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1. Numbers and the Base-Ten System 1.1 The Counting Numbers 1.2 Decimals and Negative Numbers 1.3 Comparing Numbers in Base-Ten 1.4 Rounding Numbers Chapter Summary 2. Fractions and Problem-Solving 2.1 Solving Problems and Explaining Solutions 2.2 Defining and Reasoning About 2.3 Equivalent Fractions 2.4 Comparing Fractions 2.5 Percent Chapter Summary 3. Addition and Subtraction 3.1 Interpretations of Addition and Subtraction 3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts 3.3 Why the Common Algorithms for Adding and Subtracting Numbers in the Base-Ten System Work 3.4 Adding and Subtracting Fractions 3.5 Adding and Subtracting Negative Numbers Chapter Summary 4. Multiplication 4.1 Interpretations of Multiplication 4.2 Why Multiplying by 10 is Special in Base-Ten 4.3 The Commutative and Associate Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes 4.4 The Distributive Property 4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts 4.6 Why Algorithms for Multiplying Whole Numbers Work Chapter Summary 5. Multiplication of Fractions, Decimals, and Negative Numbers 5.1 Multiplying Fractions 5.2 Multiplying Decimals 5.3 Multiplying Negative Numbers 5.4 Powers and Scientific Notation Chapter Summary 6. Division 6.1 Interpretations of Division 6.2 Division and Fractions and Division with Remainder 6.3 Why Division Algorithms Work 6.4 Fraction Division from the "How Many Groups?" Perspective 6.5 Fraction Division from the "How Many in One Group?" Perspective 6.6 Dividing Decimals Chapter Summary 7. Ratio and Proportional Relationships 7.1 Motivating and Defining Ratio and Proportional Relationships 7.2 Solving Proportion Problems by Reasoning with Multiplication and Division 7.3 Unit Rates and the Values of a Ratio 7.4 Proportional Relationships Versus Inversely Proportional Relationships 7.5 Percent Revisited: Percent Increase and Decrease Chapter Summary 8. Number Theory 8.1 Factors and Multiples 8.2 Even and Odd 8.3 Divisibility Tests 8.4 Prime Numbers 8.5 Greatest Common Factor and Least Common Multiple 8.6 Rational and Irrational Numbers 8.7 Looking Back at the Number Systems Chapter Summary 9. Algebra 9.1 Numerical Expressions 9.2 Numerical Expressions with Variables 9.3 Equations for Different Purposes 9.4 Solving Equations 9.5 Solving Algebra Word Problems with Strip Diagrams and with Algebra 9.6 Sequences 9.7 Functions 9.8 Linear Functions Chapter Summary 10. Geometry 10.1 Visualization 10.2 Angles 10.3 Angles and Phenomena in the World 10.4 Circles and Spheres 10.5 Quadrilaterals, Triangles, and Polygons Chapter Summary 11. Measurement 11.1 Fundamentals of Measurement 11.2 Length, Area, Volume, and Dimension 11.3 Error and Precision in Measurements 11.4 Converting from One Unit of Measurement to Another Chapter Summary 12. Area of Shapes 12.1 Areas of Rectangles Revisited 12.2 Moving and Additivity Principles About Area 12.3 Areas of Triangles 12.4 Areas of Paralellograms and Other Polygons 12.5 Shearing: Changing Shapes Without Changing Area 12.6 Areas of Circles and the Number Pi 12.7 Approximating Areas of Irregular Shapes 12.8 Contrasting and Relating the Perimeter and Area of Shapes 12.9 Using Moving and Additivity Principles to Prove the Pythagorean Theorem Chapter Summary 13. Solid Shapes and Their Volume and Surface Area 13.1 Polyhedra and Other Solid Shapes 13.2 Patterns and Surface Area 13.3 Volumes of Solid Shapes 13.4 Volume of Submersed Objects versus Weight of Floating Objects Chapter Summary 14. Geometry of Motion and Change 14.1 Reflections, Translations, and Rotations 14.2 Symmetry 14.3 Congruence 14.4 Constructions with Straightedge and Compass 14.5 Similarity 14.6 Areas, Volumes, and Scaling Chapter Summary 15. Statistics 15.1 Formulating Statistical Questions, Gathering Data, and Using Samples 15.2 Displaying Data and Interpreting Data Displays 15.3 The Center of Data: Mean, Median, and Mode 15.4 Summarizing, Describing, and Comparing Data Distributions Chapter Summary 16. Probability 16.1 Basic Principles of Probability 16.2 Counting the Number of Outcomes 16.3 Calculating Probabilities in Multi-Stage Experiments 16.4 Using Fraction Arithmetic to Calculate Probabilities Chapter Summary Bibliography Index Table of Contents
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