Table of Contents 1. An Introduction to Problem Solving 1-1 Mathematics and Problem Solving 1-2 Explorations with Patterns 1-3 Reasoning and Logic: An Introduction 2. Numeration Systems and Sets 2-1 Numeration Systems 2-2 Describing Sets 2-3 Other Set Operations and Their Properties 3. Whole Numbers and Their Operations 3-1 Addition and Subtraction of Whole Numbers 3-2 Algorithms for Whole-Number Addition and Subtraction 3-3 Multiplication and Division of Whole Numbers 3-4 Algorithms for Whole-Number Multiplication and Division 3-5 Mental Mathematics and Estimation for Whole-Number Operations 4. Number Theory 4-1 Divisibility 4-2 Prime and Composite Numbers 4-3 Greatest Common Divisor and Least Common Multiple Online Module: Clock & Modular Arithmetic 5. Integers 5-1 Integers and the Operations of Addition and Subtraction 5-2 Multiplication and Division of Integers 6. Rational Numbers and Proportional Reasoning 6-1 The Set of Rational Numbers 6-2 Addition, Subtraction, and Estimation with Rational Numbers 6-3 Multiplication and Division of Rational Numbers 6-4 Ratios, Proportions, and Proportional Reasoning 7. Decimals: Rational Numbers and Percent 7-1 Introduction to Decimals 7-2 Operations on Decimals 7-3 Nonterminating Decimals 7-4 Percents and Interest 8. Real Numbers and Algebraic Thinking 8-1 Real Numbers 8-2 Variables 8-3 Equations 8-4 Functions 8-5 Equations in a Cartesian Coordinate System Online Module: Using Real Numbers in Equations 9. Probability 9-1 How Probabilities Are Determined 9-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities 9-3 Using Simulations in Probability 9-4 Odds, Conditional Probability, and Expected Value 9-5 Using Permutations and Combinations in Probability 10. Data Analysis/Statistics: An Introduction 10-1 Designing Experiments/Collecting Data 10-2 Displaying Data: Part I 10-3 Displaying Data: Part II 10-4 Measures of Central Tendency and Variation 10-5 Abuses of Statistics 11. Introductory Geometry 11-1 Basic Notions 11-2 Linear Measure 11-3 Curves, Polygons, and Symmetry 11-4 More About Angles Online Module: Networks 12. Congruence and Similarity with Constructions 12-1 Congruence through Constructions 12-2 Other Congruence Properties 12-3 Other Constructions 12-4 Similar Triangles and Similar Figures Online Module: Trigonometry Ratios via Similarity 13. Congruence and Similarity with Transformations 13-1 Translations and Rotations 13-2 Reflections and Glide Reflections 13-3 Dilations 13-4 Tessellations of the Plane 14. Area, Pythagorean Theorem, and Volume 14-1 Areas of Polygons and Circles 14-2 The Pythagorean Theorem, Distance Formula, and Equation of a Circle 14-3 Geometry in Three Dimensions 14-4 Surface Areas 14-5 Volume, Mass, and Temperature Online Appendices Spreadsheets Graphing calculators Geometer’s Sketchpad GeoGebra