California mathematics grade 3

Chapter 4 Multiplication Concepts and FactsChapter 5 More Multiplication Facts Chapter 6 Division Concepts and Facts Chapter 7 More Division Facts Chapter 8 Measurement: Customary S

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

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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:

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.

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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

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Authors

Meet the Authors at ca.gr3math.com

Mary Behr Altieri

Roger Day, Ph.D

Mathematics Department Chair Pontiac Township High School Pontiac, Illinois

Stephen Krulik

Mathematics Consultant Cherry Hill, New Jersey

Carol E Malloy

Assistant Professor of Mathematics Education University of North Carolina at Chapel Hill Chapel Hill, North Carolina

Brian Mowry

Independent Math Educational Consultant/Part time Pre-K Instructional Specialist Austin Independent School District Austin, Texas

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Mary Esther Reynosa

Instructional Specialist for Elementary Mathematics Northside Independent School District San Antonio, Texas

San Diego State University

San Diego, California

Robyn Silbey

Math Content Coach Montgomery County Public Schools Gaithersburg, Maryland

Dinah Zike

Educational Consultant Dinah-Might Activities, Inc.

San Antonio, Texas

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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

Pomona, California

Eppie Chung

K-6 Teacher Modesto City Schools Modesto, California

Lisa Marie Cirrincione

Middle School Teacher Lincoln Middle School Oceanside, California

Grant A Fraser, Ph D.

Professor of Mathematics California State University, Los Angeles

Los Angeles, California

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Visalia, California

Frances Basich Whitney

Project Director, Mathematics K-12

Santa Cruz County Office of Education

Capitola, California

John McGuire

Associate Principal Pacific Union School Arcata, California

Beth Holguin

Teacher Graystone Elementary San Jose, California

Kasey St James

Mathematics Teacher Sunny Hills High School Fullerton, California

Kelly Mack

6 th Grade Teacher Captain Jason Dahl Elementary San Jose, California

Dr Donald R Price

Teacher, Adjunct Professor Rowland Unified School District

Rowland Heights, California

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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.

California State University, Los Angeles

Los Angeles, California

Arthur K Wayman, Ph.D.

Professor of Mathematics Emeritus

California State University, Long Beach

Long Beach, California

Assessment

Jane D Gawronski

Director of Assessment and Outreach

San Diego State University

Cognitive Guided Instruction

Susan B Empson

Associate Professor of Mathematics

and Science Education

University of Texas at Austin

Austin, Texas

English Learners

Cheryl Avalos

Mathematics Consultant

Los Angeles County Office of Education, Retired

Hacienda Heights, California

Mathematics Education Consultant Albany, California

LiteratureDavid M Schwartz

Children’s Author, Speaker, Storyteller Oakland, Califorinia

Vertical AlignmentBerchie Holliday

National Educational Consultant Silver Spring, Maryland

Deborah A Hutchens, Ed.D.

Principal Norfolk Highlands Elementary Chesapeake, Virginia

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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.

5 th Grade Classroom Teacher

David Reese Elementary

Sheri Leiken

Teacher Weathersfield Elementary Thousand Oaks, California

Sarab H Lopes

Teacher Anza Elementary

El Cajon, California

Karen E Lund

5 th Grade Teacher Meadow Park Elementary Irvine, California

Efrain Melendez

Teacher Livermore Valley USD Livermore, California

Jean A Nelson

Teacher Fremont Elementary School Alhambra, California

Tara Pahia

Elementary Teacher Bear Gulch Elementary Rancho Cucamonga, California

Dr Donald R Price

Teacher, Adjunct Professor Rowland Unified School District Rowland Heights, California

Kitty Ritz, M.A.

Teacher Monte Vista Elementary Rohnert Park, California

Corinne E Schwartz

First Grade Teacher Lincrest Elementary School Yuba City, CA

Deborah Shapiro

5 th Grade Teacher Nancy Cory Lancaster, California

Maureen Smith

Curriculum Specialist Fremont Unified School Dist

(retired 6/2006) Fremont, California

Joseph M Snodgrass

3 rd Grade Teacher Park Elementary School Alhambra, California

Marie W Stevens

Elementary Mathematics Coordinator

LAUSD Los Angeles, California

Jane Traut

Classroom Teacher Lang Ranch Elementary School Thousand Oaks, California

Rachel C Trowbridge

Teacher Evergreen Elementary San Jose, California

Cynthia H Vandemoortel

Educator Alderwood Basics Plus School Irvine, California

Norine Yale

Teacher Justin Elementary Simi Valley, California

Dr Darlene York

Education Consultant Associate Professor/Antioch University

Seattle, Washington

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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

