california mathematics: grade 3 · 4th grade teacher morrison elementary norwalk, california...

AuthorsAltieri • Balka • Day • Gonsalves • Grace • Krulik Malloy • Molix-Bailey • Moseley • Mowry • Myren Price • Reynosa • Santa Cruz • Silbey • Vielhaber

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, 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 permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027

ISBN-13: 978-0-02-105657-6ISBN-10: 0-02-105657-9

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 10 055/027 15 14 13 12 11 10 09 08 07 06

About the Cover

Located in the Piney Woods region of Texas, Tyler is known as the Rose Capital of America. It is also home to a popular 85-foot, 6-lane, wooden slot car track. The track is designed for 1:32 and 1:24 scale cars. You will learn more about ratios in Chapter 6.

About the Graphics

Colored Truchet bands. Created with Mathematica.A random 2D Truchet image is constructed. The connected arcs of the image are identified and randomly colored in a band-like manner. For more information, and for programs to construct such graphics, see: www.wolfram.com/r/textbook.

iii

Start SmartChapter 1 Place Value and Number Sense

Chapter 2 Addition

Chapter 3 Subtraction

Chapter 4 Multiplication Concepts and Facts

Chapter 5 More Multiplication Facts

Chapter 6 Division Concepts and Facts

Chapter 7 More Division Facts

Chapter 8 Measurement: Customary System

Chapter 9 Measurement: Metric System

Chapter 10 Measurement and Geometry

Chapter 11 Statistics: Data, Graphs, and Probability

Chapter 12 Fractions

Chapter 13 Fractions and Decimals

Chapter 14 Multiply by One-Digit Numbers

Chapter 15 Divide by One-Digit Numbers

Standards Review

Looking Ahead to Grade 4

iv

Authors

Meet the Authors at ca.gr3math.com

Mary Behr Altieri Putnam/Northern Westchester BOCES Yorktown Heights, New York

Don S. Balka Professor Emeritus Saint Mary’s CollegeNotre Dame, Indiana

Roger Day, Ph.D. Mathematics Department ChairPontiac Township High SchoolPontiac, Illinois

Philip D. Gonsalves Mathematics CoordinatorAlameda County Office of Education and California State University East BayHayward, California

Ellen C. Grace ConsultantAlbuquerque, New Mexico

Stephen Krulik Mathematics ConsultantCherry Hill, New Jersey

Carol E. Malloy Assistant Professor of Mathematics EducationUniversity of North Carolina at Chapel HillChapel Hill, North Carolina

Rhonda J. Molix-Bailey Mathematics ConsultantMathematics by DesignDesoto, Texas

Lois Gordon Moseley Staff DeveloperNUMBERS: Mathematics Professional DevelopmentHouston, Texas

Brian Mowry Independent Math Educational Consultant/Part time Pre-K Instructional SpecialistAustin Independent School DistrictAustin, Texas

Doug Martin Photography

http://ca.gr3math.com

v

Christina L. Myren Consultant TeacherConejo Valley Unified School DistrictThousand Oaks, California

Jack Price Professor Emeritus California State Polytechnic UniversityPomona, California

Mary Esther Reynosa Instructional Specialist for Elementary MathematicsNorthside Independent School DistrictSan Antonio, Texas

Viken Hovsepian Professor of MathematicsRio Hondo CollegeWhittier, California

Rafaela M. Santa Cruz SDSU/CGU Doctoral Program in EducationSan Diego State UniversitySan Diego, California

Robyn Silbey Math Content CoachMontgomery County Public SchoolsGaithersburg, Maryland

Kathleen Vielhaber Mathematics ConsultantSt. Louis, Missouri

Contributing Authors

Donna J. Long Mathematics, ConsultantIndianapolis, Indiana

Dinah Zike Educational Consultant Dinah-Might Activities, Inc.San Antonio, Texas

Doug Martin Photography

vi

Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program. They reviewed the table of contents, the prototype of the Teacher Wraparound Edition, and the California Standards Review chapter.

