GRADE 4 VOLUME 1
Volume 1 Topics 1–7 Authors Randall I. Charles Professor Emeritus Department of Mathematics San Jose State University San Jose, California Jennifer Bay-Williams Professor of Mathematics Education College of Education and Human Development University of Louisville Louisville, Kentucky Robert Q. Berry, III Professor of Mathematics Education Department of Curriculum, Instruction and Special Education University of Virginia Charlottesville, Virginia Janet H. Caldwell Professor Emerita Department of Mathematics Rowan University Glassboro, New Jersey Zachary Champagne Assistant in Research Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM) Jacksonville, Florida Juanita Copley Professor Emerita College of Education University of Houston Houston, Texas Warren Crown Professor Emeritus of Mathematics Education Graduate School of Education Rutgers University New Brunswick, New Jersey Francis (Skip) Fennell Professor Emeritus of Education and Graduate and Professional Studies McDaniel College Westminster, Maryland Karen Karp Professor of Mathematics Education School of Education Johns Hopkins University Baltimore, Maryland Stuart J. Murphy Visual Learning Specialist Boston, Massachusetts Jane F. Schielack Professor Emerita Department of Mathematics Texas A&M University College Station, Texas Jennifer M. Suh Associate Professor for Mathematics Education George Mason University Fairfax, Virginia Jonathan A. Wray Mathematics Supervisor Howard County Public Schools Ellicott City, Maryland
Mathematicians Roger Howe Professor of Mathematics Yale University New Haven, Connecticut Gary Lippman Professor of Mathematics and Computer Science California State University, East Bay Hayward, California ELL Consultants Janice R. Corona Independent Education Consultant Dallas, Texas Jim Cummins Professor The University of Toronto Toronto, Canada Reviewers Katina Arnold Teacher Liberty Public School District Kansas City, Missouri Christy Bennett Elementary Math and Science Specialist DeSoto County Schools Hernando, Mississippi Shauna Bostick Elementary Math Specialist Lee County School District Tupelo, Mississippi Samantha Brant Teacher Platte County School District Platte City, Missouri Jamie Clark Elementary Math Coach Allegany County Public Schools Cumberland, Maryland Shauna Gardner Math and Science Instructional Coach DeSoto County Schools Hernando, Mississippi Kathy Graham Educational Consultant Twin Falls, Idaho Andrea Hamilton K-5 Math Specialist Lake Forest School District Felton, Delaware Susan Hankins Instructional Coach Tupelo Public School District Tupelo, Mississippi Barb Jamison Teacher Excelsior Springs School District Excelsior Springs, Missouri Pam Jones Elementary Math Coach Lake Region School District Bridgton, Maine Sherri Kane Secondary Mathematics Curriculum Specialist Lee’s Summit R7 School District Lee’s Summit, Missouri Jessica Leonard ESOL Teacher Volusia County Schools DeLand, Florida Jill K. Milton Elementary Math Coordinator Norwood Public Schools Norwood, Massachusetts Jamie Pickett Teacher Platte County School District Kansas City, Missouri Mandy Schall Math Coach Allegany County Public Schools Cumberland, Maryland Marjorie Stevens Math Consultant Utica Community Schools Shelby Township, Michigan Shyree Stevenson ELL Teacher Penns Grove-Carneys Point Regional School District Penns Grove, New Jersey Kayla Stone Teacher Excelsior Springs School District Excelsior Springs, Missouri Sara Sultan PD Academic Trainer, Math Tucson Unified School District Tucson, Arizona Angela Waltrup Elementary Math Content Specialist Washington County Public Schools Hagerstown, Maryland Copyright © 2020 by Savvas Learning Company LLC. All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms, and the appropriate contacts within the Savvas Learning Company Rights Management group, please send your query to the address below. Savvas Learning Company LLC, 15 East Midland Avenue, Paramus, NJ 07652 Savvas™ and Savvas Learning Company™ are the exclusive trademarks of Savvas Learning Company LLC in the U.S. and other countries. Savvas Learning Company publishes through its famous imprints Prentice Hall® and Scott Foresman® which are exclusive registered trademarks owned by Savvas Learning Company LLC in the U.S. and/or other countries. enVision® and Savvas Realize™ are exclusive trademarks of Savvas Learning Company LLC in the U.S. and/or other countries. Unless otherwise indicated herein, any third party trademarks that may appear in this work are the property of their respective owners, and any references to third party trademarks, logos, or other trade dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Savvas Learning Company products by the owners of such marks, or any relationship between the owner and Savvas Learning Company LLC or its authors, licensees, or distributors. ISBN-13: 978-0-13-495370-0 ISBN-10: 0-13-495370-3 1 18
