discuss the following questions: a.

DOK-2 How could we organize the whole class data? We could place the data in a frequency table and then create a line plot.

DOK-2 Once the data is organized, in what ways could we interpret the data? Answers may vary. We could interpret the shape and spread of the data on the line plot to see which sizes are most common, and what the largest and smallest shoe lengths in the class are.

Give a Student Handout to each group, and allow groups to work together to record and organize the data. Discuss the following questions: a.

DOK-1 What is an appropriate title for this data? Shoe Lengths

DOK-2 How did you determine which values to include on your line plot and what scale to use? We determined the shortest and longest lengths. Since there is not a big spread among the data, the scale can count by 1.

DOK-2 What are some ways we could interpret the data? We can determine the range, median, mode, and mean of the data set.

DOK-2 Which lengths are included on the frequency table and line plot? Answers vary depending on the class data.

e. DOK-3 Refer to the range, mode, median, and mean. Describe how you determined each value and what these values represent in relation to the whole class data set. Values will vary. The range is the difference between the longest and shortest length, and it describes the size of the range of values in the data set. The mode is the most frequent value, or the length that appeared the most. The median is the middle value. The mean is the value of all the data points evenly distributed or the average of the data points.

REPRESENT AND INTERPRET DATA

Home

FACILITATION TIP Monitor groups and check for understanding by asking guiding questions.

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.

DOK-1 How can we use the linking cubes to determine the mean of the shoe length data? We can ﬁnd the equal share value of all the shoe length data by representing each piece of data and then distributing the linking cubes to different values until they each have the same value. We can also level out the linking cubes until each piece of data has the same amount.

FACILITATION TIP DOK-4 Which of these values do you think provides us with the best description of our whole class data set? Answers will vary, as it depends Discuss in what situations each type of on the distribution of data. Reference the shape and spread of the data, central tendency would be most useful. (For and look for outliers that might affect the mean. example, if students wanted to ﬁnd a sale on the shoe size that occurred the most, they would need to know the mode.) Notes

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 1 — Line Plots ACTIVITY PREPARATION Students collect data from a variety of sources and display the data in a line plot.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Preparation

Materials Printed • • •

1 Student Journal (per student) 1 Reaction Measurement Data Table (per group) 1 Exit Ticket (per student)

Reusable • • •

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 Reaction Measurement Data Table, on card stock for durability, for each group of students.

•

Gather a water bottle for each group. Make sure the water bottles are ﬁlled

• •

1 Ruler (per student) 1 Centimeter cube (per student) 1 Stopwatch (per group)

Consumable • • • •

• • •

1 Water bottle, __4 ﬁlled (per group) 1 Straw (per student) 1 Piece of butcher paper (per class) 1 Dot sticker (for example, garage sale stickers; per student)

•

with equal amounts of water, no more than __4 full. Gather 1 straw and 1 centimeter cube for each student. Cut a roughly 2’ × 3’ piece of butcher paper. Draw a number line at the bottom of the long side of the butcher paper. Write evenly spaced increments from 0 to 10 on the number line. Hang the number line in the room so it is visible and accessible for students. Gather a ruler, straw, and dot sticker for each student. Gather a stopwatch for each group. For students who need more support in recalling information, please see our 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. (Number Lines)

PROCEDURE AND FACILITATION POINTS 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.

412

Part I: Flip It 1. 2. 3. 4.

Read the following scenario to the class: Today, we will be participating in three challenges! We will be representing the results of our challenge on a giant line plot. Explain that the first challenge is called Flip It, and students will be putting their bottle-flipping skills to the test. Give a water bottle and stopwatch to each group, and give a Student Journal and dot sticker to each student. Explain that each student in their group will take turns flipping the bottle for one minute. They must count the number of times the bottle lands standing up within that minute. When the minute is up, the students will put a dot on the butcher paper number line above the number of times they flipped the bottle and it landed standing up. © Accelerate Learning Inc. - All Rights Reserved

Explain

Elaborate

Evaluate

DOK-2 What are some things we should remember when we make a line plot? Answers will vary. We should make the dots the same size, space them out evenly, make sure the dots line up vertically, and make sure to place them in the correct spot horizontally along the number line.

DOK-3 What other type of data representation is similar to a line plot? Answers will vary. A frequency table is like a line plot, but instead of a tally mark, you record frequency with a dot. DOK-2 What data does a line plot represent? How many times a certain event has occurred

Have students copy the ﬁrst round of results onto the Class Data Table and plot the results on the number line on their Student Journals. After students have written all the data on the Class Data Table and plotted the data on the number line on their Student Journals, ask the following: a.

Explore

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

c. 6.

