DEAR Algebra

Nyasha Okor, SLC, Title I Math Lead, okor@fultonschools.org

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Today's Focus

Maneuvering the GSE with Algebra Tiles

Learning Target

I can differentiate instruction using algebra tiles and the Concrete, Representation, and Abstract (CRA) progression model.

Agenda Items

  • Effective Use of Algebra Tiles
  • Play time - naming pieces
  • Zero Principle
  • Modeling Operations with Integers
  • Algebraic Expressions (linear and quadratic)
  • Modeling operations with Polynomials
  • Solving Perimeter and Area Problems
  • Solving linear equations and inequalities
  • Factoring trinomials
  • Solving quadratics by completing the square
  • Virtual Manipulatives (Including online textbook resources)
  • Symbaloo

How have you used manipulatives for classroom instruction?

Click on the button below and read independently.

Opening Page: Author's Reflection

Article: Blue Link at the bottom of the page

Manipulatives: The Missing Link in High School

Blue link at the bottom of the page.

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What standards do Algebra Tiles Support?

https://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspx


  • Grade 6: Units 4, 5
  • Grade 7: Units 1, 2
  • Grade 8: Unit 5
  • Algebra: Units 2, 3

http://www.doe.nv.gov/Standards_Instructional_Support/Nevada_Academic_Standards/Math/Resources/ (Deconstructed standards and learning targets)

Open you gifts!

Magnetic set for the white board

Class sets of tiles

Transparent set for the overhead projector

Virtual Tiles (see orange flyer for downloading instructions)

Workbook

Algebra Tiles Play Time

Play with the tiles (management strategy).

What can be done with the manipulatives?

What does each piece represent?

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CRA

Let's set up your graph paper to reflect this natural progression.

How does CRA increase student problem solving abilities?

Zero Principle

  • Zero can be represented by any two like quantities with opposite signs.
  • Additive Inverses/opposites

Zero Principle

On a sheet of graph paper, create 5 groups of tiles to represent the Zero Principle.

Food for Thought


  • Have students come up with the rules/properties you are trying to teach them instead of telling them. They can share their discoveries and create a class list of them.
  • Do NOT do the thinking for students. Let them discover the shortcuts when working with manipulatives. Then, you can ask them if it woks all the time.

Modeling Operations

•Integers

–Addition, subtraction, multiplication, division

–Helpful YouTube video on multiplying integers:

https://www.youtube.com/watch?v=XOGsZ2PFcI8

https://www.youtube.com/watch?v=RAb2PR4lKvY

–Helpful YouTube video on dividing integers:

https://www.youtube.com/watch?v=2BUY0trTpn4

•Expressions

–Evaluating (linear and quadratic)

https://www.youtube.com/watch?v=f2o8EI0iOYg

•Polynomials

–Addition and subtraction

https://www.youtube.com/watch?v=L4E2PnUzPXU

Perimeter and Area

Based on what we have explored thus far, can you determine the perimeter and area of this figure?


You try:

Construct 5 figures using Algebra Tiles and calculate their perimeter and area. It may help to draw a figure to get a representation (Remember CRA). Then, share two of your figures with a colleague. What would happen if you and that colleague combined your figures? What would the new perimeter and area be?

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Solving Equations and Inequalities


Helpful video on solving one, two, and multi-step equations

https://www.youtube.com/watch?v=CpnzNmw1Mg8


  • One step
  • Two step
  • Variables on both sides
  • Inequalities

Polynomials

Multiplication and Division

Quadratics: Factoring

*Review the distributive property


  • Using a mat, fill the array with the polynomial always creating a rectangle.
  • Determine which tiles should be placed in the horizontal and vertical bars.
  • These represent the factors of the polynomial.

Quadratics: Completing the Square

  • Very literal
  • Steps to complete the square
  • Going from standard to vertex form
  • Solving by completing the square

https://www.youtube.com/watch?v=wvJQqO7Jcog (First 5 minutes)

Virtual Manipilatives

•Illuminations http://illuminations.nctm.org/

–Activities

–Lessons

•National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html

•GeoGebra http://www.geogebra.org/cms/en/

•Glencoe http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html

•Algebra for All http://a4a.learnport.org/page/algebra-tiles

McGraw-Hill online Textbook (Resources, then tools)

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Next Steps/Planning Time

During this time, please make a plan for redelivery at your school. Links to our previous agendas are below. If necessary, please plan an additional date for me to come support you at your school. I will also be circulating to support you in this planning.



Midyear walkthroughs will be conducted by the last week in January.

Remaining Dates

February 18 - Meadows - Room 22 (Upstairs)

March 24 - Meadows - Large Conference Room