California Mathematics Advisory Board

Carol CronkMathematics Program SpecialistSan Bernardino City Unified School DistrictSan Bernardino, California

David J. ChamberlainSecondary Mathematics Resource TeacherCapistrano Unified School DistrictSan Juan Capistrano, California

Cheryl L. AvalosMathematics ConsultantRetired TeacherHacienda Heights, California

Ilene FosterTeacher Specialist– MathematicsPomona Unified School DistrictPomona, California

Eppie ChungK-6 TeacherModesto City SchoolsModesto, California

William M. BokeschRancho Bernardo High SchoolSan Diego, California

Patty BrownTeacherJohn Muir ElementaryFresno, California

Lisa Marie CirrincioneMiddle School TeacherLincoln Middle SchoolOceanside, California

Grant A. Fraser, Ph. D.Professor of MathematicsCalifornia State University, Los AngelesLos Angeles, California

File Photo

vii

Suzanne Bocskai FreireTeacherKingswood ElementaryCitrus Heights, California

Arthur K. Wayman, Ph. D.Professor of Mathematics EmeritusCalifornia State University, Long BeachLong Beach, California

Beverly WellsFirst Grade TeacherMineral King Elementary SchoolVisalia, California

Frances Basich WhitneyProject Director, Mathematics K-12Santa Cruz County Office of EducationCapitola, California

John McGuireAssociate PrincipalPacific Union SchoolArcata, California

Beth HolguinTeacherGraystone ElementarySan Jose, California

Juvenal MartinezDual Immersion/ESL InstructorAeolian ElementaryWhittier, California

Donna M. Kopenski, Ed. D.Mathematics Coordinator K-5City Heights Educational CollaborativeSan Diego, California

Kasey St. JamesMathematics TeacherSunny Hills High SchoolFullerton, California

Kelly Mack6th Grade TeacherCaptain Jason Dahl ElementarySan Jose, California

Dr. Donald R. PriceTeacher, Adjunct Professor Rowland Unified School DistrictRowland Heights, California

File Photo

viii

Macmillan/McGraw-Hill wishes to thank the following professionals for their feedback. They were instrumental in providing valuable input toward the development of this program in these specific areas.

Consultants

Mathematical ContentViken Hovsepian Professor of MathematicsRio Hondo CollegeWhittier, California

Grant A. Fraser, Ph.D.Professor of MathematicsCalifornia State University, Los AngelesLos Angeles, California

Arthur K. Wayman, Ph.D.Professor of Mathematics EmeritusCalifornia State University, Long BeachLong Beach, California

AssessmentJane D. GawronskiDirector of Assessment and OutreachSan Diego State UniversitySan Diego, California

Cognitive Guided InstructionSusan B. EmpsonAssociate Professor of Mathematics and Science EducationUniversity of Texas at AustinAustin, Texas

English LearnersCheryl AvalosMathematics ConsultantLos Angeles County Office of Education, RetiredHacienda Heights, California

Kathryn HeinzeGraduate School of EducationHamline UniversitySt. Paul, Minnesota

Family InvolvementPaul Giganti, Jr.Mathematics Education ConsultantAlbany, California

LiteratureDavid M. SchwartzChildren’s Author, Speaker, StorytellerOakland, Califorinia

Vertical AlignmentBerchie HollidayNational Educational ConsultantSilver Spring, Maryland

Deborah A. Hutchens, Ed.D.PrincipalNorfolk Highlands ElementaryChesapeake, Virginia

ix

California Reviewers

Each California Reviewer reviewed at least two chapters of the Student Edition, giving feedback and suggestions for improving the effectiveness of the mathematics instruction.