Engage

Intervention

Acceleration

FACILITATION TIP Be sure to discuss the number line and increments used, as it is important to interpret the scale being used before plotting the points. In this activity, students also encounter fractional increments. FACILITATION TIP An important distinction to make is that a line plot shows a visual representation of the distribution of data. A line plot reveals the shape and spread of the whole data set and enables us to see the relationship between each individual data point and among the whole set.

REPRESENT AND INTERPRET DATA

Home

DOK-1 What should you remember to include on your line plot that is also used with a frequency table and a bar graph? The title and axis label

Have students come up with a title for the line plot. Then, have students work together to analyze the data and answer the questions on their Student Journals. After Part I, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 What scale was best for this line plot and why? The scale we came up with began at 0 and ended at 10 because some students didn’t make the bottle land upright, and we needed an ending number that was friendly and showed the greatest number of times someone could get the bottle to land upright. • DOK-3 What better scale could we have used for this line plot? Explain. We could have had the number line end at 8 because no one got the bottle to land upright more than 8 times. • DOK-3 How are line plots useful? A line plot is an easy way to compare and organize data. It helps you easily learn from the set of data. • DOK-2 What information can you interpret from a line plot? You can see the most and least occurring data points. You can see the greatest overall number and the least overall number. You can see a range of numbers for the data. It tells you •

how many events occurred. Part II: Blow It Off 1. 2. 3.

Explain that the next challenge is called Blow it Off, and students will be blowing a cube along a surface. Give a stopwatch to each group and a straw and a centimeter cube to each student. Have students put the centimeter cube at one end of the desk. Tell students that each person in the group will take turns to try to use his or her straw to move a centimeter cube from one end of the desk off the other end. Remind students that they should use only their own straws and go one student at a time. Demonstrate the process for the students, if needed. While one student uses the straw, another student should keep time. Then, students should trade roles until everyone has had a turn in both roles.

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 1 — Line Plots 4.

Have one person from each group announce the group’s fastest time. Write these numbers on the board while students write them on the Group Data Table on their Student Journals. Ask questions such as the following:

FACILITATION TIP

Have students count aloud in unison by two-tenths. Then, ask a group of students to stand in a line and each say the next counting number in this sequence: 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, and so on.

DOK-3 What scale would you use for this line plot and why? Answers will vary. We should use the least number as the starting point on our number line and the greatest number as the ending point. We can also use intervals of ﬁve with lines in between the intervals to each represent two tenths (0.2).

DOK-1 What do you also need to include on the line plot? We need a title and axis label.

FACILITATION TIP Creating scaled number lines takes practice. Model the process: Choose and plot the end points (least and greatest values), mark evenly spaced increments and label them with whole numbers, decide which scale to use, determine how many increments will be drawn between each whole number (the number of increments is always one less than the denominator of the fractional part), and mark these slightly shorter and evenly spaced increments between the whole numbers. Students may benefit from drawing the number lines on larger sheets of paper or even chart paper at first so that they can practice fitting all the increments. FACILITATION TIP Have students count aloud in unison by halves and fourths. Then, ask a group of students to stand in a line and each say the next counting number in this sequence: onehalf, one, one and one-half, two, and so on; one-fourth, two-fourths, three-fourths, one, one and one-fourth, and so on.

Students should discuss what scale to use to properly represent the data, and then they should record the data on their Student Journal line plots. Students should work together to create a title and axis label and answer the questions.

Part III: Grab It 1. 2. 3. 4. 5.

Explain that the next challenge is called Grab It and students will be putting their reﬂexes to the test. Give each group a Reaction Measurement Data Table. Give a ruler to each student. Explain that the last challenge is to see how quick their reaction time is. Students should choose a partner in their groups. Make sure students understand how to read quarter-inch measurement markings 1

on a ruler. Ask students to put their ﬁngers on the ruler where it shows 4 __2 inches. 1 __

Check to make sure students are pointing to 4 2 inches on the ruler. Repeat with 1

measurements at __4 inch increments (__4 and __4 inch). Once students have practiced reading measurement markings, have them complete the activity. a.

The ﬁrst student will sit in the chair and look straight ahead. His or her forearm should extend over the edge of the desk.

The student’s partner will stand and hold the ruler vertically with the number 1 at the bottom.

The seated student should place his or her thumb and index ﬁnger on either side of the bottom of the ruler.

The seated student will let go of the ruler. The standing student will position the ruler so the bottom is about 1 inch above the seated student’s ﬁngers.

e. The standing student will release the ruler without telling the seated student. The seated student’s job is to catch the ruler with the thumb and foreﬁnger.

FACILITATION TIP During this highly engaging activity, it will be easy for students to get focused on the competition while forgetting to record data. Frequently remind students to pause between turns to record data.

