Teaching Fractions And Ratios For Understanding Essential Content Knowledge and Instructional Strategies for Teachers 2nd Edition by Susan J Lamon ISBN 0805852107 9780805852103 by Susan J. Lamon 9780585383842, 9780805852103, 9781410617132, 0585383847, 0805852107, 1410617130 instant download after payment.

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ISBN 10: 0805852107 
ISBN 13: 9780805852103
Author: Susan J Lamon

This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking--without falling back on rules and procedures they have relied on throughout their lives.

Teaching Fractions And Ratios For Understanding Essential Content Knowledge and Instructional Strategies for Teachers 2nd Table of contents:

Part I: The Foundation: Deepening Understanding of Fractions

• Chapter 1: The Enduring Challenge of Fractions
  • Why Fractions are So Difficult for Students (and Teachers)
  • The Importance of Conceptual Understanding vs. Procedural Fluency
  • Fractions as a Gateway to Higher Mathematics
  • Overview of Key Interpretations of Fractions
• Chapter 2: What is a Fraction? Unpacking the Core Concepts
  • Part-Whole Interpretation: Unit Fractions, Proper/Improper Fractions
  • Quotient Interpretation: Division as Fractions
  • Ratio Interpretation: Relationship Between Two Quantities
  • Operator Interpretation: Scaling and Transforming
  • Fractions as Numbers: Placement on the Number Line
  • Equivalent Fractions and Simplification
• Chapter 3: Comparing and Ordering Fractions
  • Strategies for Comparing Fractions (Common Denominators, Common Numerators, Benchmarks, Cross-Multiplication)
  • Developing Number Sense with Fractions
  • Visual Models and Manipulatives for Comparison
• Chapter 4: Adding and Subtracting Fractions for Understanding
  • Conceptual Basis for Common Denominators
  • Using Area Models, Number Lines, and Physical Manipulatives
  • Strategies for Unlike Denominators and Mixed Numbers
  • Addressing Common Misconceptions (e.g., adding numerators and denominators)
• Chapter 5: Multiplying Fractions: More Than Just "Times"
  • Fraction of a Fraction: Area Models and Real-World Contexts
  • Fractions as Operators (Scaling)
  • Multiplication of Mixed Numbers
  • Why "Multiplying Makes Bigger" Doesn't Always Apply
• Chapter 6: Dividing Fractions: Unpacking the "Flip and Multiply" Rule
  • Understanding Division as "How Many Groups Of" or "How Many Times Does It Go Into"
  • Using Visual Models (e.g., area models, number lines, measurement models) to Explain Division
  • Connecting Division to Multiplication
  • Addressing Common Misconceptions

Part II: Building Connections: From Fractions to Ratios and Proportional Reasoning

• Chapter 7: Fractions, Decimals, and Percentages: An Integrated View
  • Connecting Fractions to Decimal Representation
  • Understanding Percentages as Ratios "Out of 100"
  • Conversion Strategies and Their Conceptual Basis
  • Real-World Applications and Contexts
• Chapter 8: Introducing Ratios and Rates: Comparison and Relationship
  • Defining Ratios: Part-to-Part and Part-to-Whole Relationships
  • Using Ratio Language ("For Every," "To Every")
  • Understanding Rates as Ratios with Different Units
  • Unit Rates and Their Importance
• Chapter 9: Proportional Reasoning: The Heart of Ratio Understanding
  • What is Proportional Reasoning? Its Significance in Mathematics and Science
  • Identifying Proportional vs. Non-Proportional Relationships
  • Strategies for Solving Proportional Problems (Scaling, Unit Rate, Cross-Multiplication)
  • Developing Mental Models for Proportionality
• Chapter 10: Applications of Ratios and Proportions
  • Scale Drawings and Maps
  • Percentages as Proportions
  • Problem Solving in Science, Finance, and Everyday Life
  • Similarity and Geometric Applications

Part III: Effective Instructional Strategies for the Classroom

• Chapter 11: General Principles for Teaching Fractions and Ratios
  • The Concrete-Representational-Abstract (CRA) Approach
  • Using Manipulatives and Visual Models Effectively
  • Fostering Productive Struggle and Discourse
  • Connecting to Prior Knowledge and Real-World Contexts
• Chapter 12: Strategies for Teaching Fractions
  • Addressing Common Student Misconceptions about Fractions
  • Lesson Planning for Conceptual Understanding
  • Differentiation for Diverse Learners (Struggling Learners, Advanced Learners)
  • Technology Tools for Fraction Instruction
• Chapter 13: Strategies for Teaching Ratios and Proportional Reasoning
  • Developing Proportional Thinking through Rich Tasks
  • Using Ratio Tables, Double Number Lines, and Graphs
  • Promoting Flexible Problem-Solving Approaches
  • Addressing Common Student Errors in Proportional Reasoning
• Chapter 14: Assessing Understanding: Beyond Correct Answers
  • Formative Assessment Strategies for Fractions and Ratios
  • Diagnostic Assessments to Uncover Misconceptions
  • Designing Rich Performance Tasks
  • Using Student Work to Inform Instruction

Conclusion: Empowering Teachers, Empowering Learners

• Recapitulating Essential Content and Pedagogical Insights
• The Continuous Journey of Professional Learning
• Building a Deeper Understanding of Mathematics in the Next Generation

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Tags: Susan J Lamon, Fractions, Ratios