DEAR Algebra
Nyasha Okor, SLC, Title I Math Lead, okor@fultonschools.org
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
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)
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?
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
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)
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)
Next Steps/Planning Time
- October 8: https://tackk.com/dearalgebraoct8
- November 5: https://app.nearpod.com/#/?pin=43B3D50589A3E562DD963EAD5BE2D699-1
- January 14: http://bit.ly/dearalgebrajan14
Midyear walkthroughs will be conducted by the last week in January.
Remaining Dates
March 24 - Meadows - Large Conference Room