414

The seated student should write his or her name and the measurement displayed just over the thumb to the nearest quarter-inch on the group’s Reaction Measurement Data Table.

If the ruler is not caught, try again.

Students will copy their reaction times onto the Class Data Table on their Student Journals. When complete, groups will pass their group’s Reaction Measurement Data Table to another group so they can copy the data onto their Student Journals. Repeat this process until each group has copied all students’ reaction times 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 This time, when we place the numbers on the number line, what 1 1

do we have to remember to do? We need to make sure we include __4, __2,

9. 10.

3 and __4 intervals.

DOK-2 Where should the number line begin? It depends on the shortest reaction time.

DOK-2 Where should the number line end? It depends on the longest reaction time.

DOK-1 What do you also need to include on the line plot? We need to include a title and axis label.

Once students have created a line plot for all the reaction times in the class, they should work together to answer the questions. After Part III, invite the class to a Math Chat to share their observations and learning.

REPRESENT AND INTERPRET DATA

Home

Math Chat DOK-2 After we collect our data, how do we start a line plot, and what must we remember to add? We have to start on a number line. It has to include the highest and lowest numbers. We need to remember to add a title and axis label, add dots that are the same size, and make sure the dots are evenly spread out horizontally and vertically. • DOK-3 Why is it important to make the dots the same size and evenly spread out horizontally and vertically? The data could look as though it had more dots just because the dots were spread out or closer together. It could also just look like a scatterplot. It is easier to read if it is even and neat. • DOK-3 What other types of data representation does the line plot resemble? It looks like a frequency table with dots instead of tallies. It looks like a bar graph if we put a box around the dots. • DOK-3 Some line plots use Xs instead of dots, which represent the number of times something occurs. Regardless of whether Xs or dots are used, why do we use line plots? We use them to easily see how many times something happened. We can quickly see the greatest and least number of the data collected. •

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 with Complete the Anchor Chart as a class. students, remind them to lightly cross out data values as they enter them on the line Have each student complete their Interactive Notebook. plot. Some struggling students may need a masking tool or straight edge to help them read the data table carefully. Notes

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 2 — Bar Graphs ACTIVITY PREPARATION Students create business ideas and collect data responses from fellow classmates that will be represented on bar graphs. Students will then analyze those bar graphs and answer related questions.

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 Business Cards (per class) 1 Bar Graph Template (per class) 1 Exit Ticket (per student)

• • • •

Reusable • • •

1 Set of 6 linking cubes (per student) 6 Pieces of chart paper (per class) 1 Marker (per group)

•

Plan to divide the class into 6 groups to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Business Cards, on card stock for durability, for the class. Cut them apart, and place the cards around the room as stations. Place a piece of chart paper and a marker at each Business Card station. Print a Bar Graph Template, on card stock for durability, to display to the class. Gather a set of 6 linking cubes for each student in the class. 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. (Linking Cubes)

PROCEDURE AND FACILITATION POINTS Part I: Collecting and Representing Data on a Bar Graph 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.

1. 2.

Give a Student Journal to each student. Read the following scenario to the class: An entrepreneur is someone who organizes and operates their own business. Running a business can be hard because you need to provide a service that people need in order to make money. Most companies will offer multiple services and analyze how much money the business is making from those services to determine how they can make the most money. Your challenge today is to work with your group of fellow entrepreneurs to create a business and decide which services to provide. Your group of entrepreneurs will collect data from fellow classmates on which service they need the most and organize that data into a bar graph to determine how to make the most money with your business. Explain to students that there are six Business Cards around the room. The Business Cards displayed have the following business ideas: a.

Outdoor Care

Indoor Care

Athletics

Art and Crafts

e. Technology f. 416

5. 6.

10.

11.

12. 13.

14. 15.

16.

17.

18. 19.

Explore

Explain

Elaborate

Evaluate

Explain to the class that each Business Card that is displayed has possible services written on that card that the business can provide, but they are welcome to offer different services for their business or use some of the ideas on the card and some of their own ideas. Allow students time to go around the room and analyze the Business Card ideas. Challenge students to choose the business they would like to start and to stand next to that card until every student in the class has chosen their business. a.

Engage

Optionally, set a timer for 3 minutes, and encourage students to choose a business within that time frame.

