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A Story of Units

A Story of Units. Grade 4 – Module 5 Fraction Equivalence, Ordering, and Operations. Session Objectives. Examination of the development of mathematical understanding across the module with a focus on the Concept Development within the lessons

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A Story of Units

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  1. A Story of Units Grade 4 – Module 5 Fraction Equivalence, Ordering, and Operations

  2. Session Objectives • Examination of the development of mathematical understanding across the module with a focus on the Concept Development within the lessons • Introduction to mathematical models and instructional strategies to support implementation of A Story of Units

  3. Agenda Introduction to the Module Concept Development Module Review

  4. Curriculum Overview of A Story of Units

  5. Module Overview • Read the Narrative, Standards, Lesson Objectives, and Vocabulary. • What is familiar to you and your students? • What will be new learning?

  6. Mid-Module Assessment Topics A - D • Study this document, and the End Module Assessment, prior to teaching the Lessons. • Provides a snapshot of the concepts taught over the next 21 Lessons. • Scan the Mid-Module Assessment to get an idea of what topic we are about to cover.

  7. Agenda Introduction to the Module Concept Development Module Review

  8. Topic A: Decomposition and Fraction Equivalence 4.NF.3b, 4.NF.4a • 6 lessons to show fraction equivalence through decomposition of fractions • Tools: number bond, folding paper strips, tape diagram, area model

  9. Decomposition of Fractions Lesson 1, Concept Development • Use a strip of paper to represent, for example, thirds and sixths. • Show how a non-unit fraction is the sum of unit fractions. • Extend learning to show that non-unxxit fractions can be expressed as the sum of two or more fractions (unit or non-unit).

  10. Decomposition of Fractions Lesson 1, Concept Development • Extend learning to fractions representing numbers greater than one. • Use tape diagrams to represent fractional parts. • Discover that there are multiple ways to decompose fractions.

  11. Lesson 2, Concept Development • Debrief: How is decomposing a non-unit fraction similar to decomposing whole numbers in Kindergarten and Grade 1?

  12. Decomposition of Fractions Lesson 3, Concept Development • Express a non-unit fraction as a whole number times a unit fraction.

  13. Decomposition of Fractions Lesson 4, Concept Development • Decompose fractions into sums of smaller unit fractions. • Draw and label to show the equivalence of fractions.

  14. Decomposition of Fractions Lesson 5, Application Problem

  15. Decomposition of Fractions Lesson 5, Concept Development • Show fraction equivalence using an area model. • Model equivalence by drawing an area model.

  16. Decomposition of Fractions Lesson 6, Concept Development • Create equivalent fractions by drawing an area model and then dividing it into smaller parts.

  17. Decomposition of Fractions Topic A Debrief • Turn and Talk to those sitting at your table: • How can decomposing fractions lead to better understanding of the representation of non-unit fractions and to fraction equivalence? • How do number bonds, tape • diagrams, and area models aid in • the understanding of the • decomposition of fractions?

  18. Topic B: Fraction Equivalence Using Multiplication and Division 4.NF.1 • 5 lessons to show fraction equivalence using multiplication and division. • New Terms: numerator, denominator • Tools: tape diagrams, area model, number line

  19. Fraction Equivalence Lesson 7, Application Problem

  20. Fraction Equivalence Lessons 7 and 8, Concept Development • Decompose the area model to show equivalence. • Create equivalent fractions by multiplying the numerator and denominator by the same number.

  21. Fraction Equivalence Lesson 11, Application Problem

  22. Fraction Equivalence Lesson 9, Concept Development • Compose larger fractional units. • Discover that the numerator and denominator can be divided by the same number to model equivalence.

  23. Fraction Equivalence Lesson 10, Concept Development • Use knowledge of common factors to show equivalent fractions. • Show equivalence using the greatest common factor.

