I. Problem Solving -- Introduction -- Problem or Exercise? -- Problem Solving Strategies -- Beware of Patterns! -- Problem Bank -- Careful Use of Language in Mathematics -- Explaning Your Work -- The Last Step -- II. Place Value -- Dots and Boxes -- Other Rules -- Binary Numbers -- Other Bases -- Number Systems -- Even Numbers -- Problem Bank -- Exploration -- III. Number and Operations -- Introduction -- Addition: Dots and Boxes -- Subtration: Dots and Boxes -- Multiplication: Dots and Boxes -- Division: Dots and Boxes -- Number Line Model -- Area Model for Multiplication -- Properties of Operations -- Division Explorations -- Problem Bank -- IV. Fractions -- Introduction -- What is a Fraction? -- The Key Fraction Rule -- Adding and Subtracting Fractions -- What is a Fraction? Revisited -- Multiplying Fractions -- Dividing Fractions: Meaning -- Dividing Fractions: Invert and Multiply -- Dividing Fractions: Problems -- Fractions involving zero -- Problem Bank -- Egyptian Fractions -- Algebra Connections -- What is a Fraction? Part 3 -- V. Patterns and Algebraic Thinking -- Introduction -- Borders on a Square -- Careful Use of Language in Mathematics: = -- Growing Patterns -- Matching Game -- Structural and Procedural Algebra -- Problem Bank -- VI. Place Value and Decimals -- Review of Dots & Boxes Model -- Decimals -- x-mals -- Division and Decimals -- More x -mals -- Terminating or Repeating? -- Matching Game -- Operations on Decimals -- Orders of Magnitude -- Problem Bank -- VII. Geometry -- Introduction -- Tangrams -- Triangles and Quadrilaterals -- Polygons -- Platonic Solids -- Painted Cubes -- Symmetry -- Geometry in Art and Science -- Problem Bank -- VIII. Voyaging on Hokule?a -- Introduction -- Hokule?a -- Worldwide Voyage -- Navigation

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are "Why?" and "How do you know you're right?" Practice asking these questions of yourself, of your professor, and of your fellow students.Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

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In English.

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