Make sure there are no more than 5 or 6 students at a Business Card. If there are too many students at a card, encourage some students to choose a different business. Explain to the class that they will be working with their fellow business partners to determine five services they would like their business to offer. Students must choose services that relate to the topic of the business they chose. Explain to the class that they may not know how to do some of the services they offer, and that is fine because this is a pretend activity and they won’t actually have to run the real business or perform a real service for the business. Once students have discussed what services they want to offer, they will record the name of their business and their five services on Part I of their Student Journals. Display the Bar Graph Template to the class, and challenge students to represent the Bar Graph Template on their chart paper. They will need to add a title to their Bar Graph. This title will be the name of their business. Instruct students to label the x-axis -axis with “Business services” and the yy-axis with “Number of votes.” Make sure students notice the five blank boxes along the x-axis on the Bar Graph Template. Students will then write the five services their business will offer along the x-axis -axis where those blank boxes are represented on the Bar Graph Template on their group’s chart paper. Give a set of 6 linking cubes to each student. At their current Business Card, challenge each student to choose the service they like the most out of all the services provided, and each student in the group will place one linking cube on their bar graph chart paper in that column. If more than one student chooses that same service, students will join their linking cubes to the other linking cubes already displayed for that service to start building a vertical column. Explain to students that they will be rotating with their group from business to business and analyzing the services offered on the business’s chart paper. At each station, each student will select the service they like the most out of all the services offered and place or attach their linking cube in that service’s vertical column. Allow enough time at each station for each student to place one linking cube for the service of their choice. Let students know when it is time to rotate. Monitor and talk with students as needed to check for understanding by using the following questions: a.

DOK-1 Which service do you think will be the most helpful? Explain. Answers will vary. I think folding laundry will be the most helpful because it is my least favorite indoor chore.

DOK-2 How can we use our linking cubes to build a bar graph? We can choose the service we like the most and add our linking cubes to the cubes that are already in the vertical column to build different bars within the graph.

Intervention

Acceleration

FACILITATION TIP Alternatively, the class could vote on one or more businesses that they are interested in and you could guide them through the steps together.

REPRESENT AND INTERPRET DATA

Home

FACILITATION TIP Depending on your students, consider leading the class through the six businesses and using class voting to determine the ﬁve services.

FACILITATION TIP If using this Explore activity as a whole class activity rather than stations, have students vote for each business’s service that they like the most.

417

REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 2 — Bar Graphs c. DOK-2 Should our linking cubes be placed into a vertical column or a horizontal row? Our linking cubes should be placed in a vertical column because of how the x-axis and y-axis are labeled. We are building upon the x-axis, and the y-axis will tell us how many votes we had for that service. 20.

21. FACILITATION TIP

22.

Creating an appropriate scale takes practice. Review these steps before students begin Step 22.

23.

Once students have rotated and placed a linking cube at each station, they will return back to their Business Cards and analyze the data collected on which service was their classmates’ favorite. Challenge each group to work together to look at the data and determine a scale they can use for the yy-axis, -axis, or number of votes, and represent the linking cubes for each service as a bar on their bar graph. Students will work together with their groups to create the scale and bars for the bar graph on their chart paper ﬁrst and then record their work on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 What scale do you think would be best for the yy-axis of your bar graph? Answers may vary. I think the best scale would be to count by 1 or 2. I can look at the least and greatest values, determine how to create the scale for the y-axis, and see that my smallest number is 1 and my greatest number is 9, so I can count by 1 up to 10 and represent all the numbers on the bar graph.

DOK-1 What does each linking cube represent? Each linking cube represents a vote from a classmate for the service.

DOK-2 How can you represent all the linking cubes for a given service as a bar on the bar graph? I can count how many linking cubes we had altogether for one service and shade in a bar up to that number on the scale of our bar graph. I can repeat this process of counting the linking cubes and representing the bar for each service on the bar graph.

DOK-2 How can you analyze the bar graph to determine the most favorite or least favorite service? The most favorite service will have the tallest bar on the bar graph, and the least favorite service will have the shortest bar on the bar graph.

After students have completed their work on their chart paper and on their Student Journals, have students display their chart paper to use for the next part of the Explore activity.

Part II: Interpreting Data on a Bar Graph 1.

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Using the displayed bar graphs represented on the chart paper for each group’s business from Part I, students will be interpreting the data responses represented on each bar graph. Explain that students will rotate back through each business station and record which service had the most votes and which service had the least votes on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP

Project these questions to guide student collaboration or your class discussions about each graph.

DOK-1 What is the scale of this bar chart? Answers may vary. The scale of the y-axis is counting by 1.

DOK-2 How can you determine which service has the most votes? The service with the tallest bar is the service with the most votes.

DOK-2 How can you determine which service has the least votes? The service with the shortest bar is the service with the least votes.

DOK-2 How can you determine the value of the amount of votes each bar received? I can determine what the scale is counting by and see where the height of the bar stops in relation to that scale in order to ﬁnd the value. © Accelerate Learning Inc. - All Rights Reserved

5. 6.

