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A u s t r a l i a C a n a d a M e x i c o S i n g a p o r e S p a i n U n i t e d K i n g d o m U n i t e d S t a t e s

Series Authors and Senior ConsultantsMary Lou Kestell • Marian Small

Senior AuthorsHeather Kelleher • Kathy Kubota-Zarivnij • Pat Milot

Betty Morris • Doug Super

AuthorsAndrea Dickson • Jack Hope • Mary Lou Kestell

Pat Milot • Marian Small • Rosita Tseng Tam

Assessment ConsultantDamian Cooper

00-NelsonMathGr6-Prelims 7/20/05 1:57 PM Page iii

Director of PublishingBeverley Buxton

Publisher, MathematicsColin Garnham

Managing Editor, DevelopmentDavid Spiegel

Senior Program ManagerShirley Barrett

Program ManagersColin BissetMary Reeve

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Nelson Mathematics 6

COPYRIGHT © 2006 by Nelson, a division of Thomson CanadaLimited.

Printed and bound in Canada1 2 3 4 08 07 06 05

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Library and Archives CanadaCataloguing in Publication

Nelson mathematics 6 / Mary LouKestell, Marian Small.

Includes index.ISBN 0-17-625971-6

1. Mathematics—Textbooks.I. Kestell, Mary Louise II. Small,Marian III. Title: Nelsonmathematics six.

QA107.2.N436 2005510 C2005-903266-9

Series Authors and Senior ConsultantsMary Lou Kestell, Marian Small

Senior AuthorsHeather Kelleher, Kathy Kubota-Zarivnij, Pat Milot, Betty Morris, Doug Super

AuthorsAndrea Dickson, Jack Hope,Mary Lou Kestell, Pat Milot, Marian Small, Rosita Tseng Tam

Assessment ConsultantDamian Cooper

00-NelsonMathGr6-Prelims 8/3/05 9:49 AM Page iv

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Senior AdvisorDoug DuffLearning SupervisorThames Valley District School BoardLondon, Ontario

AdvisorsDonna AndersonCoal Tyee Elementary SchoolSchool District #68 Nanaimo-LadysmithNanaimo, British Columbia

Keith ChongPrincipalSchool District #41Burnaby, British Columbia

Attila CsiszarMath Helping TeacherSurrey School BoardSurrey, British Columbia

David P. CurtoPrincipalHamilton-Wentworth CatholicDistrict School BoardHamilton, Ontario

Marg CurtoPrincipal of Programs, ElementaryHamilton-Wentworth CatholicDistrict School BoardHamilton, Ontario

Lillian ForsytheRegina, Saskatchewan

Peggy GerrardDr. Morris Gibson SchoolFoothills School DivisionOkotoks, Alberta

Mary GervaisConsultantDurham Catholic District School Board

C. Marie HaukConsultantEdmonton, Alberta

Rebecca KozolSchool District #42Maple Ridge, British Columbia

A. Craig LoewenAssociate ProfessorUniversity of LethbridgeLethbridge, Alberta

Frank A. MaggioDepartment Head of MathematicsHoly Trinity Catholic Secondary SchoolHalton Catholic District School BoardOakville, Ontario

Moyra MartinPrincipalCalgary Catholic School DistrictCalgary, Alberta

Meagan MutchmorK–8 Mathematics ConsultantWinnipeg School DivisionWinnipeg, Manitoba

Mary Anne NissenConsultantElk Island Public SchoolsSherwood Park, Alberta

Darlene PeckfordPrincipalHorizon School Division #67Taber, Alberta

Kathy PerryTeacherPeel District School BoardBrampton, Ontario

Susan PerryConsultantDurham Catholic DistrictSchool BoardOshawa, Ontario

Bryan A. QuinnTeacherEdmonton Public SchoolsEdmonton, Alberta

Ann Louise RevellsPrincipalOttawa-Carleton Catholic School BoardOttawa, Ontario

Lorraine Schroetter-LaPointeVice PrincipalDurham District School BoardOshawa, Ontario

Nathalie SinclairAssistant ProfessorMichigan State UniversityEast Lansing, Michigan

Susan StuartAssistant ProfessorNipissing UniversityNorth Bay, Ontario

Doug SuperPrincipalVancouver School BoardVancouver, British Columbia

Joyce TonnerLearning SupervisorThames Valley District School BoardLondon, Ontario