Sherry G. AndersonTeacher/G.A.T.E. CoordinatorWill Rogers ElementaryLynwood, California

Ysaaca AxelrodKindergarten TeacherEl Monte ElementaryConcord, California

Cathy BullockTeacherCapri ElementaryEncinitas, California

Michelle CallenderTeacherMorgan/Kincaid Preparatory School

of Integrated StudiesVictorville, California

M. Olivia Campos4th Grade TeacherMorrison ElementaryNorwalk, California

Malaura Page Easton, M.S.Kindergarten TeacherLa Pluma SchoolLa Mirada, California

Priscilla S. Edwards5th Grade Classroom TeacherDavid Reese ElementarySacramento, California

Lisa B. Friedberg4th Grade TeacherAlderwood Basics Plus SchoolIrvine, California

Wendy Smith HernandezKindergarten TeacherHerndon-Barstow ElementaryFresno, California

Beth HolguinTeacherGraystone SchoolSan Jose, CA

Kristi IversonFirst Grade TeacherVillage Oaks ElementaryStockton, California

Sheri LeikenTeacherWeathersfield ElementaryThousand Oaks, California

Sarab H. LopesTeacherAnza ElementaryEl Cajon, California

Karen E. Lund5th Grade TeacherMeadow Park ElementaryIrvine, California

Efrain MelendezTeacherLivermore Valley USDLivermore, California

Jean A. NelsonTeacherFremont Elementary SchoolAlhambra, California

Tara PahiaElementary TeacherBear Gulch ElementaryRancho Cucamonga, California

Dr. Donald R. PriceTeacher, Adjunct ProfessorRowland Unified School DistrictRowland Heights, California

Kitty Ritz, M.A.TeacherMonte Vista ElementaryRohnert Park, California

Corinne E. SchwartzFirst Grade TeacherLincrest Elementary SchoolYuba City, CA

Deborah Shapiro5th Grade TeacherNancy CoryLancaster, California

Maureen SmithCurriculum SpecialistFremont Unified School Dist.

(retired 6/2006)Fremont, California

Joseph M. Snodgrass3rd Grade TeacherPark Elementary SchoolAlhambra, California

Marie W. StevensElementary Mathematics

CoordinatorLAUSDLos Angeles, California

Jane TrautClassroom TeacherLang Ranch Elementary SchoolThousand Oaks, California

Rachel C. TrowbridgeTeacherEvergreen ElementarySan Jose, California

Cynthia H. VandemoortelEducatorAlderwood Basics Plus SchoolIrvine, California

Norine YaleTeacherJustin ElementarySimi Valley, California

Dr. Darlene YorkEducation ConsultantAssociate Professor/Antioch

UniversitySeattle, Washington

x

Problem Solving: The Great Giants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Number Sense: Now That’s Hot! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Algebra and Functions: At the Aquarium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Measurement: Measure Away . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Geometry: Food and Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

Statistics, Data Analysis, and Probability: How Fast Can You Go? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

3, 5, 7, 9, 11, 13

Arthur Morris/CORBIS

xi

Are You Ready for Chapter 1? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

1-1 Number Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

1-2 Problem-Solving Skill: Use the Four-Step Plan . . . . . . . . . . . . . . . . . . . . . . . . . .20Explore Math Activity for 1-3: Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

1-3 Place Value through 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

1-4 Place Value through 10,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31

1-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . . .32

1-6 Compare Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

1-7 Order Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38

Problem Solving in Geography: The Mighty Mississippi . . . . . . . . . . . . . . . . . . .42

1-8 Round to the Nearest Ten and Hundred . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

Game Time: Round Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

1-9 Round to the Nearest Thousand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59

California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60

Place Value and Number Sense

CHAPTER

1

California Standards Practice• 27, 31, 37, 41, 51, 59, 60, 61

Higher Order Thinking 19, 27, 30, 37, 41, 46, 51

19, 21, 23, 27, 30, 31, 33, 37, 41, 46, 51, 59

xii

AdditionCHAPTER

2Are You Ready for Chapter 2? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64

2-1 Addition Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65

2-2 Problem-Solving Skill: Estimate or Exact Answer . . . . . . . . . . . . . . . . . . . . . . . .68

2-3 Estimate Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

2-4 Two-Digit Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74

Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77

2-5 Add Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78

Problem Solving in Geography: A Walk in the Park . . . . . . . . . . . . . . . . . . . . . . .82

2-6 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . . .84Explore Math Activity for 2-7: Add Three-Digit Numbers . . . . . . . . . . . . . . . . . . .86

2-7 Three-Digit Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88

Game Time: How Low Can You Go? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