Engage

Explore

Explain

Elaborate

Evaluate

Once students have recorded the data responses from each business onto their Student Journals, challenge students to work with their groups to create a new bar graph. The blank bar graph on their Student Journals will represent the service with the most votes from each business. Each group will then write two questions related to the bar graph and answer their own questions. Monitor and talk with students as needed to check for understanding by using the following questions: a.

DOK-2 What title can we give our bar graph? Answers may vary. We could title our bar graph Favorite Services since the bar graph represents the service with the most votes from each business.

DOK-2 What do you think would be the best scale for the y-axis? y-axis? Answers may vary. I think the best scale would be to count by two since these votes have a bigger range and the most votes goes all the way up to 15.

Intervention

Acceleration

FACILITATION TIP Before asking students to write two questions, provide some examples and some constraints.

REPRESENT AND INTERPRET DATA

Home

c. DOK-2 How can you represent the value of each service on the bar graph? I can draw a bar for each service that goes up to the number on the scale that is being represented. d.

8. 9.

DOK-3 What questions can we write that can be answered by the information represented on the bar graph? Answers may vary. We could have students put the services in order from least to greatest/greatest to least, ﬁnd the difference or sum of services, total votes for all the services, or determine the service with the most or least votes.

After students are done creating their bar graphs and writing and answering their questions related to the bar graph, have each group share a question they wrote and how they answered it using their bar graph. Allow students time to work with their groups 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 How are bar graphs useful? Bar graphs give a helpful visual model of the value of each bar, and we can easily use those bars to determine which bar is the most or the least. DOK-3 Why is it important to label the x-axis, yy-axis, -axis, and title? If the graph has no title, no one knows what is being examined. If the axes are not labeled, no one understands what the data means. They must be labeled and also include a scale. If you don’t have a scale, you can’t determine the value of the bar. DOK-3 In what situations might you want to use a bar graph? You might want to use a bar graph when you are determining or comparing the values of different categories. DOK-3 How can you decide the scale of the yy-axis? -axis? I look at the least and greatest values from the data responses. Then, I make sure the scale has a large enough range, or spread, to ﬁt all the data in and also that not a lot of the space in the graph is wasted. DOK-2 How did you make sure you graphed all the data correctly on your bar graph? I needed to analyze the scale to determine what it was counting by. Then, we used the value of the data response and drew a bar up to its value represented on the scale. DOK-3 Where have you seen a bar graph used in real life? I also saw a bar graph when I watched a weather report and we were in a drought. It showed a bar graph of our normal rainfall during a year and then the rainfall for our current year during the drought so we could compare them.

FACILITATION TIP Include some additional real-world examples of bar graphs in this Math Chat. Consider using student social studies or science books as sources.

419

REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 2 — Bar Graphs Post-Explore 1. FACILITATION TIP Continue to review horizontal, vertical, columns, rows, and the two axes.

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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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Represent and Interpret Data Explore 3 — Interpret Mean ACTIVITY PREPARATION Students analyze numerical data in real-world problems and interpret the mean as a balance point, an equal share, or leveling out.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.7 Look for and make sense of structure.

Preparation

Materials Printed • • •

• • •

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

Reusable • • •

• • •

1 Dry-erase marker (per group) 60 Centimeter cubes (per group) 24 Linking cubes (per group)

•

Plan to have students work in groups of 2 or 3 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Scenario Cards, on card stock for durability, for each group. Do not cut the cards apart. Students will need to keep cards for Part I, Part II, and Part III separate. Gather a set of 60 centimeter cubes and 24 linking cubes for each group. Gather enough dry-erase markers for each group to have one. For students who need more support in recalling information, please see our Open Number Line and Mean, Median, Mode, Range 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. (Number Lines and Linking Cubes)

PROCEDURE AND FACILITATION POINTS Part I: Mean as Balance Point 1. 2. 3. 4.

FACILITATION TIP Point out that mathematicians measure and interpret data in different ways and that one of these measures is called center. Center usually represents the typical value of the entire data set. Mean is a measure of center.

5. 6. 7.