Stella TossellMathematics ConsultantNorth Vancouver, British Columbia

Gerry VartyAISI Math CoordinatorWolf Creek School Division #72Ponoka, Alberta

Michèle WillsAssistant PrincipalCalgary Board of EducationCalgary, Alberta

Advisory Panel

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Reviewers

vi NEL

Michael BabcockLimestone District School Board

Nancy CampbellRainbow District School Board

Catherine ChauToronto District School Board

Deb Colvin-MacDormandEdmonton Public Schools

William CorriganLakeshore School Board

Anna DutfieldToronto District School Board

Susan GregsonPeel District School Board

Wendy KingColey’s Point Primary School

Gowa KongNorth Vancouver School District

Joan McDuffFaculty of EducationQueen’s University

Ken MendesOttawa-Carleton Catholic School Board

Sandie RowellHamilton-Wentworth DistrictSchool Board

Rose ScainiYork Catholic District School Board

Lindy SmithPeel District School Board

Triona WhiteOttawa-Carleton Catholic School Board

Aboriginal ContentReviewersBrenda DavisEducation ConsultantSix Nations

Laura SmithEducational ConsultantAbbotsford, British Columbia

Equity ReviewerMary SchoonesEducational Consultant/Retired TeacherOttawa-Carleton District School Board

Literacy ReviewerRoslyn DoctorowEducational Consultant

Thank you to the followingteachers for testing the Chapter Tasks.

Jason ChenierPeel District School Board

Kate PrattPeel District School Board

Marjolijne VanderkriftPeel District School Board

00-NelsonMathGr6-Prelims 7/20/05 1:57 PM Page vi

Contents

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CHAPTER Patterns in Mathematics 1Getting Started: Growth Patterns 2

Lesson 1: Writing Pattern Rules 4

Curious Math: Math Magic 7

Lesson 2: Relationships Rules for Patterns 8

Mental Math: Pairing to Multiply 11

Lesson 3: Variables in Expressions 12

Lesson 4: Representing Patterns on a Graph 14

Math Game: Who Am I? 17

Frequently Asked Questions 18

Mid-Chapter Review 19

Lesson 5: Patterns and Spreadsheets 20

Curious Math: Rice on a Chessboard 21

Lesson 6: Solve a Simpler Problem 22

Lesson 7: Equal Expressions 24

Lesson 8: Variables in Equations 26

Skills Bank 28

Problem Bank 30


Chapter Review 33

Chapter Task: Patterns in Your Life 34

Guided ActivityDirect InstructionExploration

1

Rodrigo

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CHAPTER Numeration 35Getting Started: Number Clues 36

Lesson 1: Exploring Greater Numbers 38

Curious Math: Billions 39

Lesson 2: Reading and Writing Numbers 40

Lesson 3: Comparing and Ordering Numbers 42

Lesson 4: Renaming Numbers 44

Lesson 5: Communicate about Solving Problems 46



Lesson 6: Reading and Writing Decimal Thousandths 50

Math Game: Close as You Can 53

Lesson 7: Rounding Decimals 54

Lesson 8: Comparing and Ordering Decimals 56

Mental Math: Dividing Decimals by Renaming 58

Skills Bank 59

Problem Bank 62


Chapter Review 64

Chapter Task: Reporting Numbers 66

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2

Li Ming

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CHAPTER Data Management 67Getting Started: Memorizing Pictures 68

Lesson 1: Creating and Analyzing a Survey 70

Mental Math: Determining Missing Decimals 71

Lesson 2: Plotting Coordinate Pairs 72

Lesson 3: Line Graphs 74

Curious Math: Telling Stories about Graphs 77

Lesson 4: Scatter Plots 78

Math Game: 4 in a Row 81



Lesson 5: Mean and Median 84

Lesson 6: Changing the Intervals on a Graph 86

Lesson 7: Changing the Scale on a Graph 87

Lesson 8: Communicate about Conclusions from Data Displays 88

Lesson 9: Constructing Graphic Organizers 90

Skills Bank 93

Problem Bank 95


Chapter Review 98

Chapter Task: Investigating Body Relationships 100

CHAPTERS 1–3 CUMULATIVE REVIEW 101

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3

Denise

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CHAPTER Addition and Subtraction 105Getting Started: Planning Cross-Country Routes 106