2-8 Add Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

California Standards Practice• 73, 77, 81, 95, 101, 102, 103

Higher Order Thinking 67, 73, 76, 81, 90, 95

67, 69, 73, 76, 77, 81, 85, 87, 95, 101

CORBIS

xiii

SubtractionCHAPTER

3Are You Ready for Chapter 3? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

3-1 Two-Digit Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

3-2 Estimate Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3-3 Subtract Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Problem Solving in Music: The Sounds of the Symphony . . . . . . . . . . . . . . 118

3-4 Problem-Solving Skill: Reasonable Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Explore Math Activity for 3-5:

Subtract Three-Digit Numbers with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . 122

3-5 Three-Digit Subtraction with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

3-6 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 128

3-7 Subtract Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Game Time: Do Not Zero Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

3-8 Subtract Across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3-9 Algebra: Expressions and Number Sentences . . . . . . . . . . . . . . . . . . . . . . . 138

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149



Higher Order Thinking 113, 116, 127, 137, 141

109, 113, 116, 117, 121, 123, 127, 129, 132, 137, 141, 149

xiv

Multiplication Concepts and Facts

CHAPTER

4Are You Ready for Chapter 4? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Explore Math Activity for 4-1: Meaning of Multiplication . . . . . . . . . . . . . . . . . 155

4-1 Multiplication as Repeated Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

4-2 Arrays and Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

4-3 Multiply by 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

4-4 Multiply by 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Game Time: Factor Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

4-5 Problem-Solving Skill: Extra or Missing Information . . . . . . . . . . . . . . . . . . . 172

4-6 Multiply by 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

4-7 Multiply by 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Problem Solving in Science: Lots of Arms and Legs . . . . . . . . . . . . . . . . . . . . 182


4-9 Multiply by 0 and 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195




156, 159, 163, 166, 167, 170, 176, 181, 185, 188, 195

Ellen McKnight/Alamy Images

xv

More Multiplication Facts

CHAPTER

5Are You Ready for Chapter 5? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200Explore Math Activity for 5-1: Multiplication Table . . . . . . . . . . . . . . . . . . . . . . . . 201

5-1 Multiply by 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

5-2 Multiply by 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Game Time: Three in a Row . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

5-3 Problem-Solving Strategy: Look for a Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . 212

5-4 Multiply by 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214


5-5 Multiply by 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

5-6 Multiply by 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225


5-8 Algebra: Associative Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

Problem Solving in Art: Not Just a Blanket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

5-9 Algebra: Find a Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245




202, 205, 208, 213, 216, 217, 221, 224, 227, 231, 237, 245

xvi

Division Concepts and Facts

CHAPTER

6Are You Ready for Chapter 6? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250Explore Math Activity for 6-1: Understand Division . . . . . . . . . . . . . . . . . . . . . . . 251

6-1 Relate Division and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Explore Math Activity for 6-2: Relate Multiplication to Division . . . . . . . . . . . 256

6-2 Relate Multiplication to Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

6-3 Problem-Solving Skill: Choose an Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 262

6-4 Divide by 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264


6-5 Divide by 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

Problem Solving in Community: Communities within Communities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272


6-7 Divide by 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Game Time: Number Cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

6-8 Division Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

ASSESSMENT

Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

California Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288



252, 255, 257, 261, 263, 266, 267, 271, 275, 277, 281, 287

Jim West/The Image Works

xvii

More Division FactsCHAPTER

7Are You Ready for Chapter 7? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292Explore Math Activity for 7-1: Divide Using a Multiplication Table . . . . . . . . 293

7-1 Divide by 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

7-2 Divide by 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

7-3 Problem-Solving Strategy: Make a Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

7-4 Divide by 6 and 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304


Problem Solving in Civics: Stars and Stripes . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

7-5 Divide by 8 and 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

Game Time: Facts Roll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

7-6 Determine Unit Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314


7-8 Algebra: Expressions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

7-9 Algebra: Translate Words to Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335




294, 297, 301, 303, 306, 307, 312, 317, 319, 323, 327

xviii

Measurement: Customary System

CHAPTER

8Are You Ready for Chapter 8? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340Explore Measurement Activity for 8-1: Length to the Nearest Inch . . . . . . 341

8-1 Length to the Nearest Half Inch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

