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A Problem Solving Approach to Mathematics book cover, ISBN 9780321168757

A Problem Solving Approach to Mathematics

by Billstein, Rick; Libeskind, Shlomo; Lott, Johnny W.

ISBN13: 9780321168757
ISBN10: 0321168755
Additional ISBN(s): 9780201751307, 9780321375414
Edition: 8th
Format: Hardcover
Copyright: 2003-04-01
Publisher: Addison-Wesley
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1. A Problem Solving Approach to Mathematics > ISBN13: 9780321168757

List Price: $126.67

Table of Contents

CHAPTER 1 An Introduction to Problem Solving

1

(59)

Preliminary Problem

1

(2)

1-1 Explorations with Patterns

3

(14)

1-2 Mathematics and Problem Solving

17

(17)

1-3 Algebraic Thinking

34

(12)

1-4 Logic: An Introduction

46

(9)

Hint for Solving the Preliminary Problem

55

(1)

Questions from the Classroom

56

(1)

Chapter Outline

56

(1)

Chapter Review

57

(1)

Selected Bibliography

58

(2)

CHAPTER 2 Sets, Whole Numbers, and Functions

60

(73)

Preliminary Problem

60

(2)

2-1 Describing Sets

62

(12)

2-2 Other Set Operations and Their Properties

74

(11)

2-3 Addition and Subtraction of Whole Numbers

85

(12)

2-4 Multiplication and Division of Whole Numbers

97

(13)

2-5 Functions

110

(18)

Hint for Solving the Preliminary Problem

128

(1)

Questions from the Classroom

128

(1)

Chapter Outline

129

(1)

Chapter Review

130

(2)

Selected Bibliography

132

(1)

CHAPTER 3 Numeration Systems and Whole-Number Computation

133

(53)

Preliminary Problem

133

(1)

3-1 Numeration Systems

134

(15)

3-2 Algorithms for Whole-Number Addition and Subtraction

149

(11)

3-3 Algorithms for Whole-Number Multiplication and Division

160

(14)

3-4 Mental Mathematics and Estimation for Whole-Number Operations

174

(608)

Hint for Solving the Preliminary Problem

782

Questions from the Classroom

182

(1)

Chapter Outline

183

(1)

Chapter Review

183

(2)

Selected Bibliography

185

(1)

CHAPTER 4 Integers and Number Theory

186

(79)

Preliminary Problem

186

(2)

4-1 Integers and the Operations of Addition and Subtraction

188

(13)

4-2 Multiplication and Division of Integers

201

(13)

4-3 Divisibility

214

(12)

4-4 Prime and Composite Numbers

226

(14)

4-5 Greatest Common Divisor and Least Common Multiple

240

(13)

4-6 Clock and Modular Arithmetic

253

(7)

Hint for Solving the Preliminary Problem

260

(1)

Questions from the Classroom

261

(1)

Chapter Outline

261

(2)

Chapter Review

263

(1)

Selected Bibliography

264

(1)

CHAPTER 5 Rational Numbers and Fractions

265

(53)

Preliminary Problem

265

(2)

5-1 The Set of Rational Numbers

267

(10)

5-2 Addition and Subtraction of Rational Numbers

277

(13)

5-3 Multiplication and Division of Rational Numbers

290

(15)

5-4 Proportional Reasoning

305

(9)

Hint for Solving the Preliminary Problem

314

(1)

Questions from the Classroom 314 Chapter Outline

314

(1)

Chapter Review

315

(2)

Selected Bibliography

317

(1)

CHAPTER 6 Decimals, Percents, and Real Numbers

318

(55)

Preliminary Problem

318

(2)

6-1 Introduction to Decimals

320

(6)

6-2 Operations on Decimals

326

(13)

6-3 Nonterminating Decimals

339

(6)

6-4 Percents

345

(10)

6-5 Computing Interest

355

(6)

6-6 Real Numbers

361

(8)

Hint for Solving the Preliminary Problem

369

(1)

Questions from the Classroom

369

(1)

Chapter Review

370

(1)

Chapter Outline

371

(1)

Selected Bibliography

372

(1)

CHAPTER 7 Probability

373

(66)

Preliminary Problem

373

(2)

7-1 How Probabilities Are Determined

375

(12)

7-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities

387

(19)

7-3 Using Simulations in Probability

406

(8)

7-4 Odds, Conditional Probability, and Expected Value

414

(8)

7-5 Using Permutations and Combinations in Probability

422

(11)

Hint for Solving the Preliminary Problem

433

(1)

Questions from the Classroom

434

(1)

Chapter Outline

434

(1)

Chapter Review

435

(2)

Selected Bibliography

437

(2)

CHAPTER 8 Data Analysis/Statistics: An Introduction

439

(57)

Preliminary Problem

439

(2)

8-1 Statistical Graphs

441

(19)

8-2 Measures of Central Tendency and Variation

460

(22)

8-3 Abuses of Statistics

482

(9)

Hint for Solving the Preliminary Problem

491

(1)

Questions from the Classroom

491

(1)

Chapter Outline

491

(1)

Chapter Review

492

(3)

Selected Bibliography

495

(1)

CHAPTER 9 Introductory Geometry

496

(63)

Preliminary Problem

496

(2)

9-1 Basic Notions

498

(14)

9-2 Polygons

512

(10)

9-3 More about Angles

522

(12)

9-4 Geometry in Three Dimensions

534

(11)

9-5 Networks

545

(8)

Hint for Solving the Preliminary Problem

553

(1)

Questions from the Classroom

554

(1)

Chapter Outline

554

(1)

Chapter Review

555

(2)

Selected Bibliography

557

(2)

CHAPTER 10 Constructions, Congruence, and Similarity

559

(85)

Preliminary Problem

559

(1)

10-1 Congruence Through Constructions

560

(16)

10-2 Other Congruence Properties

576

(7)

10-3 Other Constructions

583

(11)

10-4 Similar Triangles and Similar Figures

594

(16)

10-5 Trigonometry Ratios via Similarity

610

(8)

10-6 Lines in a Cartesian Coordinate System

618

(20)

Hint for Solving the Preliminary Problem

638

(1)

Questions from the Classroom

638

(1)

Chapter Outline

639

(1)

Chapter Review

640

(2)

Selected Bibliography

642

(2)

CHAPTER 11 Concepts of Measurement

644

(87)

Preliminary Problem

644

(1)

11-1 Linear Measure

645

(13)

11-2 Areas of Polygons and Circles

658

(20)

11-3 The Pythagorean Theorem and the Distance Formula

678

(14)

11-4 Surface Areas

692

(11)

11-5 Volume, Mass, and Temperature

703

(22)

Hint for Solving the Preliminary Problem

725

(1)

Questions from the Classroom

725

(1)

Chapter Outline

726

(1)

Chapter Review

727

(3)

Selected Bibliography

730

(1)

CHAPTER 12 Motion Geometry and Tessellations

731

(60)

Preliminary Problem

731

(2)

12-1 Translations and Rotations

733

(14)

12-2 Reflections and Glide Reflections

747

(12)

12-3 Size Transformations

759

(9)

12-4 Symmetries

768

(10)

12-5 Tessellations of the Plane

778

(8)

Hint for Solving the Preliminary Problem

786

(1)

Questions from the Classroom

786

(1)

Chapter Outline

787

(1)

Chapter Review

787

(3)

Selected Bibliography

790

(1)

Appendix I Using a Spreadsheet

791

(7)

Appendix II Graphing Calculators

798

(8)

Appendix III Using a Geometry Drawing Utility

806

(21)

Answers to Selected Problems

827

(48)

Index

875

Supplemental Materials

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