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Math Leadership Network Meeting
December 3, 2014
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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
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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
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The Latest From SED
• 3 – 8 Assessments– https://www.engageny.org/resource/n
ew-york-state-common-core-sample-questions
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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
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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.
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The Latest From SED
• Math Studio Talks K – 5– https://www.engageny.org/content/math-
studio-talk-common-core-instruction-video-series
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Looking at Area
THE GEOMETRY PROGRESSION
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What Is Area?
• Area as a concept begins in grade 3, however only with figures that are easily filled with units.
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Multiplying and Dividing With the Area Model
Grade 3
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What Is Area? on 1: What Is
Area?
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What Is Area?
• Then in grade 5, students partition units thus allowing us to look at figures with sides with fractional lengths.
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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?• 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%.
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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?
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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.
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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
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Discussion Groups
• Topic?
• Topic?
• Topic?
• Topic?
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Thank You!!
Grades PreK - 8
Anne Marie VoutsinasNetwork Team Member
[email protected] Keim
Network Team Member
Grades 6 - 12
Jack McLoughlin
Network Team Member
[email protected] Corcoran
Science Coordinator