Coherence – Fractions Across the Grades

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NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Units

Coherence – Fractions Across the Grades


N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Session Objectives

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• 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.



AGENDA

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FRACTIONS ACROSS THE GRADES:A Progression of StandardsA Progression of Concrete and Visual Models The Progressions Documents:

Number and Operations—Fractions



Standards of Grade 3—Module 5

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Develop understanding of fractions as numbers. 3.NF.1, 3.NF.2, 3.NF.3

Reason with shapes and their attributes. 3.G.2



Foundational Understanding and Skills

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



Foundational Standards

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• What Grade 2 standards are foundational to the G3—M5 standards?



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A Progression of Foundational Standards



Foundational Standards

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



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A Progression of Foundational Standards



A Progression of Fraction Standards

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• The G3—M5 standards are foundational to what standards in grades 4 and 5?



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A Progression of Fraction Standards



AGENDA

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FRACTIONS ACROSS THE GRADES:A Progression of StandardsA Progression of Concrete and Visual ModelsThe Progressions Documents:




Demonstration – A Progression of Concrete and Visual Models

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AGENDA

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FRACTIONS ACROSS THE GRADES:A Progression of StandardsA Progression of Concrete and Visual ModelsThe Progressions Documents:




Techniques for a Study of Progressions:

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• Denote your reactions to the text with a personalized coding system. For example:

Light bulb moment? Questions about this

Important – revisit this portion



Collaborative Study – Number and Operations— Fractions

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• Create a visual link (brackets, arrows, or color coded highlights) between standards in the margin and related text.



Selected Excerpts from the Progressions:

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• 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




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•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.”



Studying Progressions of Topics

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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?



Next Steps

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• How can you increase coherence in your school’s delivery of topics?

• How can you initiate a study of progressions with your colleagues?