# DEAR Algebra

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

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

## 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
• Algebra: Units 2, 3

Magnetic set for the white board

Class sets of tiles

Transparent set for the overhead projector

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.

## 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.

•Integers

•Expressions

•Polynomials

## 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?

## Solving Equations and Inequalities

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

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

## Polynomials

Multiplication and Division

*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.

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

## 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/

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

McGraw-Hill online Textbook (Resources, then tools)

## 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