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Coherence – Fractions Across the Grades

Coherence – Fractions Across the Grades. Session Objectives. Explore the development of fractions across the grade levels. Examine and study the PK–5 standards and related modules foundational to fractions.

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Coherence – Fractions Across the Grades

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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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