Give a Student Journal to each student and a set of Scenario Cards, centimeter cubes, and linking cubes to each group. Explain to students that they will use the Scenario Cards for Part I to complete Part I on their Student Journals. Encourage each group of students to draw the same two number lines from their Student Journals onto their desks. Instruct students to read each Scenario Card, order the data from least to greatest, and use centimeter cubes or linking cubes to create a line plot using the two number lines on their desks to represent the data. Students will analyze the line plots to determine the balance point of the data. This balance point is also called the mean. Encourage students to discuss their observations with their groups as they work through Part I. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

422

DOK-1 How can we use the line plot to represent the data? Answers may vary. For each data point being represented, we can place a centimeter cube or linking cube above that value represented on the number line. If we have more than one data point represented on a value, we will stack those data points in a vertical column. © Accelerate Learning Inc. - All Rights Reserved

Explore

Explain

Elaborate

Evaluate

DOK-2 When someone is trying to balance on a board or an object, where would be the best place to have a balancing point: the left side, right side, or middle of the object? Explain. The best place to balance would be in the middle. If you were trying to balance on the left or right side, the object would tilt in the wrong direction and would not balance.

DOK-2 What do you think of when you read the term balance point when it comes to interpreting data? I think it is the point in the data where the sums of the data on either side of it are equal. It is like a balance where the left side of the scale balances with the right side of the scale.

Engage

DOK-2 How do you think the mean would be affected if we added more data points above the balance point? That number would no longer be the balance point. The balance point would have to move higher.

After completing both scenarios for Part I, have students work with their groups to answer the reﬂection question for this part and then quickly discuss their response. a.

DOK-2 What is the balance point? How can you ﬁnd the balance point in a set of data? Answers may vary. It is a point on a line plot where the data is balanced. This means the sum of the data points to the right of the balance point is equal to the sum of the data points to the left of the balance point.

Part II: Mean as Equal Shares 1.

2. 3.

5. 6.

Read the following scenario to the class: The Martinez family is making party favors for Anna’s tenth birthday party! Anna is trying to sort through three different types of candy she wants to split equally into each bag. Each Scenario Card shows how the candy is currently distributed among the ﬁve bags. Explain to students that they will collaborate and use centimeter cubes to model each distribution of candy from each Scenario Card. Challenge each group to ﬁrst analyze each Scenario Card and represent them by drawing, on their desks, the number of bags from each card using their dry-erase marker. Students can also use the blank candy bags represented on their Student Journals to help them solve. Each group will then use their centimeter cubes and place them within those drawn circles to represent how many pieces of candy each bag is starting with. Encourage students to then redistribute the cubes so each bag has an equal share. The number of pieces of candy that will go into each bag is called the “mean.” Encourage students to discuss their observations with their groups as they work through Part II. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What did you do ﬁrst to determine the equal share? Answers may vary. I combined the cubes from the bags into one pile so I could pass them out one at a time to each bag.

DOK-2 If another friend decided to join the party, Anna would need 6 party favor bags. How would adding a bag affect the equal shares for each type of candy? If I added a bag, the number of candies in each bag would decrease. For example, we had 4 Sugar Snaps in each of the 5 bags, but if I had 6 bags, there would be 3 Sugar Snaps in each bag with 2 pieces left over.

DOK-3 How does this model show the mean? How is it different from the balance point? This model redistributes the total number of candies in the bags so that each has an equal amount. It is an equal share of the data as opposed to data that is equal on both sides of a point on a line plot.

Intervention

Acceleration

FACILITATION TIP Act out this process. Set up a life-size number line on the ﬂoor. Have one student represent each data point in this example. Have the student standing at “3 cookies” hold up their arms at the same height, with their palms faceup, to represent a balanced scale with 2 students to the left and 2 to the right. Ask one student on the left to move to the right, and have the student simulating the scale tip their arms to the right to show that there is no longer an even balance.

REPRESENT AND INTERPRET DATA

Home

FACILITATION TIP Take time to put mean, median, mode, and range on your word wall or large anchor chart. Use Picture Vocabulary and have students record necessary deﬁnitions on their Student Journals.

423

REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 3 — Interpret Mean 7.

Allow each group enough time to model and discuss each Scenario Card, record their work, and answer the reﬂection questions for Part II on their Student Journals.

Part III: Mean as Leveling Out 1.

3. FACILITATION TIP

Read the following scenario to the class: Marco and Candace are building towers out of linking cubes. They have a big box full of linking cubes. Some of the linking cubes are attached, and some are not. Marco and Candace pull out a collection of towers from the box and then work together to level out the towers so each tower in a collection is the same height. Explain to students that with their groups, they will use linking cubes to model each collection of towers from each Scenario Card. They will then move cubes around to level out the towers. The number of cubes in each leveled-out tower is called the mean. Encourage students to discuss their observations with their groups as they work through Part III. Monitor and assess students as they are working by asking the following question:

Ask students to observe whether the heights of the original towers became taller or shorter, which collection showed the greatest change in tower heights, and why they think that was the case. (Outliers and a wide range or variability impact the mean value.)

FACILITATION TIP

Math Chat

Be prepared with some relevant real-world examples of when measures of center are used. Consider your students’ interests, hobbies, grade point averages, sports, and monthly bills.