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SavvasRealize.com Contents TOPICS 1 Generalize Place Value Understanding 2 Fluently Add and Subtract Multi-Digit Whole Numbers 3 Use Strategies and Properties to Multiply by 1-Digit Numbers 4 Use Strategies and Properties to Multiply by 2-Digit Numbers 5 Use Strategies and Properties to Divide by 1-Digit Numbers 6 Use Operations with Whole Numbers to Solve Problems 7 Factors and Multiples 8 Extend Understanding of Fraction Equivalence and Ordering 9 Understand Addition and Subtraction of Fractions 10 Extend Multiplication Concepts to Fractions 11 Represent and Interpret Data on Line Plots 12 Understand and Compare Decimals 13 Measurement: Find Equivalence in Units of Measure 14 Algebra: Generate and Analyze Patterns 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement 16 Lines, Angles, and Shapes Digital Resources at SavvasRealize.com And remember your Interactive Student Edition is available at SavvasRealize.com! Contents F5
TOPIC 1 Generalize Place Value Understanding enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3-ACT MATH Preview: Page Through. . . . . . . . . . . . . . . . . . . . . . . . . . 4 Numbers Through One Million. . . . . . . . . . . . . . . . . . . . . . . 5 Place Value Relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Compare Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Round Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 PROBLEM SOLVING Construct Arguments. . . . . . . . . . . . . . . 21 1-1 1-2 1-3 1-4 1-5 Fluency Review Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 This shows how to find the value of the digits in a number. ones tens hundreds one thousands ten thousands hundred thousands one millions ten millions hundred millions ones period thousands period millions period 3 5 6, 0 3 9 F6 Contents Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
TOPIC 2 Fluently Add and Subtract Multi-Digit Whole Numbers enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Finding Sums and Differences with Mental Math. . . . . . . 37 Estimate Sums and Differences . . . . . . . . . . . . . . . . . . . . . . 41 Add Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Add Greater Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Subtract Whole Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Subtract Greater Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . 57 Subtract Across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 PROBLEM SOLVING Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 65 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 This shows one way to add whole numbers. 1 9, 1 263 + 7,951 _ 17,214 F7 Contents SavvasRealize.com
TOPIC 3 Use Strategies and Properties to Multiply by 1-Digit Numbers enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3-ACT MATH Preview: Covered Up . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Multiply by Multiples of 10, 100, and 1,000 . . . . . . . . . . . 81 Estimate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Use Arrays and Partial Products to Multiply. . . . . . . . . . . 89 Use Area Models and Partial Products to Multiply . . . . . 93 More Use Area Models and Partial Products to Multiply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mental Math Strategies for Multiplication. . . . . . . . . . . . 101 Choose a Strategy to Multiply. . . . . . . . . . . . . . . . . . . . . . 105 PROBLEM SOLVING Model with Math . . . . . . . . . . . . . . . . . 109 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 This shows how to use partial products to multiply. 245 × 3 _ 15 120 +600 _ 735 Partial products 6 hundreds 12 tens 15 ones F8 Contents Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
TOPIC 4 Use Strategies and Properties to Multiply by 2-Digit Numbers enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Multiply Multiples of 10. . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Use Models to Multiply 2-Digit Numbers by Multiples of 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Estimate: Use Rounding or Compatible Numbers . . . . . 137 Arrays and Partial Products . . . . . . . . . . . . . . . . . . . . . . . . 141 Area Models and Partial Products. . . . . . . . . . . . . . . . . . . 145 Use Partial Products to Multiply by 2-Digit Numbers . . . 149 PROBLEM SOLVING Make Sense and Persevere. . . . . . . 153 4-1 4-2 4-3 4-4 4-5 4-6 4-7 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 This shows how you can represent partial products to help multiply. 10 3 10 5 100 2 3 5 5 10 2 3 10 5 20 10 3 5 5 50 15 12 F9 Contents SavvasRealize.com
