coherence – fractions across the grades
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Units
Coherence – Fractions Across the Grades
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
2
• 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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
AGENDA
3
FRACTIONS ACROSS THE GRADES:A Progression of StandardsA Progression of Concrete and Visual Models The Progressions Documents:
Number and Operations—Fractions
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Standards of Grade 3—Module 5
4
Develop understanding of fractions as numbers. 3.NF.1, 3.NF.2, 3.NF.3
Reason with shapes and their attributes. 3.G.2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Foundational Understanding and Skills
5
• Review the standards of G3—M5. What understanding and skills are needed before learning these standards?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Foundational Standards
6
• What Grade 2 standards are foundational to the G3—M5 standards?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
7
A Progression of Foundational Standards
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Foundational Standards
8
• Continue to map backwards noting the understanding, skills and related standards from Grades 1, K, and PK.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
9
A Progression of Foundational Standards
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
A Progression of Fraction Standards
10
• The G3—M5 standards are foundational to what standards in grades 4 and 5?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
11
A Progression of Fraction Standards
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
AGENDA
12
FRACTIONS ACROSS THE GRADES:A Progression of StandardsA Progression of Concrete and Visual ModelsThe Progressions Documents:
Number and Operations—Fractions
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Demonstration – A Progression of Concrete and Visual Models
13
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
AGENDA
14
FRACTIONS ACROSS THE GRADES:A Progression of StandardsA Progression of Concrete and Visual ModelsThe Progressions Documents:
Number and Operations—Fractions
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Techniques for a Study of Progressions:
15
• Denote your reactions to the text with a personalized coding system. For example:
Light bulb moment? Questions about this
Important – revisit this portion
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Collaborative Study – Number and Operations— Fractions
16
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Techniques for a Study of Progressions:
17
• Create a visual link (brackets, arrows, or color coded highlights) between standards in the margin and related text.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Selected Excerpts from the Progressions:
18
• 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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Techniques for a Study of Progressions:
19
•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.”
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Studying Progressions of Topics
20
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?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Next Steps
21
• How can you increase coherence in your school’s delivery of topics?
• How can you initiate a study of progressions with your colleagues?