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xi

Are You Ready for Chapter 1? 16

1-1 Number Patterns 17

1-2 Problem-Solving Skill: Use the Four-Step Plan .20

Explore 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

CH APTER

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

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Addition

CH APTER

2

Are 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

2-5 Add Money 78

Problem Solving in Geography: A Walk in the Park 82

Explore 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

Chapter Test 101

• 73, 77, 81, 95, 101, 102, 103

67, 73, 76, 81, 90, 95

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

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xiii

Subtraction CH APTER 3 Are You Ready for Chapter 3? 106

3-1 Two-Digit Subtraction 107

3-2 Estimate Differences 110

3-3 Subtract Money 114

Problem Solving in Music: The Sounds of the Symphony 118

3-4 Problem-Solving Skill: Reasonable Answers 120

Explore Math Activity for 3-5: Subtract Three-Digit Numbers with Regrouping 122

3-5 Three-Digit Subtraction with Regrouping 124

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

• 113, 117, 127, 137, 141, 149, 150, 151

113, 116, 127, 137, 141

109, 113, 116, 117, 121, 123, 127,

129, 132, 137, 141, 149

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Multiplication Concepts and Facts

CH APTER

4

Explore 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

Game Time: Factor Power 171

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

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

• 163, 137, 181, 188, 195, 196, 197

159, 163, 166, 170, 176, 181, 188

156, 159, 163, 166, 167, 170, 176,

181, 185, 188, 195

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xv

More Multiplication Facts CH APTER 5 Are You Ready for Chapter 5? 200

Explore Math Activity for 5-1: Multiplication Table 201

Facts Practice 210

Game Time: Three in a Row 211

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

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

• 209, 217, 221, 231, 237, 245, 246, 247

205, 208, 216, 221, 224, 231, 237

202, 205, 208, 213, 216, 217, 221,

224, 227, 231, 237, 245

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Division Concepts and Facts

CH APTER

6

Explore Math Activity for 6-1: Understand Division 251

6-1 Relate Division and Subtraction 253

Explore 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

• 261, 267, 271, 278, 287, 288, 289

255, 261, 266, 271, 277, 281

252, 255, 257, 261, 263, 266, 267,

271, 275, 277, 281, 287

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More Division Facts CH APTER 7 Are You Ready for Chapter 7? 292

Explore 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

• 301, 307, 317, 323, 327, 335, 336, 337

297, 301, 306, 312, 317, 323, 327

294, 297, 301, 303, 306, 307, 312,

317, 319, 323, 327

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Measurement:

Customary System

CH APTER

8

Explore 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 350

Explore 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

• 349, 357, 359, 365, 371, 377, 378, 379

345, 349, 357, 365, 371

342, 345, 349, 351, 353, 357, 359,

361, 365, 371, 377

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Measurement: Metric System CH APTER 9 Are You Ready for Chapter 9? 382

Explore 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

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

• 388, 395, 401, 407, 413, 414, 415

388, 394, 401, 407

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

407, 413

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Measurement and Geometry

CH APTER

10

10-1 Geometry: Polygons 419

10-2 Measurement: Perimeter 422

Explore 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

• 425, 431, 437, 441, 446, 457, 465, 466, 467

421, 425, 430, 436, 441, 446, 449, 457

421, 425, 427, 430, 433, 436, 437,

441, 443, 446, 449, 453, 457, 465

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Statistics: Data, Graphs, and Probability CH APTER 11 Are You Ready for Chapter 11? 470

Explore 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

Explore Probability Activity for 11-6: Outcomes 492

11-6 Make Predictions 494

• 479, 482, 487, 497, 503, 504, 505

475, 478, 487, 497

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

497, 503

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Explore 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

Explore Math Activity for 12-6: Add Like Fractions 526 12-6 Add Like Fractions 528

Problem Solving in Science: The Buzz on Insects 532

Explore Math Activity for 12-7: Subtract Like Fractions 534 12-7 Subtract Like Fractions 536

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Fractions and Decimals

CH APTER

13

Explore 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 564

Explore Math Activity for 13-4: Fractions, Decimals, and Money 566

13-4 Decimals and Money 568

ASSESSMENT

Study Guide and Review 574

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Multiply by One-Digit Numbers

CH APTER

14

Are You Ready for Chapter 14? 584 14-1 Multiply Multiples of 10, 100, and 1,000 585 14-2 Problem-Solving Strategy: Use Logical Reasoning 588

Problem Solving in Art: Stamp Collecting 614

ASSESSMENT

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

Game Time: That’s Close! 645

Problem Solving in Science: Roller Coaster Physics 646

15-7 Divide Money 650

ASSESSMENT

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to Grade 4

Algebra: Function Tables (+/-) 664

Algebra: Function Tables (×/÷) 668

California Standards Review

Tips for Success CA1Multiple-Choice Questions CA2Practice by Standard CA4

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1.0 Students understand the place value of whole numbers:

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

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

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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Standard Text of Standard Primary

Citations

Supporting Citations

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).

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).

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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Citations

Supporting Citations 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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Citations

Supporting Citations 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.

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

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Let’s Get Started

Use the Scavenger Hunt below to learn where things are

located in each chapter

1 What is the title of Chapter 1?

2 What is the Main Idea of Lesson 1-1?

3 How do you know which words are vocabulary words?

4 What are the vocabulary words for Lesson 1-3?

5 What is the key concept shown in Lesson 1-9?

6 How many Examples are presented in Lesson 1-4?

7 What is the web address where you could find extra examples?

8 On page 29, there is a Remember tip box How does the Remember tip help you?

9 How many exercises are there in Lesson 1-5?

10 Suppose you need more practice on a concept Where can you go

for Extra Practice?

