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Edition: 03

Copyright: 2003

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

Copyright: 2003

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

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Also available as a two-volume set, this text is intended to give students depth and perspective in their knowledge of the mathematics taught in elementary school. The author believes that some key elements in achieving this depth and perspective are for students to write clear, logical explanations, for students to enhance their intuition by working with examples and by looking for patterns and connections, and for students to use mathematics in a variety of applications. The book is centered around "class activities," which are designed for students to work on in class in small groups. The class activities foster engagement, exploration and discussion of the material, rather than passive absorption. Many exercises and problems are included at the end of each chapter. Working on these exercises and problems and justifying their solutions carefully and clearly is crucial to achieving depth of understanding of the material. Both students and instructors should find this material fun, interesting, and rewarding.

**Beckmann, Sybilla : University of Georgia**

**1. Problem Solving**

Solving Problems

Explaining Solutions

**2. Numbers**

Introduction to the Number Systems

The Decimal System and Place Value

Representing Decimals

The Meaning of Fractions

Equivalent Fractions

Fractions as Numbers

Percent

Comparing Size of Decimals

Comparing Sizes of Fractions

Rounding Decimals

**3. Addition and Subtraction**

Interpretations of Addition and Subtraction

The Algorithms for Adding and Subtracting

Adding and Subtracting Fractions

When Do We Add Percentages?

Percent Increase and Percent Decrease

The Commutative and Associative Properties and Mental Math

**4. Multiplication**

The Meaning of Multiplication

Why Multiplying Decimals by 10 is Easy

Multiplication and Areas of Rectangles

The Commutative Property of Multiplication

Multiplication and Volumes of Boxes

The Associative Property of Multiplication

The Distributive Property

Why the Procedure for Multiplying Works

Multiplying Fractions

Powers

Multiplying Decimals

Multiplying Negative Numbers

Scientific Notation

**5. Division**

The Meaning of Division

Why the Standard Long Division Procedure Works

Fractions and Division

Relating Different Answers to Division Problems

Dividing Fractions

Dividing Decimals

Ratio and Proportion

**6. More About Numbers**

Factors and Multiples

Prime Numbers

Greatest Common Factor and Least Common Multiple

Common Factors and Commensurability

Even and Odd

Divisibility Tests

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Summary

Also available as a two-volume set, this text is intended to give students depth and perspective in their knowledge of the mathematics taught in elementary school. The author believes that some key elements in achieving this depth and perspective are for students to write clear, logical explanations, for students to enhance their intuition by working with examples and by looking for patterns and connections, and for students to use mathematics in a variety of applications. The book is centered around "class activities," which are designed for students to work on in class in small groups. The class activities foster engagement, exploration and discussion of the material, rather than passive absorption. Many exercises and problems are included at the end of each chapter. Working on these exercises and problems and justifying their solutions carefully and clearly is crucial to achieving depth of understanding of the material. Both students and instructors should find this material fun, interesting, and rewarding.

Author Bio

**Beckmann, Sybilla : University of Georgia**

Table of Contents

**1. Problem Solving**

Solving Problems

Explaining Solutions

**2. Numbers**

Introduction to the Number Systems

The Decimal System and Place Value

Representing Decimals

The Meaning of Fractions

Equivalent Fractions

Fractions as Numbers

Percent

Comparing Size of Decimals

Comparing Sizes of Fractions

Rounding Decimals

**3. Addition and Subtraction**

Interpretations of Addition and Subtraction

The Algorithms for Adding and Subtracting

Adding and Subtracting Fractions

When Do We Add Percentages?

Percent Increase and Percent Decrease

The Commutative and Associative Properties and Mental Math

**4. Multiplication**

The Meaning of Multiplication

Why Multiplying Decimals by 10 is Easy

Multiplication and Areas of Rectangles

The Commutative Property of Multiplication

Multiplication and Volumes of Boxes

The Associative Property of Multiplication

The Distributive Property

Why the Procedure for Multiplying Works

Multiplying Fractions

Powers

Multiplying Decimals

Multiplying Negative Numbers

Scientific Notation

**5. Division**

The Meaning of Division

Why the Standard Long Division Procedure Works

Fractions and Division

Relating Different Answers to Division Problems

Dividing Fractions

Dividing Decimals

Ratio and Proportion

**6. More About Numbers**

Factors and Multiples

Prime Numbers

Greatest Common Factor and Least Common Multiple

Common Factors and Commensurability

Even and Odd

Divisibility Tests

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

Published: 2003

International: No

**Beckmann, Sybilla : University of Georgia**

**1. Problem Solving**

Solving Problems

Explaining Solutions

**2. Numbers**

Introduction to the Number Systems

The Decimal System and Place Value

Representing Decimals

The Meaning of Fractions

Equivalent Fractions

Fractions as Numbers

Percent

Comparing Size of Decimals

Comparing Sizes of Fractions

Rounding Decimals

**3. Addition and Subtraction**

Interpretations of Addition and Subtraction

The Algorithms for Adding and Subtracting

Adding and Subtracting Fractions

When Do We Add Percentages?

Percent Increase and Percent Decrease

The Commutative and Associative Properties and Mental Math

**4. Multiplication**

The Meaning of Multiplication

Why Multiplying Decimals by 10 is Easy

Multiplication and Areas of Rectangles

The Commutative Property of Multiplication

Multiplication and Volumes of Boxes

The Associative Property of Multiplication

The Distributive Property

Why the Procedure for Multiplying Works

Multiplying Fractions

Powers

Multiplying Decimals

Multiplying Negative Numbers

Scientific Notation

**5. Division**

The Meaning of Division

Why the Standard Long Division Procedure Works

Fractions and Division

Relating Different Answers to Division Problems

Dividing Fractions

Dividing Decimals

Ratio and Proportion

**6. More About Numbers**

Factors and Multiples

Prime Numbers

Greatest Common Factor and Least Common Multiple

Common Factors and Commensurability

Even and Odd

Divisibility Tests