to help students visualize abstract concepts introduce a new topic; students then can discover the...

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Page 1: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher
Page 2: 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

Page 3: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

Positive Tiles Negative Tiles 1 1

1 1

1 1

x x

x X

x X x x

X

1 1

X

Page 4: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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

Page 5: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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

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1

1

1

1

1

1

1

Page 6: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

5 – (-2) = ?Start with 5

“take away” Answer = 7

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1

1

1

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1

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1Now you can take away 2 “-1 tiles”

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

Page 7: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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 +

+

Page 8: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

(x² - 2x -3) – (2x² + x – 2) = ?

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

+

Page 9: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

2x -2 = 4

X

X

1 1 = 1 111

Page 10: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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

Page 11: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

2x -2 = 4Arrange the tiles into groups

Answer: X = 3

1

1

X =X

1

1 1

1

Page 12: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

(x + 3) (x + 2)

X 1 11

1

X

1

L W

Page 13: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

(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

Page 14: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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

Page 15: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

2x² + 5x + 3

1 11

1

XX

X

x + 1

2x + 3

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

Page 16: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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)

Page 17: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher

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