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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 | |