8-2 Customary Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

8-3 Problem-Solving Strategy: Work Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350Explore Measurement Activity for 8-4: Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 352

8-4 Customary Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

Game Time: Capacity Guess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358



8-6 Customary Units of Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Problem Solving in Science: Lengths, Heights, and Weights, Oh My! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

8-7 Convert Units of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377




342, 345, 349, 351, 353, 357, 359, 361, 365, 371, 377

xix

Measurement: Metric System

CHAPTER

9Are You Ready for Chapter 9? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382Explore Measurement Activity for 9-1: Millimeter and Centimeter . . . . . . . 383

9-1 Metric Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Game Time: Hit the Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

9-2 Problem-Solving Strategy: Guess and Check . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

9-3 Metric Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

9-4 Problem-Solving Ivestigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . . 396

9-5 Metric Units of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Problem Solving in Science: A Visit to the Supermarket . . . . . . . . . . . . . . . 402

9-6 Metric Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413



Higher Order Thinking 388, 394, 401, 407

384, 388, 391, 394, 395, 397, 401, 407, 413

John Cancalosi/Peter Arnold, Inc.

xx

Measurementand Geometry

CHAPTER

10Are You Ready for Chapter 10? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

10-1 Geometry: Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

10-2 Measurement: Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422Explore Measurement Activity for 10-3: Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

10-3 Measurement: Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

10-4 Problem-Solving Strategy: Solve a Simpler Problem . . . . . . . . . . . . . . . . . . . 432

10-5 Triangles and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434


10-6 Geometry: Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438


10-8 Geometry: Solid Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

Game Time: Guess the Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

10-9 Complex Solid Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

Problem Solving in Art: Gardens Under Glass . . . . . . . . . . . . . . . . . . . . . . . . . . 450

Explore Measurement Activity for 10-10: Volume . . . . . . . . . . . . . . . . . . . . . . . 452

10-10 Measurement: Find Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465


California Standards Practice• 425, 431, 437, 441, 446, 457, 465, 466, 467

Higher Order Thinking 421, 425, 430, 436, 441, 446, 449, 457

421, 425, 427, 430, 433, 436, 437, 441, 443, 446, 449, 453, 457, 465

PETE OXFORD/Minden Pictures

xxi

Statistics: Data, Graphs, and Probability

CHAPTER

11Are You Ready for Chapter 11? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470Explore Graphing Activity for 11-1: Make a Bar Graph . . . . . . . . . . . . . . . . . . . . 471

11-1 Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

11-2 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

11-3 Problem-Solving Strategy: Make an Organized List . . . . . . . . . . . . . . . . . . . . 480


Game Time: Catch Me if You Can! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

11-4 Identify Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

Problem Solving in Science: Eggs! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

11-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 490Explore Probability Activity for 11-6: Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . 492

11-6 Make Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503



Higher Order Thinking 475, 478, 487, 497

472, 475, 478, 481, 487, 491, 493, 497, 503

xxii

FractionsCHAPTER

12



511, 513, 515, 518, 521, 524, 525, 527, 531, 535, 538, 545

Are You Ready for Chapter 12? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

12-1 Parts of a Whole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

12-2 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 512Explore Math Activity for 12-3: Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . 514

12-3 Find Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

Game Time: Fraction Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

12-4 Problem-Solving Strategy: Draw a Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

12-5 Compare Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525Explore Math Activity for 12-6: Add Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . 526

12-6 Add Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

Problem Solving in Science: The Buzz on Insects . . . . . . . . . . . . . . . . . . . . . . 532Explore Math Activity for 12-7: Subtract Like Fractions . . . . . . . . . . . . . . . . . . . 534

12-7 Subtract Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545


CORBIS

xxiii

Fractions and DecimalsCHAPTER

13Are You Ready for Chapter 13? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550Explore Math Activity for 13-1: Fractions and Decimals . . . . . . . . . . . . . . . . . . . 551

13-1 Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

Game Time: Fractoes and Decimoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

13-2 Hundredths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558


Problem Solving in Science: Continents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562

13-3 Problem-Solving Strategy: Act It Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564Explore Math Activity for 13-4: Fractions, Decimals, and Money . . . . . . . . . 566

