Mathematics for Elementary Teachers with Activities [5 ed.] 9780134392790, 0134392795

Table of contents :
Cover
Title Page
Copyright Page
Dedication
Contents
Foreword
About the Author
Preface
Acknowledgments
1. Numbers and the Base-Ten System
1.1. The Counting Numbers
1.2. Decimals and Negative Numbers
1.3. Reasoning to Compare Numbers in Base Ten
1.4. Reasoning about Rounding
Chapter Summary
2. Fractions and Problem Solving
2.1. Solving Problems and Explaining Solutions
2.2. Defining and Reasoning About Fractions
2.3. Reasoning About Equivalent Fractions
2.4. Reasoning to Compare Fractions
2.5. Reasoning About Percent
Chapter Summary
3. Addition and Subtraction
3.1. Interpretations of Addition and Subtraction
3.2. The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts
3.3. Why the Standard Algorithms for Addition and Subtraction in Base Ten Work
3.4. Reasoning About Fraction Addition and Subtraction
3.5. Why We Add and Subtract with Negative Numbers the Way We Do
Chapter Summary
4. Multiplication
4.1. Interpretations of Multiplication
4.2. Why Multiplying by 10 Is Special in Base Ten
4.3. The Commutative and Associative Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes
4.4. The Distributive Property
4.5. Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts
4.6. Why the Standard Algorithm for Multiplying Whole Numbers Works
Chapter Summary
5. Multiplication of Fractions, Decimals, and Negative Numbers
5.1. Making Sense of Fraction Multiplication
5.2. Making Sense of Decimal Multiplication
5.3. Extending Multiplication to Negative Numbers
5.4. Powers and Scientific Notation
Chapter Summary
6. Division
6.1. Interpretations of Division
6.2. Division and Fractions and Division with Remainder
6.3. Why Division Algorithms Work
6.4. Fraction Division from the How-Many-Groups Perspective
6.5. Fraction Division from the How-Many-Units-in-1-Group Perspective
6.6. Dividing Decimals
Chapter Summary
7. Ratio and Proportional Relationships
7.1. Motivating and Defining Ratio and Proportional Relationships
7.2. Solving Proportion Problems by Reasoning with Multiplication and Division
7.3. The Values of a Ratio: Unit Rates and Multipliers
7.4. Proportional Relationships
7.5. Proportional Relationships Versus Inversely Proportional Relationships
7.6. Percent Revisited: Percent Increase and Decrease
Chapter Summary
8. Number Theory
8.1. Factors and Multiples
8.2. Even and Odd
8.3. Divisibility Tests
8.4. Prime Numbers
8.5. Greatest Common Factor and Least Common Multiple
8.6. Rational and Irrational Numbers
Chapter Summary
9. Algebra
9.1. Numerical Expressions
9.2. Expressions with Variables
9.3. Equations
9.4. Solving Algebra Word Problems with Strip Diagrams and with Algebra
9.5. Sequences
9.6. Functions
9.7. Linear and Other Relationships
Chapter Summary
10. Geometry
10.1. Lines and Angles
10.2. Angles and Phenomena in the World
10.3. Circles and Spheres
10.4. Triangles, Quadrilaterals, and Other Polygons
Chapter Summary
11. Measurement
11.1. Concepts of Measurement
11.2. Length, Area, Volume, and Dimension
11.3. Error and Precision in Measurements
11.4. Converting from One Unit of Measurement to Another
Chapter Summary
12. Area of Shapes
12.1. Areas of Rectangles Revisited
12.2. Moving and Additivity Principles About Area
12.3. Areas of Triangles
12.4. Areas of Parallelograms and Other Polygons
12.5. Shearing: Changing Shapes Without Changing Area
12.6. Area and Circumference of Circles and the Number Pi
12.7. Approximating Areas of Irregular Shapes
12.8. Contrasting and Relating the Perimeter and Area of Shapes
12.9. Using the Moving and Additivity Principles to Prove the Pythagorean Theorem
Chapter Summary
13. Solid Shapes and Their Volume and Surface Area
13.1. Polyhedra and Other Solid Shapes
13.2. Patterns and Surface Area
13.3. Volumes of Solid Shapes
13.4. Volume of Submersed Objects Versus Weight of Floating Objects
Chapter Summary
14. Geometry of Motion and Change
14.1. Reflections, Translations, and Rotations
14.2. Symmetry
14.3. Congruence
14.4. Constructions with Straightedge and Compass
14.5. Similarity
14.6. Dilations and Similarity
14.7. Areas, Volumes, and Similarity
Chapter Summary
15. Statistics
15.1. Formulating Statistical Questions, Gathering Data, and Using Samples
15.2. Displaying Data and Interpreting Data Displays
15.3. The Center of Data: Mean, Median, and Mode
15.4. Summarizing, Describing, and Comparing Data Distributions
Chapter Summary
16. Probability
16.1. Basic Principles of Probability
16.2. Counting the Number of Outcomes
16.3. Calculating Probabilities of Compound Events
