Mathematics for Elementary Teachers Volume I: Numbers and Operations Preliminary Edition (with Activities Manual)

by Beckmann, Sybilla

• ISBN13: 9780321129802
• ISBN10: 0321129806
• Format: Package
• Copyright: 2003-01-01
• Publisher: Addison Wesley

Summary

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.

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.