13-4 Decimals and Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568


ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579


California Standards Practice• 556, 561, 571, 579, 580, 581

Higher Order Thinking 556, 560, 571

552, 556, 560, 561, 565, 567, 571, 573, 579

xxiv

Multiply by One-Digit Numbers

CHAPTER


14-1 Multiply Multiples of 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

14-2 Problem-Solving Strategy: Use Logical Reasoning . . . . . . . . . . . . . . . . . . . . . 588

14-3 Estimate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590


14-4 Multiply by a One-Digit Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

14-5 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . . . . . . . . . . . . 598Explore Math Activity for 14-6: Multiplication with Rerouping . . . . . . . . . . . . 600

14-6 Multiply Two-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602

14-7 Multiply Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606

Game Time: High and Low . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

14-8 Multiply Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610

Problem Solving in Art: Stamp Collecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621




587, 589, 592, 593, 597, 599, 601, 605, 608, 613, 621

Bill Ross/CORBIS

xxv

Divide by One-Digit Numbers

CHAPTER


15-1 Divide Multiples of 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

15-2 Estimate Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630Explore Math Activity for 15-3: Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634

15-3 Two-Digit Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636


15-4 Problem-Solving Strategy: Work Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

15-5 Three-Digit Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642

Game Time: That’s Close! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645

Problem Solving in Science: Roller Coaster Physics . . . . . . . . . . . . . . . . . . . . 646


15-7 Divide Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

ASSESSMENT


Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659


California Standards Practice• 633, 639, 653, 659, 660, 661


629, 633, 635, 638, 639, 641, 644, 649, 653, 659

xxvi

to Grade 4

Algebra: Function Tables (+/-) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664

Algebra: Function Tables (×/÷) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668

Ordered Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672

Geometry: Congruent Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676

Geometry: Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678


667, 671, 675, 677, 679

California Standards ReviewTips for Success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CA1

Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CA2

Practice by Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CA4

Stockbyte

xxvii

Built-In Workbooks

Extra Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R2

Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R41

Reference

English-Spanish Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R49

Photo Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R69

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R70

Student Handbook

xxviii

California Standards for Mathematics Grade 3

Standard Text of Standard PrimaryCitations

SupportingCitations

Number Sense

1.0 Students understand the place value of whole numbers:

1.1 Count, read, and write whole numbers to 10,000 17–19 24–30

1.2 Compare and order whole numbers to 10,000. 34–43 17–19

1.3 Identify the place value for each digit in numbers to 10,000. 22–30 34–41, 44–46, 48–51

1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

44–51, 70–76, 110–113

1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

24–30

2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:

2.1 Find the sum or difference of two whole numbers between 0 and 10,000.

32–33, 65–67, 74–77, 82–83, 86–87, 107–116, 120–127, 490–491, 640–641

20–21, 68–73, 78–81, 84–85, 88–95, 128–137, 512–513, 588–589

2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.

157–159, 164–181, 184–185, 201–202, 210, 214–216, 218–225

155–156, 226–227

2.3 Use the inverse relationship of multiplication and division to compute and check results.

114–116, 256–261, 264–271, 274–281, 293–301, 304–312, 642–644, 636–638

318–319, 251–255, 262–263, 272–273

2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 × 3 = ̲ ).

585–587, 590–597, 600–608

442–443, 598–599, 614–615

2.5 Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = ̲ ).

627–638, 642–644, 648–649

2.6 Understand the special properties of 0 and 1 in multiplication and division.

186–188, 280–281

2.7 Determine the unit cost when given the total cost and number of units.

314–317, 360–361, 650–653

350–351

2.8 Solve problems that require two or more of the skills mentioned above.

8–3; 8–5; 396–397, 432–433, 648–649

3.0 Students understand the relationship between whole numbers, simple fractions, and decimals:

3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g.,1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4).

514–518, 522–524 509–511, 526–531, 534–539

denotes Key standards

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3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).

526–539

3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.

78–81, 88–95, 610–613, 650–653

512–513, 572–573

3.4 Know and understand that fractions are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).

548–560, 566–571 564–565

Algebra and Functions

1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve number relationships:

1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.