  24. Fraction Equivalence Lesson 11, Concept Development • Use a number line to show equivalence.

  25. Fraction Equivalence Topic B • Turn and Talk to those sitting at your table: • How does the modeling used within this Topic help students to conceptually understand fractional equivalence?

  26. Topic C: Fraction Comparison 4.NF.2 • 4 lessons to show comparison of fractions using benchmark numbers and common units • New Term: benchmarks • Tools: number line, tape diagrams, area models, number bonds

  27. Fraction Comparison Lesson 12, Concept Development • Think about fractions in relation to 0, ½ , and 1, first in isolation and then in fraction comparison.

  28. Fraction Comparison Lesson 13, Concept Development • Compare two fractions greater than one using benchmarks.

  29. Fraction Addition and Subtraction Lesson 17, Concept Development • Subtraction of a fraction from a whole using different methods

  30. Fraction Comparison Lesson 14, Concept Development • Common numerators • Numerators with related units

  31. Fraction Comparison Lesson 14, Concept Development • Denominators with related units

  32. Fraction Comparison Lesson 15, Concept Development • Denominators with unrelated units • Use of the area model to create common units for comparison • Use of number bonds to ‘pull out’ a whole and then compare the parts

  33. Fraction Comparison Topic C • Turn and Talk: • What methods of fraction comparison are familiar? • What methods of fraction comparison are new? • How can each of the methods be used to help students as they compare fractions?

  34. Topic D: Fraction Addition and Subtraction 4.NF.3a, 4.NF.4d • 6 lessons to show addition and subtraction of fractions with an emphasis on common units • New Terms: common denominators, mixed units • Tools: number line, tape diagram, number bond

  35. Fraction Addition and Subtraction Lesson 16, Concept Development • Unit language is used to relate addition and subtraction of fractions to addition and subtraction of whole numbers.

  36. Fraction Addition and Subtraction Lesson 16, Concept Development • Conversion from a fraction greater than one to a mixed number using a number bond

  37. Fraction Addition and Subtraction Lesson 18, Concept Development Students work in groups to find multiple ways of solving

  38. Fraction Addition and Subtraction telling time buying deli meat measuring inches cooking a recipe gas gauge money measuring turns measuring spoons and cups Lesson 19, Application Problem

  39. Fraction Addition and Subtraction Lesson 19, Concept Development • Students use multiple solution strategies to solve. • Use RDW to solve. Try solving 2 ways.

  40. Fraction Addition and Subtraction Lesson 20, Concept Development • Adding with related units

  41. Fraction Addition and Subtraction Lesson 21, Concept Development

  42. Fraction Addition and Subtraction Topic D • Turn and Talk: • How is subtracting fractions similar to subtracting whole numbers? • Discuss the progression and the importance of the number bond model across grades.

  43. Topic E: Extending Fraction Equivalence to Fractions Greater Than One 4.NF.1, 4.NF.2, 4.NF.3 • 7 lessons working with fractions greater than one to rename, order, and compare. • New Terms: line plot • Tools: number line, tape diagram, number bond, line plot

  44. Extending Fraction Equivalence to Fractions >1 Lesson 22, Concept Development

  45. Extending Fraction Equivalence to Fractions >1 Lesson 23, Concept Development

  46. Extending Fraction Equivalence to Fractions >1 Lesson 24, Concept Development • Rename fractions as mixed units using decomposition • Convert using multiplication

  47. Extending Fraction Equivalence to Fractions >1 Lesson 25, Application Problem Use RDW to solve:

  48. Extending Fraction Equivalence to Fractions >1 Lesson 25, Concept Development • Convert a mixed number to a fraction greater than one.

  49. Extending Fraction Equivalence to Fractions >1 Lesson 26, Concept Development • Compare fractions greater than one by reasoning using benchmark numbers.

  50. Extending Fraction Equivalence to Fractions >1 Lesson 27, Concept Development • Comparison with related denominators • Comparison with unrelated denominators

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