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