Deep Dive into the Math Shifts

Understanding Focus and Coherence in the Common Core State Standards for

Mathematics

The Three Shifts in Mathematics

•Focus: Strongly where the standards focus•Coherence: Think across grades and link to major topics within grades•Rigor: Require conceptual understanding, fluency, and application

Engaging with the 6-8 Content

• How would you summarize the major work of grades 6-8?

• What would you have expected to be a part of the major work that is not?

• Give an example of how you would approach something differently in your teaching if you thought of it as supporting the major work, instead of being a separate, discrete topic.

Algebra I Overview

GeometryOverview

http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

Engaging with the HS Content

• How would you summarize the major work of Algebra I and Geometry?

• What would you have expected to be a part of the major work that is not?

• Give an example of how you would approach something differently in your teaching if you thought of it as supporting the major work, instead of being a separate, discrete topic.

Coherence Across and Within Grades

• It’s about math making sense.• The power and elegance of math comes out

through carefully laid progressions and connections within grades.

Taken from the M/J Pre- Algebra Course Description on C-Palms website: Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Looking For Coherence Within Grades

• Examples: 6th grade: Solve problems by graphing in all 4

quadrants. (1st year of rational numbers) 8th grade: “Understand the connections between

proportional relationships, lines and linear equations.”

Algebra 1: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related

Coherence Within A Grade

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.6

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Coherence Within Geometry

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.5

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Looking for Coherence Across Grades

• Coherence is an important design element of the standards.

• “The Standards are not so much built from topics as they are woven out of progressions.”

DIVING IN! Let’s explore for evidence of coherence!

Coherence Card Activity

Activity: Place the standards of each theme under the appropriate grade or course.

– Separate the cards by theme.– No grade has two of the same theme.– Some “themes” that have only a few cards might represent

consecutive grades and some may not.– Read each card in it’s entirety to help determine placement.– Do not check your Standards until you and your colleagues

agree on the final product.– Discuss horizontal and vertical observations with your

partners.21

Engaging with the Content

• Review your work on Coherence.

• Revisit the major focus of each grade/course

• Which standards in your progressions are part of the major work, the supporting work, or additional work? Mark them appropriately on your posters using green, blue, or yellow makers.

• Discuss the connection between focus and coherence and how the two work in tandem to influence instruction

Next Month.......• Your school has been provided with an

electronic file containing the 2013-2014 math course descriptions

• Next month we will delve even deeper into the CCSS course content

CCSS COURSE DESCRIPTIONS

Resources• Common Core Progressions http://ime.math.arizona.edu/progressions/

• PARCC Content Frameworkshttp://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

• C-Palms Unpacking Maphttp://www.cpalms.org/cpalms/unpack_map.aspx

• Flip Chartshttp://www.azed.gov/azcommoncore/files/2012/11/high-school-ccss-flip-book-usd-259-2012.pdf