TOPIC 5 Use Strategies and Properties to Divide by 1-Digit Numbers enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 3-ACT MATH Preview: Snack Attack. . . . . . . . . . . . . . . . . . . . . . . . . 168 Mental Math: Find Quotients. . . . . . . . . . . . . . . . . . . . . . . 169 Mental Math: Estimate Quotients. . . . . . . . . . . . . . . . . . . 173 Mental Math: Estimate Quotients for Greater Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Interpret Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Use Partial Quotients to Divide . . . . . . . . . . . . . . . . . . . . . 185 Use Partial Quotients to Divide: Greater Dividends. . . . 189 Use Sharing to Divide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Continue Sharing to Divide . . . . . . . . . . . . . . . . . . . . . . . . 197 Choose a Strategy to Divide. . . . . . . . . . . . . . . . . . . . . . . . 201 PROBLEM SOLVING Model with Math . . . . . . . . . . . . . . . . . 205 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 5-10 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 This shows how place value can help you divide. 13 R3 4⟌ ___ 55 − 40 _ 15 − 12 _ 3 3 10 } F10 Contents Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
TOPIC 6 Use Operations with Whole Numbers to Solve Problems enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Solve Comparison Problems . . . . . . . . . . . . . . . . . . . . . . . 225 Continue to Solve Comparison Problems . . . . . . . . . . . . 229 Model Multi-Step Problems. . . . . . . . . . . . . . . . . . . . . . . . 233 More Model Multi-Step Problems . . . . . . . . . . . . . . . . . . 237 Solve Multi-Step Problems. . . . . . . . . . . . . . . . . . . . . . . . . 241 PROBLEM SOLVING Make Sense and Persevere. . . . . . . 245 6-1 6-2 6-3 6-4 6-5 6-6 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 This shows how you can represent a comparison situation. 3 42 n times as many F11 Contents SavvasRealize.com
TOPIC 7 Factors and Multiples enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 3-ACT MATH Preview: Can-Do Attitude . . . . . . . . . . . . . . . . . . . . . 260 Understand Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 PROBLEM SOLVING Repeated Reasoning . . . . . . . . . . . . . . 269 Prime and Composite Numbers . . . . . . . . . . . . . . . . . . . . 273 Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 7-1 7-2 7-3 7-4 7-5 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G1 This shows how you can use arrays to model factor pairs for a number. Copyright © SAVVAS Learning Company LLC. All Rights Reserved. F12 Contents
TOPIC 8in volume 2 Extend Understanding of Fraction Equivalence and Ordering enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Equivalent Fractions: Area Models . . . . . . . . . . . 293 Equivalent Fractions: Number Lines. . . . . . . . . . 297 Generate Equivalent Fractions: Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Generate Equivalent Fractions: Division . . . . . . 305 Use Benchmarks to Compare Fractions . . . . . . . 309 Compare Fractions. . . . . . . . . . . . . . . . . . . . . . . . . 313 PROBLEM SOLVING Construct Arguments. . . . . 317 8-1 8-2 8-3 8-4 8-5 8-6 8-7 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 TOPIC 9in volume 2 Understand Addition and Subtraction of Fractions enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 3-ACT MATH Preview: Just Add Water . . . . . . . . . . . . . . . 332 Model Addition of Fractions . . . . . . . . . . . . . . . . 333 Decompose Fractions . . . . . . . . . . . . . . . . . . . . . . 337 Add Fractions with Like Denominators . . . . . . . 341 Model Subtraction of Fractions. . . . . . . . . . . . . . 345 Subtract Fractions with Like Denominators . . . 349 Add and Subtract Fractions with Like Denominators . . . . . . . . . . . . . . . . . . . . . . . . 353 Model Addition and Subtraction of Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Add Mixed Numbers. . . . . . . . . . . . . . . . . . . . . . . 361 Subtract Mixed Numbers . . . . . . . . . . . . . . . . . . . 365 PROBLEM SOLVING Model with Math. . . . . . . . 369 9-1 9-2 9-3 9-4 9-5 9-6 9-7 9-8 9-9 9-10 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 F13 Contents SavvasRealize.com
Copyright © SAVVAS Learning Company LLC. All Rights Reserved. TOPIC 10in volume 2 Extend Multiplication Concepts to Fractions enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 Fractions as Multiples of Unit Fractions. . . . . . . 385 Multiply a Fraction by a Whole Number: Use Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Multiply a Fraction by a Whole Number: Use Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Solve Time Problems. . . . . . . . . . . . . . . . . . . . . . . 397 PROBLEM SOLVING Model with Math. . . . . . . . 401 10-1 10-2 10-3 10-4 10-5 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 TOPIC 11in volume 2 Represent and Interpret Data on Line Plots enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 3-ACT MATH Preview: It’s a Fine Line . . . . . . . . . . . . . . . . 416 Read Line Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Make Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Use Line Plots to Solve Problems . . . . . . . . . . . . 425 PROBLEM SOLVING Critique Reasoning. . . . . . . 429 11-1 11-2 11-3 11-4 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 F14 Contents
