# 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

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)

## CRA

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

How does CRA increase student problem solving abilities?

## 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: 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