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Cover -- Contents -- Preface -- Acknowledgments -- About the Authors -- PART 1 FIGURING OUT FLUENCY: KEY IDEAS -- What Is Fluency With Rational Numbers and Algebraic Equations? -- Why Focus on Fluency for Rational Numbers and Algebraic Equations? -- What Do Fluency Actions Look Like for Rational Numbers and Algebraic Equations? -- What Conceptual Foundations Do Students Need? -- What Automaticities Do Students Need? -- What Properties and Utilities Support Strategic Competence? -- What Are Strategies for Computational Estimation? -- What Are Significant Reasoning Strategies? -- How Do I Teach, Practice, and Assess Strategies? -- How Do I Support Students' Fluency Over Time? -- In Sum, Ways to Support "Real" Fluency -- PART 2 STRATEGY MODULES -- Module 1: Reasoning Strategies for Addition -- Strategy Overview: Count On -- Teaching Activities for Count On -- Practice Activities for Count On -- Strategy Overview: Make Tens (Extended) -- Teaching Activities for Make Tens -- Practice Activities for Make Tens -- Strategy Overview: Compensation -- Teaching Activities for Compensation -- Practice Activities for Compensation -- Strategy Overview: Partial Sums -- Teaching Activities for Partial Sums -- Practice Activities for Partial Sums -- Module 2: Reasoning Strategies for Subtraction -- Strategy Overview: Count Back -- Teaching Activities for Count Back (USE JUMPS) -- Practice Activities for Count Back (USE JUMPS) -- Strategy Overview: Think Addition (Find the Difference) -- Teaching Activities for Think Addition -- Practice Activities for Think Addition -- Strategy Overview: Compensation -- Teaching Activities for Compensation -- Practice Activities for Compensation -- Strategy Overview: Partial Differences -- Teaching Activities for Partial Differences -- Practice Activities for Partial Differences. Module 3: Reasoning Strategies for Multiplication -- Strategy Overview: Break Apart by Addends -- Teaching Activities for Break Apart by Addends -- Practice Activities for Break Apart by Addends -- Strategy Overview: Break Apart by Factors (Including Halve and Double) -- Teaching Activities for Break Apart by Factors -- Practice Activities for Break Apart by Factors -- Strategy Overview: Compensation (for Multiplication) -- Teaching Activities for Compensation -- Practice Activities for Compensation -- Module 4: Reasoning Strategies for Division -- Strategy Overview: Think Multiplication -- Teaching Activities for Think Multiplication -- Practice Activities for Think Multiplication -- Strategy Overview: Partial Quotients -- Teaching Activities for Partial Quotients -- Practice Activities for Partial Quotients -- Module 5: Reasoning Strategies for Ratios and Proportions -- What Are Good Representations for Ratios and Proportions? -- Strategies for Comparing Ratios and Solving Proportions -- Strategy Overview: Build Up/Break Down -- Strategy Overview: Find a Unit Rate -- Strategy Overview: Use a Scale Factor -- Strategy Overview: Use y = kx -- Algorithm Overview: Find Cross Products -- Teaching Activities for Ratios and Proportions -- Practice Activities for Ratios and Proportions -- Module 6: Strategies for Solving Equations for an Unknown -- Strategies for Solving Equations for an Unknown -- Strategy Overview: Using Relational Reasoning -- Strategy Overview: Choosing a Basic Transformation -- Teaching Activities for Solving Equations for an Unknown -- Practice Activities for Solving Equations for an Unknown -- Module 7: Strategies for Solving Systems of Linear Equations -- Strategies for Solving a System of Linear Equations -- Teaching Activities for Solving Systems of Linear Equations -- Practice Activities for Solving Systems of Linear Equations. PART 3 PUTTING IT ALL TOGETHER: DEVELOPING FLUENCY -- Fluency Is . . . -- Assessing Fluency -- Fluency Activities -- Appendix: Tables of Activities -- References -- Index.