Teaching fractions and ratios for understanding : essential content knowledge and instructional strategies for teachers /: essential content knowledge and instructional strategies for teachers. (2020)

• Record Type: Book
• Further Information: Note: Susan J. Lamon.
• Authors: Lamon, Susan J, 1949-
• Contents: Preface 1. Proportional Reasoning: An Overview Student Strategies Introduction The Constant of Proportionality Reasoning: Beyond Mechanization Invariance and Covariance Solving Proportions Using K Multiplicative Thinking Critical Components of Powerful Reasoning Getting Started Analyzing Children’s Thinking Activities 2. Fractions and Rational Numbers Student Strategies New Units and a New Notational System The Psychology of Units New Operations and Quantities Interference of Whole Number Ideas Problems with Terminology Development of Sets of Numbers Kinds of Fractions What are Fractions? Rational Numbers Fractions as Numbers Fractions, Ratios, and Rates Many Sources of Meaning Multiple Interpretations of the Fraction 3/4 Activities 3. Relative Thinking and Measurement Student Strategies Two Perspectives on Change Relative Thinking and Understanding Fractions Encouraging Multiplicative Thinking Two Meanings for "More" The Importance of Measurement The Compensatory Principle The Approximation Principle Recursive Partitioning Principle Measuring More Abstract Qualities Other Strategies Activities 4. Quantities and Covariation Student Strategies Building on Children’s Informal Knowledge Quantities Unquantified Quantifiable Characteristics Discussing Proportional Relationships in Pictures Visualizing, Verbalizing, and Symbolizing Changing Relationships Covariation and Invariance Cuisenaire Strips Scale Factors Areas and Volumes of Scaled Figures Similarity Indirect Measurement Testing for Similarity Mockups and Pudgy People Activities 5. Proportional Reasoning Student Strategies The Unit Units Defined Implicitly Using Units of Various Types Reasoning Up and Down Units and Unitizing Unitizing Notation Flexibility in Unitizing Children’s Thinking Classroom Activities to Encourage Unitizing Visual Activities Reasoning with Ratio Tables Problem Types Ratio Tables Increasing the Difficulty Analyzing Relationships Percentage Percentages as an Instructional Task Reasoning with Percentages Activities 6. Reasoning with Fractions Student Strategies Visualizing Operations Equivalent Fractions and Unitizing Comparing Fractions Fractions in Between Activities 7. Fractions as Part–Whole Comparisons Student Strategies Part–Whole Fractions: The Big Ideas Unitizing and Equivalence Problems in Current Instruction Fraction Models Fraction Strips Comparing Part–Whole Fractions Discrete Units Multiplication Partitive and Quotative Division Division Other Rational Number Interpretations Activities 8. Fractions as Quotients Student Strategies Quotients Partitioning as Fair Sharing Partitioning Activities Children’s Partitioning Equivalence Simplifying Fractions Understanding Fractions as Quotients More Advanced Reasoning Sharing Different Pizzas Activities 9. Fractions as Operators Student Strategies Operators Exchange Models Composition Area Model for Multiplication Area Model for Division Compositions and Paper Folding Understanding Operators Activities 10. Fractions as Measures Student Strategies Measures of Distance Static and Dynamic Measurement The Goals of Successive Partitioning Understanding Fractions as Measures Units, Equivalent Fractions, and Comparisons Fraction Operations Activities 11. Ratios and Rates Student Strategies What is a Ratio? Notation and Terminology Equivalence and Comparison of Ratios Ratios as an Instructional Task What is a Rate? Operations with Rates and Ratios Linear Graphs Comparing Ratios and Rates Graphically Speed: The Most Important Rate Characteristics of Speed Students’ Misconceptions About Speed Average Speed Distance– Speed–Time and Graphs Activities 12. Changing Instruction Student Comments Why Change? A Summary of Fraction Interpretations Central Structures Characteristics of Proportional Thinkers Obstacles to Change Sequencing Topics Directions for Change Challenging Problems
• Edition: Fourth edition
• Publisher Details: London : Routledge
• Publication Date: 2020
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 372.72; Fractions -- Study and teaching (Elementary); Ratio and proportion -- Study and teaching (Elementary)
• Languages: English
• ISBNs: 9781000037333; 9781000037272; 9781003008057
• Related ISBNs: 9780367441647; 9780367441678
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.