TOPIC 12in volume 2 Understand and Compare Decimals enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Fractions and Decimals. . . . . . . . . . . . . . . . . . . . . 445 Fractions and Decimals on the Number Line. . . 449 Compare Decimals . . . . . . . . . . . . . . . . . . . . . . . . 453 Add Fractions with Denominators of 10 and 100. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 Solve Word Problems Involving Money. . . . . . . 461 PROBLEM SOLVING Look For and Use Structure . . . . . . . . . . . . . . . . . 466 12-1 12-2 12-3 12-4 12-5 12-6 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 TOPIC 13in volume 2 Measurement: Find Equivalence in Units of Measure enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 3-ACT MATH Preview: A Pint’s a Pound . . . . . . . . . . . . . . 480 Equivalence with Customary Units of Length. . . 481 Equivalence with Customary Units of Capacity. . .485 Equivalence with Customary Units of Weight . . . 489 Equivalence with Metric Units of Length. . . . . . 493 Equivalence with Metric Units of Capacity and Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Solve Perimeter and Area Problems. . . . . . . . . . 501 PROBLEM SOLVING Precision . . . . . . . . . . . . . . . 505 13-1 13-2 13-3 13-4 13-5 13-6 13-7 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 F15 Contents SavvasRealize.com
Copyright © SAVVAS Learning Company LLC. All Rights Reserved. TOPIC 14in volume 2 Algebra: Generate and Analyze Patterns enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Number Sequences . . . . . . . . . . . . . . . . . . . . . . . . 521 Patterns: Number Rules . . . . . . . . . . . . . . . . . . . . 525 Patterns: Repeating Shapes . . . . . . . . . . . . . . . . . 529 PROBLEM SOLVING Look For and Use Structure . . . . . . . . . . . . . . . . . 533 14-1 14-2 14-3 14-4 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 541 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 TOPIC 15in volume 2 Geometric Measurement: Understand Concepts of Angles and Angle Measurement enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 3-ACT MATH Preview: Game of Angles . . . . . . . . . . . . . . . 548 Lines, Rays, and Angles. . . . . . . . . . . . . . . . . . . . . 549 Understand Angles and Unit Angles. . . . . . . . . . 553 Measure with Unit Angles . . . . . . . . . . . . . . . . . . 557 Measure and Draw Angles . . . . . . . . . . . . . . . . . . 561 Add and Subtract Angle Measures . . . . . . . . . . . 565 PROBLEM SOLVING Use Appropriate Tools. . . . 569 15-1 15-2 15-3 15-4 15-5 15-6 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 577 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 F16 Contents
TOPIC 16in volume 2 Lines, Angles, and Shapes enVision®STEM Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 Review What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 Pick a Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Classify Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . 589 Classify Quadrilaterals. . . . . . . . . . . . . . . . . . . . . 593 Line Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 Draw Shapes with Line Symmetry. . . . . . . . . . . 601 PROBLEM SOLVING Critique Reasoning. . . . . . . 605 16-1 16-2 16-3 16-4 16-5 16-6 Fluency Practice Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 Vocabulary Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610 Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 Topic Assessment Practice . . . . . . . . . . . . . . . . . . . . . . . . . . 613 Topic Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 F17 Contents SavvasRealize.com
Math Practices and Problem Solving Handbook I The Math Practices and Problem Solving Handbook is available at SavvasRealize.com. Math Practices Problem Solving Guide Problem Solving Recording Sheet Bar Diagrams Math Practices and Problem Solving Handbook • Objects • Grid Paper • Rulers • Technology • Paper and Pencil Some Math Tools 5QOG 9C[U VQ 4GRTGUGPV|2TQDNGOU • Draw a Picture • Make a Bar Diagram • Make a Table or Graph • Write an Equation Math practices can help you solve problems. /CMG 5GPUG QH VJG 2TQDNGO 4GCUQP #DUVTCEVN[ CPF 3WCPVKVCVKXGN[ • What do I need to find? • What given information can I use? • How are the quantities related? 6JKPM #DQWV 5KOKNCT 2TQDNGOU • Have I solved problems like this before? 2GTUGXGTG KP 5QNXKPI VJG 2TQDNGO /QFGN YKVJ /CVJ • How can I use the math I know? • How can I represent the problem? • Is there a pattern or structure I can use? 7UG #RRTQRTKCVG 6QQNU 5VTCVGIKECNN[ • What math tools could I use? • How can I use those tools strategically? %JGEM VJG #PUYGT /CMG 5GPUG QH VJG #PUYGT • Is my answer reasonable? %JGEM HQT 2TGEKUKQP • Did I check my work? • Is my answer clear? • Did I construct a viable argument? • Did I generalize correctly? 