Problem Solving | |

Solving Problems | |

Explaining Solutions | |

Numbers and the Decimal System | |

Overview of the Number Standards | |

The Decimal System and Place Value | |

Representing Decimal Numbers | |

Comparing Decimal Numbers | |

Rounding Decimal Numbers | |

Fractions | |

The Meaning of Fractions | |

Fractions as Numbers | |

Equivalent Fractions | |

Comparing Fractions | |

Percent | |

Addition and Subtraction | |

Interpretations of Addition and Subtraction | |

Why the Standard Algorithms for Adding and Subtracting Decimal Numbers Work | |

Adding and Subtracting Fractions | |

When Do We Add Percentages? | |

Percent Increase and Percent Decrease | |

The Commutative and Associative Properties of Addition and Mental Math | |

Multiplication | |

The Meaning of Multiplication and Ways to Show Multiplication | |

Why Multiplying Decimal Numbers by 10 is Easy | |

The Commutative Property of Multiplication and Areas of Rectangles | |

The Associative Property of Multiplication and Volumes of Boxes | |

The Distributive Property | |

Mental Math, Properties of Arithmetic, and Algebra | |

Why the Procedure for Multiplying Whole Numbers Works | |

Multiplication of Fractions, Decimals, and Negative Numbers | |

Multiplying Fractions | |

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 | |

Fundamentals of Measurement | |

Length, Area, Volume, and Dimension | |

Calculating Perimeters of Polygons, Areas of Rectangles, and Volumes of Boxes | |

Error and Accuracy in Measurements | |

Converting from One Unit of Measurement to Another | |

More About Area and Volume | |

The Moving and Additivity Principles About Area | |

Using the Moving and Additivity Principles to Prove the Pythagorean Theorem | |

Areas of Triangles | |

Areas of Parallelograms | |

Cavalieri's Principle About Shearing and Area | |

Areas of Circles and the Number Pi | |

Approximating Areas of Irregular Shapes | |

Relating the Perimeter and Area of a Shape | |

Principles for Determining Volumes | |

Volumes of Prisms, Cylinders, Pyramids, and Cones | |

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 Using Number Sense, Strip Diagrams, and Algebra | |

Sequences | |

Series | |

Functions | |

Linear Functions | |

Statistics | |

Formulating Questions, Designing Investigations, and Gathering Data | |

Displaying Data and Interpreting Data Dis | |

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