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Enhancing Fraction Understanding: Progressions and Coherence

Explore how fractions develop across grades, study standards and progressions supporting coherence in teaching, and delve into foundational concepts and skills needed for Grade 3 - Module 5. Engage with concrete and visual models, progression documents, and learn techniques to study progressions effectively. Reflect on the benefits of understanding progressions versus standards, and consider ways to increase coherence in teaching fractions at your school. Initiate collaborative studies with colleagues to enhance teaching practices.

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Enhancing Fraction Understanding: Progressions and Coherence

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  1. Coherence – Fractions Across the Grades

  2. Session Objectives • Explore the development of fractions across the grade levels. • Examine and study the PK–5 standards and related modules foundational to fractions. • Examine the K–5 progressions documents with particular emphasis on Number and Operations—Fractions. • Explore how content knowledge directed by the standards and progressions documents supports the implementation of coherence in the classroom. • Consider how G3—M5 supports the fraction progression.

  3. AGENDA • FRACTIONS ACROSS THE GRADES: • A Progression of Standards • A Progression of Concrete and Visual Models • The Progressions Documents: • Number and Operations—Fractions

  4. Standards of Grade 3—Module 5 • Develop understanding of fractions as numbers. • 3.NF.1, 3.NF.2, 3.NF.3 • Reason with shapes and their attributes. • 3.G.2

  5. Foundational Understanding and Skills • Review the standards of G3—M5. What understanding and skills are needed before learning these standards?

  6. Foundational Standards • What Grade 2 standards are foundational to the G3—M5 standards?

  7. A Progression of Foundational Standards

  8. Foundational Standards • Continue to map backwards noting the understanding, skills and related standards from Grades 1, K, and PK.

  9. A Progression of Foundational Standards

  10. A Progression of Fraction Standards • The G3—M5 standards are foundational to what standards in grades 4 and 5?

  11. A Progression of Fraction Standards

  12. AGENDA • FRACTIONS ACROSS THE GRADES: • A Progression of Standards • A Progression of Concrete and Visual Models • The Progressions Documents: • Number and Operations—Fractions

  13. Demonstration – A Progression of Concrete and Visual Models

  14. AGENDA • FRACTIONS ACROSS THE GRADES: • A Progression of Standards • A Progression of Concrete and Visual Models • The Progressions Documents: • Number and Operations—Fractions

  15. Techniques for a Study of Progressions: • Denote your reactions to the text with a personalized coding system. For example: Light bulb moment ?Questions about this Important – revisit this portion

  16. Collaborative Study – Number and Operations— Fractions

  17. Techniques for a Study of Progressions: • Create a visual link (brackets, arrows, or color coded highlights) between standards in the margin and related text.

  18. Selected Excerpts from the Progressions: • Words / sentences to use when defining or describing content: • For example, we “partition” the shape, not “divide.” • Connection to mathematical practices • Models and representations • High level goals for this content in a given grade • Areas of possible student misconceptions

  19. Techniques for a Study of Progressions: • Read the first five paragraphs of page 5 in the Number and Operations—Fractions progression is a line by line fashion. • Check for comprehension at every component of each sentence. • Mark anything that ties back to Grade 3 with a “3,” and anything that is new content with a “4.”

  20. Studying Progressions of Topics • Reflections: • How does what is gained from a study of the progressions differ from what is gained from a study of the standards? • What do these two essential documents offer to our profession?

  21. Next Steps • How can you increase coherence in your school’s delivery of topics? • How can you initiate a study of progressions with your colleagues?

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