2TQDNGO 5QNXKPI )WKFG 11 Math Practices and Problem Solving Handbook Math Practices and Problem Solving Handbook • Objects • Grid Paper • Rulers • Technology • Paper and Pencil Som Math Tools 5QOG 9C[U VQ 4GRTGUGPV|2TQDNGOU • Draw a Picture • Make a Bar Diagram • Make a Table or Graph • Write an Equation Math practices can help you solve problems. /CMG 5GPUG QH VJG 2TQDNGO 4GCUQP #DUVTCEVN[ CPF 3WCPVKVCVKXGN[ • What do I need to find? • What given information can I use • How are the quantities related? 6JKPM #DQWV 5KOKNCT 2TQDNGOU • Have I solved problems like this before? 2GTUGXGTG KP 5QNXKPI VJG 2TQDNGO /QFGN YKVJ /CVJ • How can I use the math I know? • How can I represent the problem? • Is there a pattern or structure I can use? 7UG #RRTQRTKCVG 6QQNU 5VTCVGIKECNN[ • What math tools could I use? • How can I use those tools strategically? %JGEM VJG #PUYGT /CMG 5GPUG QH VJG #PUYGT • Is my answer reasonable? %JGEM HQT 2TGEKUKQP • Did I check my work? • Is my answer clear? • Did I construct a viable argument? • Did I generalize correctly? 2TQDNGO 5QNXKPI )WKFG 11 Math Practices and Problem Solving Handbook TH20_SE04_NA_FM_PSH.indd Page 11 3/1/19 12:59 PM f Math Practices and Problem Solving Handbook • Objects • Grid Paper • Rulers • Technology • Paper and Pencil Some Math Tools 5QOG 9C[U VQ 4GRTGUGPV|2TQDNGOU • Draw a Picture • Make a Bar Diagram • Make a Table or Graph • Write an Equation Math practices can help you solve problems. /CMG 5GPUG QH VJG 2TQDNGO 4GCUQP #DUVTCEVN[ CPF 3WCPVKVCVKXGN[ • What do I need to find? • What given information can I use? • How are the quantities related? 6JKPM #DQWV 5KOKNCT 2TQDNGOU • Have I solved problems like this before? 2GTUGX T KP 5QNXKPI VJG 2TQDNGO /QFGN YKVJ /CVJ • How can I use the math I know? • How can I represent the problem? • Is there a patt rn or structure I can use? 7UG #RRTQRTKCVG 6QQNU 5VTCVGIKECNN[ • What a h tools could I use? • How ca I use those tools strategically? %JGEM VJG PU GT /CMG 5GPUG QH VJG #PUYGT • Is my answer reasonable? %JGEM HQT 2TGEKUKQP • Did I check my work? • Is my answer clear? • Did I construct a viable argument? • Did I generalize correctly? 2TQDNGO 5QNXKPI )WKFG 11 Math Practices and Problem Solving Handbook i t/NA/TE/ENV FL Reprint/G2/XXXXXXXXXX/Layout/Inter .. Math Practices and Problem Solving Handbook • Objects • Grid Paper • Rulers • Technology • Paper and Pencil Some Math Tools 5QOG 9C[U VQ 4GRTGUGPV|2TQDNGOU • Draw a Picture • Make a Bar Diagram • Make a Table or Graph • Write an Equation Math practices can help you solve problems. /CMG 5GPUG QH VJG 2TQDNGO 4GCUQP #DUVTCEVN[ CPF 3WCPVKVCVKXGN[ • W at do I need to find? • What given information can I us ? • How are the quantities related? 6JKPM #DQWV 5KOKNCT 2TQDNGOU • Have I solved proble s like this before? 2GTUGXGTG KP 5QNXKPI VJG T N /QFGN YKVJ /CVJ • How can I use the mat I kn • How can I re resent the p ble ? • Is there a pattern or structure I can use? 7UG #RRTQRTKCVG 6QQNU 5VTCVGIKECNN[ • What math tool could I use? • How can I use those tools strategically? %JGEM VJG #PUYGT /CMG 5GPUG QH VJG #PUYGT • Is my answer reasonable? %JGEM HQT 2TGEKUKQP • Did I check my work? • Is my answer clear? • Did I construct a viable argument? • Did I generalize correctly? 2TQDNGO 5QNXKPI )WKFG 11 Math Practices and Problem Solving Handbook Grade 4 Math Practices and Problem Solving Handbook F18 Video 1 Here I listed what I know and what I am trying to find. Mia buys 2 T-shirts for $7 each and a dress that costs $15. She uses a $4 coupon and pays with $40. How much change will Mia get back? Make sense of problems and persevere in solving them. What I know: • Mia has $40 and a $4 coupon. • Mia buys 2 T-shirts for $7 each. • Mia buys a dress for $15. What I need to find: • The amount of change Mia gets. Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, they don’t give up. Thinking Habits Be a good thinker! These questions can help you. • What do I need to find? • What do I know? • What’s my plan for solving the problem? • What else can I try if I get stuck? • How can I check that my solution makes sense? 3 Math Practices and Problem Solving Handbook Video 1 Here I listed what I know and what I am trying to find. Mia buys 2 T-shirts for $7 each and a dress that costs $15. She uses a $4 coupon and pays with $40. How much change will Mia get back? Make s nse of problems and persevere in solving them. What I know: • Mia has $40 and a $4 coupon. • Mia buys 2 T-shirts for $7 each. • Mia buys a dress for $15. What I need to find: • The amount of change Mia gets. Go d math thinkers make sense f problems and think of ways to solve them. If they get stuck, they don’t give up. Thinking Habits Be a good thinker! These questions can help you. • What do I need to find? • What do I know? • What’s my plan for solving the problem? • What else can I try if I get stuck? • How can I check that my solution makes sense? 