•

• •

•

DOK-2 How is leveling out similar to equal shares? For both, I started with unequal groups of objects and then worked to ﬁnd the mean.

After groups complete Part III, students will individually 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.

DOK-1 What are some scenarios in which finding the balance point would be the best way to determine the mean? When I can see symmetry in data represented on a line plot or numbers ordered least to greatest. DOK-1 What are some scenarios in which equal shares would be the best way to determine the mean? I would use equal shares if there was a situation in which I needed to distribute the same amount of something to each person/group. DOK-1 How did you define mean? Mean is the middle point in a set of data; it is the average. DOK-2 What similarities and differences do you see between the balance point, equal shares, and leveling out? They all find the middle points. I noticed that with balance point, we looked for distance between the points, but leveling out and equal shares distribute something evenly. DOK-1 What operation(s) are you modeling as you find the mean of a data set? I noticed that when we leveled out and used equal shares, we first put the data points together and then distributed them, so addition then division.

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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Home

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Represent and Interpret Data Explore 4 — Mean, Mode, Median, and Range ACTIVITY PREPARATION Students analyze data tables and line plots and interpret the data in order to determine the mean, mode, median, and range of whole number values.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Set of Data Cards (per class) 1 Set of Data Work Mats (per group) 1 Exit Ticket (per student)

•

Reusable • • • •

• •

2 Sheet protectors (per group) 1 Dry-erase marker (per group) 1 Set of 100 linking cubes (per group) 1 Resealable bag (per group)

•

Plan to have students work in groups of 2 or 3 to complete this activity. Print a Student Journal and an Exit Ticket for each student. Print a set of Data Cards, on card stock for durability, for the class. Cut each card apart, and place the cards around the room. Print a set of Data Work Mats, on card stock for durability, for each group of students. To create an erasable surface, place each Data Work Mat in a separate sheet protector. Gather enough dry-erase markers for each group to have one. Create a set of 100 linking cubes for each group, and place them in a resealable bag. For students who need more support in recalling information, please see our Open Number Line and Mean, Median, Mode, Range 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 and Linking Cubes)

PROCEDURE AND FACILITATION POINTS 1.

FACILITATION TIP The Data Work Mat contains many new concepts: mode, median, and range. It might be valuable to discuss the meaning of each measure of data and what it reveals about a data set. (Mean, mode, and median are measures of center. They describe typical values, and they relate to the distribution of the data. Range is the measure of spread; it describes how far apart the data values are and relates to the variability of data.) 426

2. 3.

4. 5.

Read the following scenario to the class: The job of a sports data analyst is to collect on-field and off-field data from a variety of sports and players and analyze and interpret that data to give meaningful insights and reports. These insights and reports help fans make decisions on games if they are part of a fantasy league. The data also benefits coaches so they know how to best prepare their team for an upcoming game. You have just been hired as a sports data analyst for a local basketball team. It is your job to analyze the given data and report back to the head coach of the team. Give a Student Journal to each student and a set of Data Work Mats, a set of linking cubes, and a dry-erase marker to each group. Explain to students that around the room are Data Cards for the different basketball teams they need to collect data on and analyze. They must choose a card to start with and locate that team on their Student Journals. Each group will record their numerical data from least to greatest in the correct location on their Student Journals. Instruct students to return to their desks after they have collected their data and to work with their groups to analyze that data using their Data Work Mats. Explain to students that they will use their Data Work Mats to determine the mean, mode, median, and range of their sports data. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Encourage each group of students to use the information on their Data Work Mats about mean, mode, median, and range to help them explore these new vocabulary terms. Remind students that in the previous Explore they learned about the vocabulary word mean and that they can use their linking cubes to make equal shares of the data they collected from the Data Cards. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

Acceleration

FACILITATION TIP Continue to review the meanings of each of these vocabulary words and reassure students that they will use these math concepts in upper grades and often in real life. FACILITATION TIP

In addition to confirming their understanding of how to calculate the i. DOK-1 What do you notice about the vocabulary term mean mean? I notice mean, mode, median, and range, have students make comparisons between that the definition of mean is that we are going to equally share the these measures and discuss what insights values. each provides when interpreting a data ii. DOK-2 How do you think we can find the mean by using the strategy set. Ask them to consider which measures of equal share? In order to determine the mean, we must create are almost always the same. (The mean, the value of each piece of data in the scenario. We can then add all median, and mode are usually close in size those cubes together and distribute them equally to all the players. because they all measure center. When an When each player has the same amount of linking cubes, then we outlier is present, median is often the best have found the mean. representation of center.) iii. DOK-1 What are some other strategies we can use to find the mean of the given data? We can also find the balance point on the line plot or use leveling out to level out the linking cubes so each player has the same amount of cubes. STEMscopes Tip Mean questions

Mode questions

i. DOK-1 What do you notice about the vocabulary term mode? I notice that the deﬁnition of mode is that it is the number that occurs the most. ii. DOK-2 What is the mode if all the numbers occur the same number of times? There will be no mode if all the numbers occur the same number of times. iii. DOK-2 Do you think a set of data can have more than one mode? Explain. Yes, if a data set has multiple numbers that occur the most, then all those numbers will be the mode. The term for this is multimodal. c.

