1. Using Algebra Tiles for Student Understanding

2. Examining the Tiles Colors and shapes = 1, = x, = x2 = -1, = -x, = -x2
Model the following expressions
+ 3
-2x
x – 4
x2 + 3x - 2

3. Zero Pairs
Called zero pairs because they are additive inverses of each other.
When put together, they model zero.

4. Model Simplify Initial illustration: before combining terms
Final illustration

5. Modeling Polynomials
2x2
-4x
3 or +3

6. Polynomials
Represent each of the given expressions with algebra tiles.
Draw a pictorial diagram of the process.
Model the symbolic expression -2x + 4

7. Modeling Polynomials
2x2 + 3
4x – 2

8. Multiplying Polynomials
Algebra tiles can be used to multiply polynomials.
Use tiles and frame to represent the problem. The factors will form the dimensions of the frame.
(vertical) and (horizontal)
The product will form a rectangular array inside frame. “Area Model”

9. Multiplication using “Area Model”
(2)(3) =
Place 2 sm. squares on the vertical and 3 sm. squares on the horizontal
Fill in the interior of the area model with appropriate algebra tiles to form a rectangular array.
2 x 3 = 6

10. Multiplying Polynomials
(x )(x + 3)
Fill in each section of the area model
x2 + x + x + x =
x2 + 3x
Algebraically

11. Multiplying Polynomials
(x + 2)(x + 3)
Fill in each section of the area model
x2+ 2x+ 3x + 6
= x2+ 5x + 6
Algebraically

12. Multiplying Polynomials
(x – 1)(x + 4)
Fill in each section of the area model
Make zero pairs or
combine like terms
and simplify x2
+ 4x
– 1x
– 4
= x2 + 3x – 4

13. Multiplying Polynomials
Use the tile frame and tile pieces to model the product of each problem below. Think about how you will connect the algebraic procedure to the model. Verify your solution using the box method and distributive property.
(2x + 3)(x – 2)
(x – 2)(x – 3)

14. Virtual Algebra Tiles

15. Factoring Polynomials
Algebra tiles can be used to factor polynomials. Use tiles and the frame to represent the problem.
Use the tiles to form a rectangular array inside the frame. (area model)
Be prepared to use zero pairs to fill in the array.
Draw pictures.

16. Factoring When using tiles….. Big squares can't touch little squares.
Little squares must all be together.
Only equal length sides may touch.
You may not lay two equally sized tiles of different colors next to each other.
Use all of the pieces to make a rectangle.
Once you have correctly arranged the tiles into a rectangle, the factors of the quadratic are the length and width of the rectangle.

17. Factoring Polynomials
3x + 3
2x – 6
= 3 ·
(x + 1)
= 2 ·
(x – 3)
Note the two are positive, this needs to be developed

18. Factoring Polynomials
x2 + 6x + 8
= (x + 2)(x +4)
x2 + 4x + 2x + 8

19. Factoring Polynomials
x2 – 5x + 6
= (x – 2)(x – 3)
x2 - 3x - 2x + 6

20. Factoring Polynomials
x2 + 5x + 8
= prime

21. Factoring Polynomials
x2 – x – 6
= (x + 2)(x – 3)
x2 - 3x + 2x - 6

22. Factoring Polynomials
x2 – 9
= (x + 3)(x – 3)
x2 - 3x + 3x - 9

23. Factoring Polynomials
2x2 + x – 6
= (2x - 3)(x + 2)
2x2 - 3x + 4x - 6

24. Factoring Polynomials
2x2 + 3x – 4
= prime

25. Virtual Algebra Tiles

26. Factoring Polynomials
Practice factoring
x2 + x – 6
x2 – 4
4x2 – 9
2x2 – 3x – 2
3x2 + x – 2
-2x2 + x + 6