3 Math Practices and Problem Solving Handbook /G2/XXXXXXXXXX/Layout/Inter Video 1 Here I listed what I know and what I am trying to find. Mia buys 2 T-shirts for $7 each and a dress that costs $15. Sh uses a $4 coupon and pays with $40. How much change will Mia get back? Make sense of problems and per ver in solving them. What I know: • Mia has $40 and a $4 coupon. • Mia buys 2 T-shirts for $7 each. • Mia buys a dress for $15. What I need to find: • The amount of change Mia gets. Good math thinkers make sense of problems a d think of ways t solve them. If they get stuck, they don’t give up. Thinking Habits Be a good thinker! These question can help you. • What do I nee o find? • What do I know? • What’s my plan for solving the problem? • What else can I try if I get stuck? • How can I check that my solution makes sense? 3 Math Practices and Problem Solving Handbook H20_SE04 NA FM MPH indd P Video 1 Here I listed what I know and what I am trying to find. Mia buys 2 T-shirts for $7 each and a dress that costs $15. She us s a $4 cou ays with $40. Ho nge will Mia get back? Make sense of problems and persevere in solving them. What I know: • Mia has $4 4 coupon. • Mia buys 2 T-shirts for $7 each. • Mia buys a dres for $15. What I need to find: • The amount of change Mia gets. Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, they don’t give up. Thinking Habits Be a good thinker! These questions can help you. • What do I need to find? • What do I know? • What’s my plan for s lving the problem? • What else can I try if I get stuck? • How can I check that my solution makes sen e? 3 Math Practices and Problem Solving Handbook
Tools Games Assessment Glossary Visual Learning Activity Practice Interactive Student Edition Video TOPIC 1 Generalize Place Value Understanding Essential Questions: How are greater numbers written? How can whole numbers be compared? How are place values related? Digital Resources Water, wind, and ice can change the shapes of rocks over thousands of years. This is called erosion. Kannesteinen Rock in Norway got its shape from the sea that surrounds it. Mountains, caves, and some islands are kinds of rock formations. Here is a project about caves and greater numbers. Do Research Use the Internet or other sources to find the depths in feet of the 5 deepest caves in the world. Journal: Write a Report Include what you found. Also in your report: • Make a place-value chart that includes the five depths. • Write each depth in expanded form. • Use “greater than” or “less than” to compare the depths of two of the caves. Project: Caves Topic 1 1
Name Vocabulary Choose the best term from the box. Write it on the blank. 1. The numbers 0, 1, 2, 3, 4, and so on are called . 2. A number written using only words is written using a . 3. Replacing a number with a number that tells about how many or how much is called . 4. is the value given to the place of a digit in a number. • expanded form • number line • number name • place value • rounding • whole numbers Comparing Numbers Compare each set of numbers using >, <, or =. 5. 201 ⃝ 21 6. 313 ⃝ 313 7. 289 ⃝ 290 8. 7 ⃝ 70 9. 725 ⃝ 726 10. 82 ⃝ 82 11. 614 ⃝ 641 12. 618 ⃝ 618 13. 978 ⃝ 987 Place Value Tell if the underlined digit is in the ones, tens, hundreds, or thousands place. 14. 9,482 15. 8,000 16. 1,506 17. 8,005 18. 5,100 19. 2,731 Rounding 20. Construct Arguments Use the number line to describe how to round 450 to the nearest hundred. 400 450 500 In this topic, you will learn more about place value. 2 Topic 1 Review What You Know Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Name P ick a Projec t How many bones are in your body? Project: Make a Bones Poster 1A PROJECT 1B PROJECT Would you like to be a construction manager? Project: Design a Building 1C PROJECT Which stadium is your favorite? Project: Create a Stadium Model 3 Topic 1 Pick a Project
Video 3-ACT MATH PREVIEW ○ ○ ○ Math Modeling Page Through Before watching the video, think: Last week, I read an entire book in one sitting. I could not put it down. How long is your reading list? Do you think this pile will take me a year to read? Time to get started. I can … model with math to solve a problem that involves rounding, estimating, and computing with whole numbers. 4 Topic 1 3-Act Math Preview Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Activity Name Lesson1-1 Numbers Through One Million Mrs. Darcy saved ten $100 bills. How much money did Mrs. Darcy save? You can use reasoning in solving a problem. Think about what you know about ten $10 bills to help you find how much money you would have if you had ten $100 bills. Look Back! How did you decide how many zeros you needed to write in your answer? read and write numbers through one million in expanded form, with numerals, and using number names. I can … I can also reason about math. 5 Topic 1 Lesson 1-1 Go Online | SavvasRealize.com