Lesson 1: Adding and Subtracting Whole Numbers 108

Curious Math: Number Reversal 109

Lesson 2: Estimating Sums and Differences 110

Lesson 3: Adding Whole Numbers 112

Lesson 4: Subtracting Whole Numbers 114

Curious Math: Subtracting a Different Way 117


Mid-Chapter Review 104 119

Lesson 5: Adding and Subtracting Decimals 120

Math Game: Mental Math with Money 121

Lesson 6: Adding Decimals 122

Lesson 7: Subtracting Decimals 124

Mental Math: Using Whole Numbers to Add and Subtract Decimals 127

Lesson 8: Communicate about Solving a Multi-Step Problem 128

Skills Bank 130

Problem Bank 133


Chapter Review 136

Chapter Task: Gold Coins 138

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CHAPTER Measuring Length 139Getting Started: Racing Snails 140

Lesson 1: Measuring Length 142

Lesson 2: Metric Relationships 144

Lesson 3: Perimeters of Polygons 146



Lesson 4: Solve Problems Using Logical Reasoning 150

Curious Math: Triangle Sides 152

Math Game: Lines, Lines, Lines 153

Lesson 5: Exploring Perimeter 154

Mental Math: Calculating Lengths of Time 155

Skills Bank 156

Problem Bank 158


Chapter Review 160

Chapter Task: Mapping a Triathlon Course 162

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5

Jorge

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CHAPTER Multiplication and Division 163Getting Started: Recycling Milk Cartons 164

Lesson 1: Identifying Factors, Primes, and Composites 166

Curious Math: Separating Primes fromComposites 169

Lesson 2: Identifying Multiples 170

Lesson 3: Calculating Coin Values 172

Mental Math: Halving and Doubling to Multiply 173

Lesson 4: Multiplying by Hundreds 174

Lesson 5: Estimating Products 176

Lesson 6: Multiplying by Two-Digit Numbers 178

Curious Math: Lattice Multiplication 181



Lesson 7: Dividing by 1000 and 10 000 184

Lesson 8: Dividing by Tens and Hundreds 186

Lesson 9: Estimating Quotients 188

Lesson 10: Dividing by Two-Digit Numbers 190

Math Game: Coin Products 193

Lesson 11: Communicate About Creating and Solving Problems 195

Lesson 12: Order of Operations 196

Curious Math: Egyptian Division 197

Skills Bank 198

Problem Bank 201


Chapter Review 204

Chapter Task: Chartering Buses 206

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CHAPTER 2-D Geometry 207Getting Started: Mystery Design 208

Lesson 1: Estimating Angle Measures 210

Lesson 2: Investigating Properties of Triangles 212

Mental Imagery: Visualizing Symmetrical Shapes 213

Lesson 3: Communicate About Triangles 214



Lesson 4: Constructing Polygons 218

Curious Math: Folding Along Diagonals 221

Lesson 5: Sorting Polygons 222

Lesson 6: Investigating Properties of Quadrilaterals 224

Skills Bank 226

Problem Bank 228


Chapter Review 230

Chapter Task: Furnishing a Bedroom 232


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7

68°

44° 4 cm

4 cmTara

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CHAPTER Area 237Getting Started: Area Puzzle 238

Lesson 1: Unit Relationships 240

Lesson 2: Area Rule for Parallelograms 242

Mental Imagery: Estimating Area 244

Lesson 3: Geometric Relationships 245

Lesson 4: Area Rule for Triangles 246



Lesson 5: Solve Problems Using Equations 250

Lesson 6: Areas of Polygons 252

Curious Math: Changing Parallelograms 254

Skills Bank 255

Problem Bank 257


Chapter Review 260

Chapter Task: Design a Placemat and Napkin Set 262

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8

Raven

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CHAPTER Multiplying Decimals 263Getting Started: Downloading Songs 264

