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| The Art of Problem Solving | |
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| Solving Problems by Inductive Reasoning | |
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| An Application of Inductive Reasoning: Number Patterns | |
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| Strategies for Problem Solving | |
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| Calculating, Estimating, and Reading Graphs | |
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| Extension: Using Writing to Learn About Mathematics | |
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| Collaborative Investigation: Discovering Mathematics in Pascal's Triangle | |
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| Chapter 1 Test | |
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| The Basic Concepts Of Set Theory | |
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| Symbols and Terminology | |
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| Venn Diagrams and Subsets | |
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| Set Operations and Cartesian Products | |
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| Cardinal Numbers and Surveys | |
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| Infinite Sets and Their Cardinalities | |
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| Collaborative Investigation: A Survey of Your Class | |
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| Chapter 2 Test | |
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| Introduction to Logic | |
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| Statements and Quantifiers | |
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| Truth Tables and Equivalent Statements | |
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| The Conditional and Circuits | |
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| More on the Conditional | |
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| Analyzing Arguments with Euler Diagrams | |
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| Extension: Logic Puzzles | |
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| Analyzing Arguments with Truth Tables | |
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| Collaborative Investigation: Logic Puzzles Revisited | |
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| Chapter 3 Test | |
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| Numeration and Mathematical Systems | |
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| Historical Numeration Systems | |
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| Arithmetic in the Hindu-Arabic System | |
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| Conversion Between Number Bases | |
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| Finite Mathematical Systems | |
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| Groups | |
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| Collaborative Investigation: A Perpetual Calendar Algorithm | |
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| Chapter 4 Test | |
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| Number Theory | |
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| Prime and Composite Numbers | |
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| Selected Topics from Number Theory | |
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| Greatest Common Factor and Least Common Multiple | |
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| Modular Systems | |
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| The Fibonacci Sequence and the Golden Ratio | |
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| Extension: Magic Squares | |
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| Collaborative Investigation: Investigating an Interesting Property of Number Squares | |
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| Chapter 5 Test | |
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| The Real Numbers and Their Representations | |
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| Real Numbers, Order, and Absolute Value | |
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| Operations, Properties, and Applications of Real Numbers | |
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| Rational Numbers and Decimal Representation | |
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| Irrational Numbers and Decimal Representation | |
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| Applications of Decimals and Percents | |
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| Extension: Complex Numbers | |
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| Collaborative Investigation: Budgeting to Buy a Car | |