To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.

To help students visualize abstract concepts

Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

Reinforce a topic for a struggling student

Positive Tiles Negative Tiles 1 1

1 1

1 1

x x

x X

x X x x

X

X²

1 1

X

X²

Addition and Subtractions of Integers Distributive Property Combining Like Terms Solving Equations Multiplying Binominals Factoring Polynomials

3  +  ( -5 )  =  ? Additions means “ Combine”

Use the zero property to

cancel/take away a pair of blue and red tiles

Left with 2 “-1 tiles” Answer = -2

1

1

1

1

1

1

1

1

5 – (-2) = ?Start with 5

“take away” Answer = 7

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1Now you can take away 2 “-1 tiles”

Add a zero pair in order to be able to take away 2 “-1 tiles”

3 (2x + 1) is equivalent to 6x + 33 (2x + 1) {using repeated addition) Rearrange

the tilesX X

1

XX

XX

1

1

X

X

X

X

X

X

1

1

1 +

+

(x² - 2x -3) – (2x² + x – 2) = ?

X²

X

X

1

1

1

Subtraction would be represented by “adding the opposite of each term in parenthesis”

X²X²

X

1

1

Cross out all zero pairs, what you have left over is your answer

Answer = -x² – 3x – 1

+

2x -2 = 4

X

X

1 1 = 1 111

2x -2 = 4Add two tiles to the left to make a zero pair

* To keep scale balanced - do the same to both sides *

X

X

1 1 = 1 111

1 1 1 1

2x -2 = 4Arrange the tiles into groups

Answer: X = 3

1

1

X =X

1

1 1

1

(x + 3) (x + 2)

X 1 11

1

X

1

L W

(x + 3) (x + 2)

X 1 11

1

X

1

X² X X X

X

X

1 1 1

1 1 1

Answer = x² + 5x + 6

Fill in the space so that lines between tiles are continuous

2x² + 5x + 3

X² X² X

X

X X

X 1 1 1

First fill in the “x² tiles” and “1 tiles” Then arrange the “x tiles” to match

2x² + 5x + 3

1 11

1

XX

X

x + 1

2x + 3

Answer = (2x +3) ( x + 1)

Teaching the rules of Algebra Tiles Multiplying a Polynomial by a Binomial More difficult using negative number for:

Distributing Factoring Multiplying two binomials(It is possible but students might struggle)

Visualizing an abstract concept

Students generating rules Practice with basic problems then have

students find patterns to then apply to more challenging problems

Another tool in the tool box