Mathematics for Elementary Teachers plus Activities Manual, 2nd Edition

Elementary school classrooms are increasingly relying on a discovery method for the teaching of mathematics. Mathematics for Elementary Teachers thoroughly prepares preservice teachers to use this approach as it has been proven to increase their depth of understanding of mathematics. In this text, topics are organized by operation, rather than number type, and time is spent explaining why the math works, rather than just on the mechanics of how it works. Fully integrated activities are found in the book and in an accompanying Activities Manual. As a result, students engage, explore, discuss, and ultimately reach true understanding of the approach and of mathematics.

Chapter 1 Problem Solving

1.1  Solving Problems

1.2  Explaining Solutions

Chapter 2 Numbers and the Decimal System

2.1 Overview of the Number Standards

2.2 The Decimal System and Place Value

2.3 Representing Decimal Numbers

2.4 Comparing Decimal Numbers

2.5 Rounding Decimal Numbers

Chapter 3 Fractions

3.1 The Meaning of Fractions

3.2 Fractions as Numbers

3.3 Equivalent Fractions

3.4 Comparing Fractions

3.5 Percent

Chapter 4 Addition and Subtraction

4.1 Interpretations of Addition and Subtraction

4.2 Why the Standard Algorithms for Adding and Subtracting Decimal Numbers Work

4.3 Adding and Subtracting Fractions

4.4 When Do We Add Percentages?

4.5 Percent Increase and Percent Decrease

4.6 The Commutative and Associative Properties of Addition and Mental Math

Chapter 5 Multiplication

5.1 The Meaning of Multiplication and Ways to Show Multiplication

5.2 Why Multiplying Decimal Numbers by 10 is Easy

5.3 The Commutative Property of Multiplication and Areas of Rectangles

5.4 The Associative Property of Multiplication and Volumes of Boxes

5.5 The Distributive Property

5.6 Mental Math, Properties of Arithmetic, and Algebra

5.7 Why the Procedure for Multiplying Whole Numbers Works

Chapter 6 Multiplication of Fractions, Decimals, and Negative Numbers

6.1 Multiplying Fractions

6.2 Multiplying Decimals

6.3 Multiplying Negative Numbers

6.4 Scientific Notation

Chapter 7 Division

7.1 The Meaning of Division

7.2 Understanding Long Division

7.3 Fractions and Division

7.4 Dividing Fractions

7.5 Dividing Decimals

7.6 Ratio and Proportion

Chapter 8 Geometry

8.1 Visualization

8.2 Angles

8.3 Circles and Spheres

8.4 Triangles, Quadrilaterals, and Other Polygons

8.5 Constructions with Straightedge and Compass

8.6 Polyhedra and Other Solid Shapes

Chapter 9 Geometry of Motion and Change

9.1 Reflections, Translations, and Rotations

9.2 Symmetry

9.3 Congruence

9.4 Similarity

Chapter 10 Measurement

10.1 Fundamentals of Measurement

10.2 Length, Area, Volume, and Dimension

10.3 Calculating Perimeters of Polygons, Areas of Rectangles, and Volumes of Boxes

10.4 Error and Accuracy in Measurements

10.5 Converting from One Unit of Measurement to Another

Chapter 11 More About Area and Volume

11.1 The Moving and Additivity Principles About Area

11.2 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem

11.3 Areas of Triangles

11.4 Areas of Parallelograms

11.5 Cavalieri’s Principle About Shearing and Area

11.6 Areas of Circles and the Number Pi

11.7 Approximating Areas of Irregular Shapes

11.8 Relating the Perimeter and Area of a Shape

11.9 Principles for Determining Volumes

11.10 Volumes of Prisms, Cylinders, Pyramids, and Cones

11.11 Areas, Volumes, and Scaling

Chapter 12 Number Theory

12.1 Factors and Multiples

12.2 Greatest Common Factor and Least Common Multiple

12.3 Prime Numbers

12.4 Even and Odd

12.5 Divisibility Tests

12.6 Rational and Irrational Numbers

Chapter 13 Functions and Algebra

13.1 Mathematical Expressions, Formulas, and Equations

13.2 Solving Equations Using Number Sense, Strip Diagrams, and Algebra

13.3 Sequences

13.4 Series

13.5 Functions

13.6 Linear Functions

Chapter 14 Statistics

14.1 Formulating Questions, Designing Investigations, and Gathering Data

14.2 Displaying Data and Interpreting Data Displays

14.3 The Center of Data: Mean, Median, and Mode

14.4 Percentiles and the Distribution of Data

Chapter 15 Probability

15.1 Basic Principles and Calculation Methods of Probability

15.2 Using Fraction Arithmetic to Calculate Probabilities