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| Problem Solving | |
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| Solving Problems | |
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| Explaining Solutions | |
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| Numbers and the Decimal System | |
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| Introduction to the Number Systems | |
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| The Decimal System and Place Value | |
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| Representing Decimal Numbers | |
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| Comparing Sizes of Decimal Numbers | |
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| Rounding Decimal Numbers | |
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| Fractions | |
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| The Meaning of Fractions | |
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| Equivalent Fractions | |
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| Fractions as Numbers | |
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| Comparing Sizes of Fractions | |
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| Percent | |
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| Addition and Subtraction | |
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| Interpretations of Addition and Subtraction | |
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| The Algorithms for Adding and Subtracting | |
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| Adding and Subtracting Fractions | |
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| When Do We Add Percentages | |
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| Percent Increase and Percent Decrease | |
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| The Commutative and Associative Properties and Mental Math | |
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| Multiplication | |
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| The Meaning of Multiplication | |
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| Why Multiplying Decimal Numbers by 10 Is Easy | |
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| Multiplication and Areas of Rectangles | |
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| The Commutative Property of Multiplication | |
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| Multiplication and Volumes of Boxes | |
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| The Associative Property of Multiplication | |
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| The Distributive Property | |
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| Mental Math, Properties of Arithmetic, and Algebra | |
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| Why the Procedure for Multiplying Works | |
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| Multiplication of Fractions, Decimals, and Negative Numbers | |
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| Multiplying Fractions | |
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| Powers | |
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| Multiplying Decimals | |
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| Multiplying Negative Numbers | |
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| Scientific Notation | |
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| Division | |
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| The Meaning of Division | |
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| Understanding Long Division | |
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| Fractions and Division | |
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| Dividing Fractions | |
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| Dividing Decimals | |
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| Ratio and Proportion | |
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| Geometry | |
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| Visualization | |
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| Angles | |
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| Circles and Spheres | |
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| Triangles | |
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| Quadrilaterals and Other Polygons | |
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| Constructions With Straightedge and Compass | |
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| Polyhedra and Other Solid Shapes | |
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| Geometry of Motion and Change | |
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| Reflections, Translations, and Rotations | |
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| Symmetry | |
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| Congruence | |
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| Similarity | |
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| Measurement | |
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| The Concept of Measurement | |
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| Error and Accuracy in Measurements | |
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| Length, Area, Volume, and Dimension | |
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| Calculating Perimeter, Area, and Volume | |
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| Comparing Sizes of Objects | |
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| Converting From one Unit of Measurement to Another | |
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| More About Area and Volume | |
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| The Moving and Combining Principles About Area | |
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| The Pythagorean Theorem | |
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| Approximating Areas of Irregular Shapes | |
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| Cavalieri's Principle About Shearing and Area | |
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| Areas of Triangles | |
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| Areas of Parallelograms | |
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| Areas of Circles and the Number Pi | |
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| Relating the Perimeter and Area of a Shape | |
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| Principles for Determining Volumes | |
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| Volumes of Solid Shapes | |
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| Areas, Volumes, and Scaling | |
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| Number Theory | |
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| Factors and Multiples | |
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| Greatest Common Factor and Least Common Multiple | |
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| Prime Numbers | |
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| Even and Odd | |
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| Divisibility Tests | |
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| Rational and Irrational Numbers | |
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| Functions and Algebra | |
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| Mathematical Expressions, Formulas, and Equations | |
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| Solving Equations With Pictures and With Algebra | |
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| Sequences | |
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| Series | |
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| Functions | |
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| Linear Functions | |
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| Statistics | |
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| Designing Investigations and Gathering Data | |
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| Displaying Data and Interpreting Data Displays | |
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| The Center of Data: Mean, Median and Mode | |
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| The Spread of Data: Percentiles | |
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| Probability | |
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| Basic Principles and Calculation Methods of Probability | |
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| Calculating Probabilities by considering the Ideal Outcome | |