11 Suppose you’re doing your homework on page 36 and you get stuck

on Exercise 18 Where could you find help?

12 What is the web address that would allow you to take a self-check

quiz to be sure you understand the lesson?

13 On what pages will you find the Chapter 1 Study Guide and Review?

14 Suppose you can’t figure out how to do Exercise 7 in the Study Guide and Review on page 53 Where could you find help?

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Photo SS-01P Photo of Giant Coast Redwood Trees in CA

2 Start Smart

Problem Solving

C alifornia is home to some of the tallest trees in the

world A Coast Redwood tree is the tallest at 321 feet tall

A Coast Douglas Fir is the second tallest at 301 feet tall

How much taller is the Coast Redwood than the Coast

Douglas Fir?

You can use the four-step plan to solve math problems

The four steps are Understand, Plan, Solve, and Check

• Read the problem carefully.

• What facts do you know?

• What do you need to find?

You know the height of the Coast Redwood and the Coast

Douglas Fir You need to find how much taller the Coast

Redwood is than the Coast Douglas Fir

Reinforcement of 2NS2.2 Find the sum or difference of two whole numbers

up to three digits long.

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Start Smart 3

The third tallest tree is the General Sherman Tree in Sequoia National Park It is 275 feet tall and is still growing!

• Think about how the facts relate to each other.

• Make a plan to solve the problem.

To find how much taller the Coast Redwood is than the

Coast Douglas Fir, you can use subtraction

The Coast Redwood is 20 feet taller than the Coast

Douglas Fir

• Look back at the problem.

• Does your answer make sense?

• If not, solve the problem another way.

You can check the subtraction by using addition

20 + 301 = 321 So, the answer is correct

1 List the four steps of the Four-Step Problem-Solving Plan.

2 Describe each step of the four-step plan

pages 2 and 3 to write a real-world problem

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NOW THAT’S HOT!

Photo SS-02P

Photo of Death Valley; also include another photo/art of a map showing location of Death

The model shows the

value of each digit in 282

1 Copy and complete the place value chart below.

Ones

2 8

2 282

134

120

903

2 Write each number in Exercise 1 in expanded form.

Reinforcement of 2NS1.3 Order and compare whole numbers to 1,000 by using the symbols < , >, =.

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Start Smart 5

Death Valley is one

of the hottest places

307 is greater than 36, you can write 307 > 36

Month June July August September Average

Temperature 109° F 115° F 113° F 106° F

9 Which month is the warmest?

10 Which month is the least warm?

11 Order these numbers from greatest to least.

from least to greatest

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6 Start Smart

T he Monterey Bay Aquarium is home to sea life such

as sea stars, sharks, stingrays, penguins, jellyfish, and

giant octopuses.

Addition Rules

Ming sees 3 sharks and 4 penguins Tomás sees 4 penguins

and 3 sharks The total number is the same since the order in

which numbers are added does not change the answer

1 Hernando sees 5 sea otters and 8 sharks Draw a picture

using circles to show that 5 + 8 = 8 + 5

2 Draw a picture to show that 3 + 2 + 4 = 2 + 4 + 3

Tell what number is missing in each number sentence.

5 10 + 7 + 1 = 1 + 7 + 6 9 + 12 + 3 = 3 + + 9

Algebra and Functions

Reinforcement of 2AF1.2 Relate problem situations to number sentences involving addition and subtraction.

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Start Smart 7

Number Sentences

Suppose that 25 students went on a field trip to the Monterey Bay Aquarium This includes 12 boys How many girls went? The number sentence shows this problem situation

boys girls students

⎧ ⎨ ⎩ ⎧ ⎨ ⎩ ⎧ ⎨ ⎩

25 − 12 = 13 So, 13 girls went on the field trip

Choose the number sentence that can be used to solve the problem Then solve the problem.

7 Carlos had $12 He bought a toy

shark He now has $5 How much was the shark?

8 Twelve penguins are standing on a

rock Seven jump into the water

How many are now on the rock?

9 There were 5 fish in a tank Now there are 12 fish How

many fish were added?

10 A toy star fish costs $7 A stuffed octopus costs $12 What

is the total cost?

the result to 10 Will she get the same number if she adds 7 to the result of 5 + 10? Explain

A variety of sea

stars can be found

at the Monterey

Bay Aquarium The

Sunflower Star can

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8 Start Smart

Measurement

C alifornia’s state quarter was released in January 2005 The

U.S Mint made more than 520 million California quarters.

is the inch One California state

quarter has a length of about 1 inch

Estimate the length of each set of coins to the nearest inch

Then use a ruler to measure the length to the nearest inch.

3 How many pennies in a row would measure about 5 inches?

Reinforcement of 2MG1.3 Measure the length of an object to the nearest inch and/or centimeter.

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