Lesson 1: Estimating Products 266

Mental Math: Multiplying by 5 and 50 267

Lesson 2: Multiplying by 1000 and 10 000 268

Lesson 3: Mulitplying Tenths by Whole Numbers 270



Lesson 4: Multiplying by 0.1, 0.01, or 0.001 274

Lesson 5: Multiplying Multiples of Ten by Tenths 276

Lesson 6: Communicate about Problem Solving 278

Lesson 7: Choosing a Multiplication Method 280

Curious Math: Decimal Equivalents 281

Math Game: Race to 50 282

Skills Bank 283

Problem Bank 286


Chapter Review 288

Chapter Task: Growing Up 290

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9

Chandra

Akeem

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CHAPTER Dividing Decimals 291Getting Started: Ancient Length Measurements 292

Lesson 1: Estimating Quotients 294

Math Game: Estimate the Range 297

Lesson 2: Dividing Money 298

Mental Math: Adding Decimals by Renaming 299

Lesson 3: Dividing Decimals by One-Digit Numbers 300

Curious Math: Dividing Magic Squares 303



Lesson 4: Dividing by 10, 100, 1000, and 10 000 306

Math Game: Calculate the Least Number 309

Lesson 5: Solve Problems by Working Backward 310

Skills Bank 312

Problem Bank 315


Chapter Review 317

Chapter Task: Judging Fairness 318

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10

Tom

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CHAPTER 3-D Geometry and 3-D Measurement 319Getting Started: Solving Net Puzzles 320

Lesson 1: Visualizing and ConstructingPolyhedrons 322

Mental Imagery: Drawing Faces of Polyhedrons 323

Lesson 2: Surface Area of Polyhedrons 324

Lesson 3: Volume of Rectangular and Triangular Prisms 326

Curious Math: Cross-Sections 329

Lesson 4: Solve Problems by Making a Model 330



Lesson 5: Creating Isometric Sketches 334

Lesson 6: Creating Cube Structures from Sketches 336

Lesson 7: Different Views of a Cube Structure 338

Lesson 8: Creating Cube Structures from Different Views 340

Curious Math: Plane of Symmetry 341

Skills Bank 342

Problem Bank 344


Chapter Review 346

Chapter Task: Painting Bids 348


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CHAPTER Fractions, Decimals, and Ratios 353Getting Started: Filling a Pancake Order 354

Lesson 1: Comparing and Ordering Fractions 356

Lesson 2: Comparing Fractions with Unlike Denominators 358

Lesson 3: Fraction and Decimal Equivalents 360

Mental Math: Using Factors to Multiply 361

Lesson 4: Ratios 362

Lesson 5: Equivalent Ratios 364



Lesson 6: Percents as Special Ratios 368

Lesson 7: Relating Percents to Decimals and Fractions 370

Lesson 8: Estimating and Calculating Percents 372

Lesson 9: Unit Rates 374

Lesson 10: Solving Problems Using Guess and Test 376

Math Game: Ratio Concentration 378

Skills Bank 379

Problem Bank 382


Chapter Review 384

Chapter Task: Running with Terry 386

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12

James

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K

CHAPTER Probability 387Getting Started: Lucky Seven 388

Lesson 1: Conducting Probability Experiments 390

Mental Imagery: Visualizing Fractions on a Number Line 391

Lesson 2: Using Percents to Describe Probabilities 392

Lesson 3: Solving a Problem by Conducting an Experiment 394

Curious Math: Random Numbers and Letters 397



Lesson 4: Theoretical Probability 400

Lesson 5: Tree Diagrams 402

Lesson 6: Comparing Theoretical and Experimental Probability 404

Math Game: No Tails Please! 406

Skills Bank 407

Problem Bank 409


Chapter Review 412

Chapter Task: Winning Races 414

13

Kurt

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CHAPTER Patterns and Motion in Geometry 415Getting Started: Creating a Design Using Transformations 416

Lesson 1: Describing Rotations 418

Lesson 2: Performing and Measuring Rotations 420

Lesson 3: Rotational Symmetry 422

Curious Math: Alphabet Symmetry 425



Lesson 4: Communicate Using Diagrams 428

Lesson 5: Exploring Transformation Patterns with Technology 430

Lesson 6: Creating Designs 432

Mental Imagery: Identifying Transformations 434

Skills Bank 435

Problem Bank 437


Chapter Review 439

Chapter Task: Creating Nets 440


GLOSSARY 445

ANSWERS TO SELECTED PROBLEMS 465

INDEX 466

CREDITS 473

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