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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 | |