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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