Intervention

REPRESENT AND INTERPRET DATA

Home

Median questions i. DOK-1 What do you notice about the vocabulary term median median? I notice that the definition of the word median is that it is the middle number of my data that is represented from least to greatest. ii. DOK-1 How do I find the median if there are two middle numbers in a data set? If we have two middle numbers, then I will need to add those middle numbers together and divide by two because we used two data values to find the median.

Range question i. DOK-1 What do you notice about the vocabulary term range? I notice that the deﬁnition of the word range is that it is the difference between the greatest number in the data set and the smallest number in the data set.

10.

Once students have completed their Data Work Mats for their selected basketball teams, they will individually record their data ﬁndings for mean, mode, median, and range on their Student Journals. Student groups will then ﬁnd another basketball team’s Data Card around the room and repeat the process.

FACILITATION TIP Before calculating the average of 2 middle numbers, allow students to conceptualize the process by ﬁnding the middle number in a listed set of values. For example, in the Los Angeles data set, the two middle numbers are 4 and 6. List 4, 5, 6, and observe that the middle number is 5. Then, calculate (4 + 6)/2 to see that the result is also 5.

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REPRESENT AND INTERPRET DATA

Represent and Interpret Data Explore 4 — Mean, Mode, Median, and Range 11. 12. 13.

14.

Continue monitoring and asking the guiding questions as necessary. Guide and correct any misunderstandings. Allow students to complete the data for each card and record their ﬁndings on their Student Journals. Students will individually answer the reﬂection questions on their Student Journals after they have completed the work for the mean, mode, median, and range for each basketball team. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat FACILITATION TIP Depending on your students’ interests, include some real-world examples about mean, median, mode and range as they relate to “likes,” “views,” or “clicks” on media sites.

•

• 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.

•

DOK-3 Why would ﬁnding the mean of a large set of numbers be useful? Finding the mean of a large set of numbers would be useful because when the numbers are pretty close together, you can ﬁnd out the average or the typical value near the center of our data set. DOK-1 What do you notice about the value of the mean and the median for each basketball team? I notice that the mean and median are usually pretty close in value. DOK-2 Why do you think the mean and median are pretty close in value? The average value of a data set and the middle point of the data are usually pretty close in value when all the data points are close in value. DOK-2 Why do you think the values of the mean and median might be far apart? I think the values of the mean and median might be far apart if the data set has a wide spread of numbers. DOK-2 Why do you think the mode is important? I think the mode is important because you can see which value occurred the most. It can be important when it pertains to a basketball team because you can see which players have the greatest number of rebounds, points, or minutes playing in a game. DOK-2 Why do you think the range is important? The range is important because you can determine if there is a big difference or a small difference between your set of numbers.

Post-Explore 1. 2. 3. 4.

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Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT AND INTERPRET DATA

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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

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

Bar Graphs 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

Interpret Mean

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

Mean, Mode, Median, and Range

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

430

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 Tea Party

Pharmacist

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 Orchid Report

Represent and Interpret Data

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

REPRESENT AND INTERPRET DATA

Home

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

431

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

432

 Interactive Practice

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

Engage

Explore

Explain

Elaborate

Evaluate Evaluate

Intervention

Acceleration Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Fundamental Questions I can create a statistical investigative question that can be answered by gathering data.

What prompts will be used?

What does mastery look like?

REPRESENT AND INTERPRET DATA

Home

I can graphically represent and describe the distribution of numerical data through line plots.

I can graphically represent and describe the distribution of categorical data through bar graphs.

I can describe and interpret the spread and center of a data distribution.

433

Kindergarten ten Published by Acceler ve, Suite 800, Houston, on, TX 77056. Copyright © 2023, by Acceler Accelerate Learning Inc. All rights reserved. ved. No par partt of this publication may be repr reproduced or distributed in any form or by any means, or stored in a database or retriev retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic onic storage or transmission, tr T

5 Georgia Math Teacher Guide

Grade 5 Teacher Guide

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

ISBN: 979-8-88826-664-9

5 GEORGIA

MATH G5