Visual Learning Glossary What Are Some Ways to Write Numbers to One Million? Visual Learning Bridge A The graph shows the attendance at a ballpark over one year. Write the total attendance in expanded form and using number names. Place value is the position of a digit in a number that tells the value of the digit. Baseball Attendance One Year 356,039 300,000 200,000 100,000 B The place-value chart shows periods of three places, starting at the ones period from the right and including the thousands and millions period. Each period is separated by a comma and has three place values: ones, tens, and hundreds. Each digit in 356,039 is written in its place on the chart. Expanded form shows the sum of the values of each digit. Expanded form: 300,000 + 50,000 + 6,000 + 30 + 9 Number name: three hundred fifty-six thousand, thirty-nine ones tens hundreds one thousands ten thousands hundred thousands one millions ten millions hundred millions 6, 0 3 9 3 5 ones period thousands period millions period Notice the comma separates the periods when the number name is written. Convince Me! Look for Relationships What pattern exists in the three places in each period? 6 Topic 1 Lesson 1-1 Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Name Tools Assessment Practice Another Example! 21,125 can be expanded and written in different ways. 20,000 + 1,000 + 100 + 20 + 5 21,000 + 100 + 25 20,000 + 1,100 + 20 + 5 Every form is equal to 21,125. ones thousands millions 2 1, 1 2 5 Do You Understand? 1. What do you notice about the comma in the number on the previous page? 2. Write an example of a number that would include 2 commas. Do You Know How? 3. Write 7,320 in expanded form. 4. Write 55,426 using number names. 5. In a recent year, 284,604 fans attended the hockey playoffs in Chicago. What digit is in the thousands place in 284,604? For 6–8, write each number in expanded form. 6. 7,622 7. 294,160 8. 43,702 For 9–11, write each number name. 9. 1,688 10. 331,872 11. 44,444 7 Topic 1 Lesson 1-1
12. Letitia wrote one thousand, two hundred four in a place-value chart. What mistake did she make? ones tens hundreds one thousands ten thousands hundred thousands one millions ten millions hundred millions 1, 2 4 ones thousands millions 13. Reasoning In 2016, the world’s oldest tree was 5,066 years old. Write the number that is one hundred more using number names. 14. Jessica wants to buy a new team jacket that costs $35. If Jessica saves $5 a week for 4 weeks and $4 a week for 3 weeks, will she have enough money to buy the team jacket? Explain. 15. Vocabulary Drew wrote the following sentence: “A period is a group of any 3 three digits in a number.” Do you agree with Drew? If not, how would you correct him? 16. Higher Order Thinking Two numbers have the same digit in the millions period, the same digits in the thousands period, and the same digits in the ones period. Do these two numbers have the same value? Explain. 17. Wallace writes the number 72,204 in a place-value chart. Select the places that will be filled on the chart. Ones Tens Thousands Ten thousands Hundred thousands 18. Select all that are equal to 96,014. 96,000 + 10 + 4 90,000 + 60,000 + 10 + 4 90,000 + 6,000 + 4 90,000 + 6,000 + 10 + 4 96,000 + 14 Assessment Practice 8 Topic 1 Lesson 1-1 Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Activity Name Lesson1-2 Place Value Relationships Place-value blocks are shown below for 1, 10, and 100. What patterns in the shapes and sizes of the blocks do you see? Use reasoning. You can use place value to analyze the relationship between the digits of a number. Look Back! Describe two ways 100 and 10 are related. recognize that a digit in one place has ten times the value of the same digit in the place to its right. I can … I can also generalize from examples. 9 Topic 1 Lesson 1-2 Go Online | SavvasRealize.com
Visual Learning Glossary How Are Place Values Related to Each Other? Visual Learning Bridge A Kiana had bottle caps. She wants to collect ten times as many bottle caps. How many bottle caps will Kiana have in her collection then? Think place value. 100 bottle caps B A hundreds flat represents 100 bottle caps. 100 C To find ten times as many bottle caps, group 10 hundreds flats together. 1,000 One thousand is ten times 100. 100 × 10 = 1,000 One hundred is one-tenth of 1,000. 