CRA with Algebra Tiles in MS and HS
Nyasha Okor, SLC, Title I Math Lead, okor@fultonschools.org
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Today's Focus: Implementing CRA using Algebra Tiles
Learning Target
I can differentiate instruction using the Concrete, Representation, and Abstract (CRA) progression model with algebra tiles
Agenda Items
- Effective Use of Algebra Tiles
- 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
- Virtual Manipulatives (Including online textbook resources)
- Symbaloo
What standards do Algebra Tiles Support?
- 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)
CRA
Let's set up your notes to reflect this natural progression. Allow students to used colored pencils, markers, or crayons to appropriately color code their notes.
How does CRA increase student problem solving abilities?
Tiles in All Forms
Traditional Algebra Tiles (Manipulites)
"Home-made" Tiles (laminated sets)
Virtual Tiles
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) - access through employee portal
Zero Principle
- Zero can be represented by any two like quantities with opposite signs (or colors for algebra tiles).
- Additive Inverses/opposites
Zero Principle
In your notes, 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
Perimeter and Area
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?
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
- Multiplying: https://www.youtube.com/watch?v=2FbEEgGq46o
- Division
Quadratics: Factoring
- 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)
Next Steps/Planning Time
Brainstorm with your neighbors about how you can use Algebra Tiles to start your school year.
What if I don't have Algebra Tiles
- Laminate paper template and create class sets
- Teacher demonstration tiles (magnetic for white boards)
- Are you at at Title I school? There may be room in the budget
- PTSA