**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

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