Copyright 2013 by aha! Process, Inc. All rights reserved. December 3, 2014.

Copyright 2013 by aha! Process, Inc. All rights reserved. www.ahaprocess.com

Math Leadership Network Meeting

December 3, 2014


Agenda

• The Latest from SED• The Progression to Geometry:

Looking at Area• An Up-Close Look at Student Centered

Math Teaching• Discussion Topics• Q & A


The Latest From SED• Module Updates

– https://www.engageny.org/resource/curriculum-module-updates

• PreK Modules– https://www.engageny.org/content/preki

ndergarten-mathematics

• Pacing Charts– http://commoncore.org/maps/math/pacing-guides

https://www.engageny.org/resource/curriculum-module-updates

https://www.engageny.org/resource/curriculum-module-updates

https://www.engageny.org/content/prekindergarten-mathematics

https://www.engageny.org/content/prekindergarten-mathematics

http://commoncore.org/maps/math/pacing-guides


The Latest From SED

• 3 – 8 Assessments– https://www.engageny.org/resource/n

ew-york-state-common-core-sample-questions

https://www.engageny.org/resource/new-york-state-common-core-sample-questions




The Latest From SED

• Geometry Regents– https://www.engageny.org/resource/rege

nts-exams-mathematics-geometry-sample-items

– https://www.engageny.org/resource/regents-exams-mathematics-geometry-test-guide

https://www.engageny.org/resource/regents-exams-mathematics-geometry-sample-items



https://www.engageny.org/resource/regents-exams-mathematics-geometry-test-guide




Guide to the Regents Examination in Geometry (Common Core)

• In response to field feedback, the Educator Guide to the Regents Examination in Geometry (Common Core) has been updated.

• One important refinement is that there will be two 6-credit constructed-response questions: one 6-credit question will require students to develop multi-step, extended logical arguments and proofs involving major content, and one 6-credit question will require students to use modeling to solve real-world problems. This refinement balances field expectations with what the standards require, and will allow students the opportunity to exhibit the knowledge and skills associated with both types of questions.

• The guide also provides additional information about the types of

questions that will appear on the test in June 2015.


The Latest From SED

• Math Studio Talks K – 5– https://www.engageny.org/content/math-

studio-talk-common-core-instruction-video-series

https://www.engageny.org/content/math-studio-talk-common-core-instruction-video-series




Looking at Area

THE GEOMETRY PROGRESSION


What Is Area?

• Area as a concept begins in grade 3, however only with figures that are easily filled with units.


Grade 3


Multiplying and Dividing With the Area Model

Grade 3


What Is Area? on 1: What Is

Area?


What Is Area?

• Then in grade 5, students partition units thus allowing us to look at figures with sides with fractional lengths.


What Is Area?


What Is Area?

Finding the area of a rectangle whose side lengths are irrational.

•1’s: Complete a table of approximations of the side lengths and area of rectangles that are less than those of the given rectangle.

•2’s: Complete a table of approximations of the side lengths and area of rectangles that are greater than those of the given rectangle.


What Is Area?

What Is Area?• Approximating the percent error for our approximated

areas.• We know the true area is between 2.38 and 2.7.• What is the Maximum Absolute Error? (This is first

introduced in Grade 7 Module 4)• The absolute value of their difference…|2.7−2.38|=0.32• Using the above approximations, what is the maximum percent error?• 0.32/2.38≈0.134453, Our approximation must

have an error of less than 13.45%.


What Is Area?

Finally, reasoning about area matures to develop a universal method for determining area, even when the areas are not finite unions of unit squares or simple parts of unit squares. This is referred to by mathematicians as Jordan Measure. This outlook on area forms an important bridge to calculus.

What Is Area?If it takes one can of paint to cover a square unit in the coordinate plane, how many cans of paint are needed to paint the region within the curved figure?

What Is Area?


What Is Area?• Area is introduced in Grade 3, but only figures that are

easy to ‘fill’ with units are considered. • In Grade 5, the need to use parts of unit squares for

some figures is understood, and is applied in Grade 6. • In Grade 7, students realize that a figure may have an

area even if, like the disk, it cannot be decomposed into a finite number of unit squares, but (appropriately) this is treated at the intuitive level.

• The culmination is a universal method for measuring areas, even when they are not finite unions of unit squares or simple parts of unit squares. Mathematicians refer to this as Jordan measure. The concept forms an important bridge to calculus, as Jordan measure is the idea employed in defining the Riemann Integral.


A Close Read…• An Up-Close Look at Student

Centered Math Teaching

http://www.nmefoundation.org/global/featured-research/homepage/an-up-close-look-at-student-centered-math-teaching







Discussion Groups

• Topic?

• Topic?

• Topic?

• Topic?


Questions??


Thank You!!

Grades PreK - 8

Anne Marie VoutsinasNetwork Team Member

[email protected] Keim

Network Team Member

[email protected]

Grades 6 - 12

Jack McLoughlin

Network Team Member

[email protected] Corcoran

Science Coordinator

[email protected]

Copyright 2013 by aha! Process, Inc. All rights reserved. December 3, 2014.

Documents

Transcript of Copyright 2013 by aha! Process, Inc. All rights reserved. December 3, 2014.