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Mathematical Reasoning for Elementary Teachers,9780321013309

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Mathematical Reasoning for Elementary Teachers

by LONG,C

ISBN13:

9780321013309

ISBN10:

0321013301

Format:

Paperback

Pub. Date:

1/1/1996

Publisher(s):

PRENTICE HALL PTR

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This is the edition with a publication date of 1/1/1996.

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.

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Summary

The fourth edition of Mathematical Reasoning has an increased focus on professional development and connecting the material from this class to the elementary and middle school classroom. The authors have provided more meaningful content and pedagogy to arm readers with all the tools that they will need to become excellent elementary or middle school teachers. Thinking Critically. Sets and Whole Numbers. Numeration and Computation. Number Theory. Integers. Fractions and Rational Numbers. Decimals and Real Numbers. Algebraic Reasoning and Representation. Statistics: The Interpretation of Data. Probability. Geometric Figures. Measurement. Transformations, Symmetries, and Tilings. Congruence, Constructions, and Similarities. For all readers interested in mathematical reasoning for elementary teachers.

Table of Contents

Preface

xi

To the Student

xxviii

Thinking Critically

1

(76)

Some Surprising Tidbits

4

(7)

An Introduction to Problem Solving

11

(5)

Polya's Problem-Solving Principles

16

(11)

More Problem-Solving Strategies

27

(20)

Still More Problem-Solving Strategies

47

(10)

Problem Solving in the Real World

57

(20)

Chapter 1 Summary

70

(2)

Chapter Review Exercises

72

(3)

Chapter Test

75

(2)

Sets, Whole Numbers, and Functions

77

(81)

Sets and Operations on Sets

80

(15)

Sets, Counting, and the Whole Numbers

95

(12)

Addition and Subtraction of Whole Numbers

107

(13)

Multiplication and Division of Whole Numbers

120

(17)

Relations and Functions

137

(21)

Chapter 2 Summary

153

(2)

Chapter Review Exercises

155

(1)

Chapter Test

156

(2)

Numeration and Computation

158

(88)

Numeration Systems Past and Present

160

(15)

Nondecimal Positional Systems

175

(8)

Algorithms for Adding and Subtracting Whole Numbers

183

(16)

Algorithms for Multiplication and Division of Whole Numbers

199

(15)

Mental Arithmetic and Estimation

214

(13)

Getting the Most Out of Your Calculator

227

(19)

Chapter 3 Summary

241

(2)

Chapter Review Exercises

243

(1)

Chapter Test

244

(2)

Number Theory

246

(66)

Divisibility of Natural Numbers

249

(13)

Tests for Divisibility

262

(9)

Greatest Common Divisors and Least Common Multiples

271

(20)

Clock Arithmetic

291

(21)

Chapter 4 Summary

309

(1)

Chapter Review Exercises

310

(1)

Chapter Test

311

(1)

Integers

312

(56)

Representations of Integers

314

(10)

Addition and Subtraction of Integers

324

(22)

Multiplication and Division of Integers

346

(22)

Chapter 5 Summary

364

(2)

Chapter Review Exercises

366

(1)

Chapter Test

367

(1)

Fractions and Rational Numbers

368

(62)

The Basic Concepts of Fractions and Rational Numbers

370

(17)

The Arithmetic of Rational Numbers

387

(20)

The Rational Number System

407

(23)

Chapter 6 Summary

425

(2)

Chapter Review Exercises

427

(1)

Chapter Test

428

(2)

Decimals and Real Numbers

430

(61)

Decimals

433

(18)

Computations with Decimals

451

(12)

Ratio and Proportion

463

(11)

Percent

474

(17)

Chapter 7 Summary

488

(1)

Chapter Review Exercises

489

(1)

Chapter Test

490

(1)

Statistics: The Interpretation of Data

491

(57)

The Graphical Representation of Data

493

(22)

Measures of Central Tendency and Variability

515

(16)

Statistical Inference

531

(17)

Chapter 8 Summary

545

(1)

Chapter Review Exercises

545

(2)

Chapter Test

547

(1)

Probability

548

(57)

Empirical Probability

550

(15)

Principles of Counting

565

(17)

Theoretical Probability

582

(23)

Chapter 9 Summary

601

(2)

Chapter Review Exercises

603

(1)

Chapter Test

604

(1)

Geometric Figures

605

(96)

Figures in the Plane

609

(20)

Curves and Polygons in the Plane

629

(21)

Tiling with Polygons

650

(16)

Networks

666

(11)

Figures in Space

677

(24)

Chapter 10 Summary

695

(1)

Chapter Review Exercises

696

(3)

Chapter Test

699

(2)

Congruence, Constructions, and Similarity

701

(59)

Congruent Triangles

702

(20)

Constructing Geometric Figures

722

(19)

Similar Triangles

741

(19)

Chapter II Summary

755

(1)

Chapter Review Exercises

756

(2)

Chapter Test

758

(2)

Measurement

760

(74)

The Measurement Process

762

(14)

Area and Perimeter

776

(21)

The Pythagorean Theorem

797

(9)

Surface Area and Volume

806

(28)

Chapter 12 Summary

828

(1)

Chapter Review Exercises

829

(2)

Chapter Test

831

(3)

Geometric Transformations

834

(63)

Rigid Motions

836

(26)

Patterns and Symmetries

862

(18)

Similarity Transformations

880

(17)

Chapter 13 Summary

891

(2)

Chapter Review Exercises

893

(1)

Chapter Test

894

(3)

Coordinate Geometry

897

(65)

The Cartesian Coordinate System

899

(15)

Lines and Their Graphs

914

(20)

Solving Geometric Problems Using Coordinates

934

(9)

Graphing Functions and Relations

943

(19)

Chapter 14 Summary

957

(2)

Chapter Review Exercises

959

(2)

Chapter Test

961

(1)

Appendix A Manipulatives in the Mathematics Classroom

962

(4)

Appendix B Logic and Mathematical Reasoning

966

(19)

Appendix C Logo: A Programming Language for Learning Mathematics

985

(17)

Appendix D A Brief Guide to The Geometer's Sketchpad

1002

Answers to Selected Problems

A-1

Acknowledgments

A-91

Lexicon

A-93

Index and Pronunciation Guide

A-95

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