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ALGEBRA TILES

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INTRODUCTION Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions. Here are three types of ‘tiles’: 1. Large square with x as its length and width. 2. Rectangle with x and 1 as its length and its width 3. Small square with 1 as its length and width. x 1 1 x x 1

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**INTRODUCTION Each tile represents an area.**

x Area of large square = x (x) = x2 x 1 x Area of rectangle = 1 (x) = x 1 1 Area of small square = 1 (1) = 1

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**INTRODUCTION Does an x-tile need to be any particular length?**

Does its length matter? x-tile does not have to be a particular length because it represents a variable. Its length does not matter. NOTE

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**ALGEBRAIC EXPRESSIONS**

To model 2x2, you need 2 large squares x2 x2

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AGEBRAIC EXPRESSIONS To model x2 + 3x, you need 1 large square and 3 rectangles x2 x x x

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**ALGEBRAIC EXPRESSIONS**

How would you model 2x2 + x + 4? ANSWER x2 x2 x 1 1 1 1

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**ALGEBRAIC EXPRESSIONS**

What algebraic expression is modeled below? ANSWER 2x + 3

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ALGEBRAIC OPERATIONS We can use algebra tiles to model adding, subtracting, multiplying, and dividing algebraic expressions

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**ALGEBRAIC ADDITION 3 + 2x + 4 2x + 7 = = +**

To use algebra tiles to model 3 + (2x + 4) represent each addend with tiles. 3 + 2x + 4 2x + 7 = x x x x = + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Combine the tiles

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**ALGEBRAIC ADDITION + = 2x + (5x + 4) = 7x + 4 Find the sum:**

ANSWER x x x x x x x + x x x x x = 1 1 1 1 x x 1 1 1 1 2x + (5x + 4) = 7x + 4

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**ALGEBRAIC ADDITION + = (x + 3) + (2x + 4) = 3x + 7 Find the sum:**

ANSWER x x x x x x + = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (x + 3) + (2x + 4) = 3x + 7

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**ALGEBRAIC ADDITION + = (x2 + 3) + (2x2 + x +2) = 3x2 + x + 5**

Find the sum: (x2 + 3) + (2x2 + x + 2) ANSWER x2 x2 + x2 x2 = x2 x 1 1 1 x 1 1 1 1 1 x2 1 1 (x2 + 3) + (2x2 + x +2) = 3x2 + x + 5

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**ALGEBRAIC SUBTRACTION**

To use algebra tiles to model subtraction, represent each expression with tiles. Put the second expression under the first. (5x + 4) – (2x + 3) Now remove the tiles which match in each expression. 5x + 4 x x x x x The answer is the expression that is left. 1 1 1 1 x x 2x + 3 1 1 1 (5x + 4) – (2x + 3)= 3x +1

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**ALGEBRAIC SUBTRACTION**

Use algebra tiles to find the difference. (8x + 5) – (6x + 1) ANSWER 8x + 5 x x x x x x x x 1 1 1 1 1 6x + 1 - x x x x x x 1 (8x + 5) – (6x + 1) = 2x + 4

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**ALGEBRAIC SUBTRACTION**

Find the difference. (6x + 1) – (3x) ANSWER 6x + 1 x x x x x x 1 - x 3x x x (6x + 1) – (3x) = 3x +1

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**ALGEBRAIC SUBTRACTION**

Find the difference. (5x + 6) – (5x) ANSWER 5x + 6 x x x x x 1 1 1 1 1 1 - 5x x x x x x (5x + 6) – (5x) = 6

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**ALGEBRAIC SUBTRACTION**

Use algebra tiles to find the difference. (3x2 + 4x + 5) – (x2 + 3x + 4) 3x2 + 4x + 5 ANSWER x2 x2 x2 x x x x 1 1 1 1 1 x2 + 3x + 4 - x2 x x x 1 1 1 1 (3x2 + 4x + 5) – (x2 + 3x + 4) = 2x2 + x + 1

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Let’s Practice!

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