16.4. Using Fraction Arithmetic to Calculate Probabilities
Chapter Summary
Downloads
Bibliography
Index
Contents
Class Activities 1. Numbers and the Base-Ten System
1.1. The Counting Numbers
1.2. Decimals and Negative Numbers
1.3. Reasoning to Compare Numbers in Base Ten
1.4. Reasoning about Rounding
Class Activities 2. Fractions and Problem Solving
2.1. Solving Problems and Explaining Solutions
2.2. Defining and Reasoning About Fractions
2.3. Reasoning About Equivalent Fractions
2.4. Reasoning to Compare Fractions
2.5. Reasoning About Percent
Class Activities 3. Addition and Subtraction
3.1. Interpretations of Addition and Subtraction
3.2. The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts
3.3. Why the Standard Algorithms for Addition and Subtraction in Base Ten Work
3.4. Reasoning About Fraction Addition and Subtraction
3.5. Why We Add and Subtract with Negative Numbers the Way We Do
Class Activities 4. Multiplication
4.1. Interpretations of Multiplication
4.2. Why Multiplying by 10 Is Special in Base Ten
4.3. The Commutative and Associative Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes
4.4. The Distributive Property
4.5. Properties of Arithmetic, Mental Math, and Single- Digit Multiplication Facts
4.6. Why the Standard Algorithm for Multiplying Whole Numbers Works
Class Activities 5. Multiplication of Fractions, Decimals, and Negative Numbers
5.1. Making Sense of Fraction Multiplication
5.2. Making Sense of Decimal Multiplication
5.4. Powers and Scientific Notation
Class Activities 6. Division
6.1. Interpretations of Division
6.2. Division and Fractions and Division with Remainder
6.3. Why Division Algorithms Work
6.4. Fraction Division from the How-Many-Groups Perspective
6.5. Fraction Division from the How-Many-Units-in-1- Group Perspective
6.6. Dividing Decimals
Class Activities 7. Ratio and Proportional Relationships
7.1. Motivating and Defining Ratio and Proportional Relationships
7.2. Solving Proportion Problems by Reasoning with Multiplication and Division
7.3. The Values of a Ratio: Unit Rates and Multipliers
7.4. Proportional Relationships
7.5. Proportional Relationships Versus Inversely Propor-tional Relationships
7.6. Percent Revisited: Percent Increase and Decrease
Class Activities 8. Number Theory
8.1. Factors and Multiples
8.2. Even and Odd
8.3. Divisibility Tests
8.4. Prime Numbers
8.5. Greatest Common Factor and Least Common Multiple
8.6. Rational and Irrational Numbers
Class Activities 9. Algebra
9.1. Numerical Expressions
9.2. Expressions with Variables
9.3. Equations
9.4. Solving Algebra Word Problems with Strip Dia-grams and with Algebra
9.5. Sequences
9.6. Functions
9.7. Linear and Other Relationships
Class Activities 10. Geometry
10.1. Lines and Angles
10.2. Angles and Phenomena in the World
10.3. Circles and Spheres
10.4. Triangles, Quadrilaterals, and Other Polygons
Class Activities 11. Measurement
11.1. Concepts of Measurement
11.2. Length, Area, Volume, and Dimension
11.3. Error and Precision in Measurements
11.4. Converting from One Unit of Measurement to Another
Class Activities 12. Area of Shapes
12.1. Areas of Rectangles Revisited
12.2. Moving and Additivity Principles About Area
12.3. Areas of Triangles
12.4. Areas of Parallelograms and Other Polygons
12.5. Shearing: Changing Shapes Without Changing Area
12.6. Area and Circumference of Circles and the Number Pi
12.7. Approximating Areas of Irregular Shapes
12.8. Contrasting and Relating the Perimeter and Area of Shapes
12.9. Using the Moving and Additivity Principles to Prove the Pythagorean Theorem
Class Activities 13. Solid Shapes and Their Volume and Surface Area
13.1. Polyhedra and Other Solid Shapes
13.2. Patterns and Surface Area
13.3. Volumes of Solid Shapes
13.4. Volume of Submersed Objects Versus Weight of Floating Objects
Class Activities 14. Geometry of Motion and Change
14.1. Reflections, Translations, and Rotations
14.2. Symmetry CA-286
14.3. Congruence CA-287
14.4. Constructions with Straightedge and Compass
14.5. Similarity
14.6. Dilations and Similarity
14.7. Areas, Volumes, and Similarity
Class Activities 15. Statistics
15.1. Formulating Statistical Questions, Gathering Data, and Using Samples
15.2. Displaying Data and Interpreting Data Displays
15.3. The Center of Data: Mean, Median, and Mode
15.4. Summarizing, Describing, and Comparing Data Distributions
Class Activities 16. Probability
16.1. Basic Principles of Probability
16.2. Counting the Number of Outcomes
16.3. Calculating Probabilities of Compound Events
16.4. Using Fraction Arithmetic to Calculate Probabilities
Activity Downloads
Bibliography
Index
Credits