65–67, 138–141, 320–327

182–183, 600–601

1.2 Solve problems involving numeric equations or inequalities. 320–323

1.3 Select appropriate operational and relational symbols to make an expression true (e.g., if 4 ̲ 3 = 12, what operation symbol goes in the blank?).

138–141, 320–323

1.4 Express simple unit coversions in symbolic form (e.g., ̲ inches = ̲ feet × 12).

404–407 368–371

1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if 5 × 7 = 35, then what is 7 × 5? And if 5 × 7 × 3 = 105, then what is 7 × 3 × 5?).

160–163, 228–230

2.0 Students represent simple functional relationships:

2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit).

14–8 314–317

2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4).

212–213, 234–237, 302–303

Measurement and Geometry

1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects

1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure length, liquid volume, and weight/mass.

341–349, 352–357, 362–365, 383–388, 392–394, 398–401, 404–407, EX 8–1; 8–1; 8–2; EX 8–4; 8–4; 8–6; 8–7; CC

385–388, 390–391, 398–401

1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them.

426–431, 442–443, 452–457,

480–481

1.3 Find the perimeter of a polygon with integer sides. 422–425, 432–433,

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1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).

346–349, 9–6 352–357, 362–365, 368–371

2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:

2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).

419–421, 450–451

2.2 Identify attributes of triangles (e.g. two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).

434–436

2.3 Identify attributes of quadrilaterals (e.g. parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).

438–441

2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.

434–441

2.5 Identify, describe, and classify common three–dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, and cylinder).

444–446

2.6 Identify common solid objects that are the components needed to make a more complex solid object.

448–449

Statistics, Data Analysis, and Probability

1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions:

1.1 Identify whether common events are certain, likely, unlikely, or improbable. 484–487

1.2 Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times.

492–493

1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).

476–479 Preparation for 471–475, 492–493

1.4 Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day).

494–497

Mathematical Reasoning

1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing, prioritizing information, and observing patterns

20–21, 32–33, 84–85, 128–129, 172–173, 184–185, 212–213, 226–227, 262–263, 274–275, 302–303, 318–319, 350–351, 390–391,396–397, 442–443, 480–481, 490–491, 520–521, 598–599, 648–649

360–361, 366–367, 426–427, 432–433, 512–513, 640–641

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1.2 Determine when and how to break a problem into simpler parts. 350–351, 432–433, 572–573, 640–641

360–361, 448–453, 585–587, 627–629, 634–635

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results. 74–81, 88–95, 426–427, 590–592, 602–605, 630–633

110–116,120–121, 343–349, 354–357, 362–365, 428–431, 442–443, 452–457, 594–597, 606–608, 650–653

2.2 Apply strategies and results from simpler problems to more complex problems.

585–587, 600–601, 86–87, 155–159,177, 189, 210,225, 253–255, 264–271, 324–327, 343–345, 432–441, 444–453, 452–453, 492–493, 528–531, 536–539, 627–629

2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

20–21, 68–69, 155–159, 203–209, 214–216, 218–224, 251–255, 341–342, 352–353, 396–397, 512–513, 526–527, 564–565, 588–589, 634–635

22–23, 32–33, 84–85, 107–109, 120–127, 160–181, 184–185, 256–261, 274–281, 302–303, 419–421, 426–431, 434–443, 471–479, 490–491, 494–497, 509–511, 514–524, 558–560, 566–567, 636–641

2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

65–67, 324–327, 568–571, 642–644

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

68–73, 383–388 590–592, 630–633

2.6 Make precise calculations and check the validity of the results from the context of the problem.

78–81, 128–132, 134–137, 512–513, 642–644

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.

588–589 74–81, 341–342, 602–604

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

86–95, 138–141, 295–301–306, 310–312, 320–323, 341–342, 404–407, 422–427, 426–427, 448–449, 452–453, 512–513, 551–556

3.3 Develop generalizations of the results obtained and apply them in other circumstances.

494–497 201–202, 293–294, 426–427, 484–487, 610–613

california mathematics: grade 3 · 4th grade teacher morrison elementary norwalk, california...

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