1,000 ÷ 10 = 100 Kiana will have 1,000 bottle caps in her collection. Convince Me! Generalize Use place-value blocks to model 1 and 10, 10 and 100, 100 and 1,000. What pattern do you see? 10 Topic 1 Lesson 1-2 Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Tools Assessment Practice Name Another Example! Joe scored 2,000 points on a progressive video game. It took him 5 weeks to get his total point value to 20,000. It took him 3 months to get his total point value to 200,000 points. How many times greater than his first score were his points after 5 weeks? After 3 months? After 5 weeks, Joe’s points were 10 times greater. After 3 months, Joe’s points were 100 times greater. 2,000 ×10= 20,000 20,000 ×10= 200,000 10×10= 100 Do You Understand? 1. Is the value of the 2 in 23,406 ten times as great as the value of the 3? Explain. Do You Know How? For 2, use the relationship between the values of the digits to solve. 2. Write a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864. For 3–5, use the relationship between the values of the digits to solve. 3. Baseten School District bought 5,000 pencils. They are distributing the pencils evenly to 10 schools in the district. How many pencils will each school get? 4. Place Elementary School is raising money. They raise $90 a week. How long will it take them to raise $900? 5. A donation of 50 rulers was given to Value Elementary School. The school had 10 times as many erasers donated. How many erasers were donated? 11 Topic 1 Lesson 1-2
6. What can you say about the 3s in 43,862 and 75,398? 7. Critique Reasoning Mia says in 5,555, all the digits have the same value. Is Mia correct? Explain. 8. Number Sense In 1934, there was an extreme drought in the Great Plains. In the number 1,934, is the value of the 9 in the hundreds place ten times as great as the value of the 3 in the tens place? Explain. 9. Critique Reasoning Vin says in 4,346, one 4 is 10 times as great as the other 4. Is Vin correct? Explain. 10. Describe 2 ways to find the area of the shaded rectangle. 5 1 square unit 11. Higher Order Thinking In 448,244, how is the relationship between the first pair of 4s the same as the relationship between the second pair of 4s? 12. Which group of numbers shows the values of the 4s in 44,492? 40,000; 4,000; 400 40,000; 400; 40 4,000; 400; 4 400; 40; 4 13. In which number is the value of the red digit ten times as great as the value of the blue digit? 335,531 335,531 335,531 335,531 Assessment Practice 12 Topic 1 Lesson 1-2 Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Activity Name Lesson1-3 Compare Whole Numbers A robotic submarine can dive to a depth of 26,000 feet. Which oceans can the submarine explore all the way to the bottom? Solve this problem any way you choose. You can model with math. Use what you know about place value to help solve the problem. DATA Ocean Depth Atlantic 28,232 ft Pacific 35,840 ft Indian 23,376 ft Look Back! Which of the oceans listed is the shallowest? Explain. use place value to compare numbers and record my comparisons using <, =, or >. I can … I can also model with math. 13 Topic 1 Lesson 1-3 Go Online | SavvasRealize.com
Visual Learning Glossary How Do You Compare Numbers? Visual Learning Bridge A Earth is not perfectly round. The North Pole is 6,356 kilometers from Earth’s center. The equator is 6,378 kilometers from the center. Which is closer to Earth’s center, the North Pole or the equator? Earth’s Center North Pole: 6,356 km from center Equator: 6,378 km from center The symbol > means “is greater than,” and the symbol < means “is less than.” B Step 1 Write the numbers, lining up places. Begin at the left and compare. 6,356 6,378 The thousands digit is the same in both numbers. C Step 2 Look at the next digit. Compare the hundreds. 6,356 6,378 The hundreds digit is also the same in both numbers. D Step 3 The first place where the digits are different is the tens place. Compare the tens. 6,356 5 tens <7 tens, 6,378 so 6,356 < 6,378. The North Pole is closer than the equator to Earth’s center. Convince Me! Reasoning Is a whole number with 4 digits always greater than or less than a whole number with 3 digits? Explain. 14 Topic 1 Lesson 1-3 Copyright © SAVVAS Learning Company LLC. All Rights Reserved.
Tools Assessment Practice Name Do You Understand? 1. Which place do you use to compare the numbers 60,618 and 60,647? 2. Morocco has a total area of 442,300 square kilometers. Uzbekistan has a total area of 447,400 square kilometers. Use >, <, or =to compare the two areas. Do You Know How? For 3–7, complete by writing >, =, or <in each ⃝ . 3. 2,643 ⃝ 2,643 4. 62,519 ⃝ 64,582 5. 218,701 ⃝ 118,692 6. 32,467 ⃝ 32,467 7. 19,219 ⃝ 19,209 For 8–12, complete by writing >, =, or <in each ⃝ . 8. 22,873 ⃝ 22,774 9. 912,706 ⃝ 912,706 10. 22,240 ⃝ 2,224 11. 30,000 + 5,000 + 3 ⃝ 300,000 + 5,000 12. 40,000 + 2,000 + 600 + 6 ⃝ 40,000 + 3,000 + 10 For 13–17, write which place to use when comparing the numbers. 13. 394,284 328,234 14. 6,716 6,714 15. 32,916 32,819 16. 12,217 11,246 17. 812,497 736,881 Remember to compare each place value, starting on the left! 15 Topic 1 Lesson 1-3
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