Problem Solving | |

Solving Problems | |

Explaining Solutions | |

Numbers and the Decimal System | |

Introduction to the Number Systems | |

The Decimal System and Place Value | |

Representing Decimal Numbers | |

Comparing Sizes of Decimal Numbers | |

Rounding Decimal Numbers | |

Fractions | |

The Meaning of Fractions | |

Equivalent Fractions | |

Fractions as Numbers | |

Comparing Sizes of Fractions | |

Percent | |

Addition and Subtraction | |

Interpretations of Addition and Subtraction | |

The Algorithms for Adding and Subtracting | |

Adding and Subtracting Fractions | |

When Do We Add Percentages | |

Percent Increase and Percent Decrease | |

The Commutative and Associative Properties and Mental Math | |

Multiplication | |

The Meaning of Multiplication | |

Why Multiplying Decimal Numbers by 10 Is Easy | |

Multiplication and Areas of Rectangles | |

The Commutative Property of Multiplication | |

Multiplication and Volumes of Boxes | |

The Associative Property of Multiplication | |

The Distributive Property | |

Mental Math, Properties of Arithmetic, and Algebra | |

Why the Procedure for Multiplying Works | |

Multiplication of Fractions, Decimals, and Negative Numbers | |

Multiplying Fractions | |

Powers | |

Multiplying Decimals | |

Multiplying Negative Numbers | |

Scientific Notation | |

Division | |

The Meaning of Division | |

Understanding Long Division | |

Fractions and Division | |

Dividing Fractions | |

Dividing Decimals | |

Ratio and Proportion | |

Geometry | |

Visualization | |

Angles | |

Circles and Spheres | |

Triangles | |

Quadrilaterals and Other Polygons | |

Constructions With Straightedge and Compass | |

Polyhedra and Other Solid Shapes | |

Geometry of Motion and Change | |

Reflections, Translations, and Rotations | |

Symmetry | |

Congruence | |

Similarity | |

Measurement | |

The Concept of Measurement | |

Error and Accuracy in Measurements | |

Length, Area, Volume, and Dimension | |

Calculating Perimeter, Area, and Volume | |

Comparing Sizes of Objects | |

Converting From one Unit of Measurement to Another | |

More About Area and Volume | |

The Moving and Combining Principles About Area | |

The Pythagorean Theorem | |

Approximating Areas of Irregular Shapes | |

Cavalieri's Principle About Shearing and Area | |

Areas of Triangles | |

Areas of Parallelograms | |

Areas of Circles and the Number Pi | |

Relating the Perimeter and Area of a Shape | |

Principles for Determining Volumes | |

Volumes of Solid Shapes | |

Areas, Volumes, and Scaling | |

Number Theory | |

Factors and Multiples | |

Greatest Common Factor and Least Common Multiple | |

Prime Numbers | |

Even and Odd | |

Divisibility Tests | |

Rational and Irrational Numbers | |

Functions and Algebra | |

Mathematical Expressions, Formulas, and Equations | |

Solving Equations With Pictures and With Algebra | |

Sequences | |

Series | |

Functions | |

Linear Functions | |

Statistics | |

Designing Investigations and Gathering Data | |

Displaying Data and Interpreting Data Displays | |

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

The Spread of Data: Percentiles | |

Probability | |

Basic Principles and Calculation Methods of Probability | |

Calculating Probabilities by considering the Ideal Outcome | |

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