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Published byAdriel Carr Modified over 2 years ago

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

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INTRODUCTION Each tile represents an area. Each tile represents an area. x x Area of large square = x (x) = x 2 x Area of rectangle = 1 (x) = x Area of small square = 1 (1) = 1 1 1 1

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INTRODUCTION Does an x-tile need to be any particular length? Does an x-tile need to be any particular length? Does its length matter? Does its length matter? x-tile does not have to be a particular length because it represents a variable. Its length does not 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 2x 2, you need 2 large squares To model 2x 2, you need 2 large squares x2x2 x2x2

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AGEBRAIC EXPRESSIONS To model x 2 + 3x, you need 1 large square and 3 rectangles To model x 2 + 3x, you need 1 large square and 3 rectangles x2x2 xxx

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ALGEBRAIC EXPRESSIONS How would you model 2x 2 + x + 4? How would you model 2x 2 + x + 4? ANSWER x2x2 x x2x2 1111

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ALGEBRAIC EXPRESSIONS What algebraic expression is modeled below? 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 We can use algebra tiles to model adding, subtracting, multiplying, and dividing algebraic expressions

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ALGEBRAIC ADDITION To use algebra tiles to model 3 + (2x + 4) represent each addend with tiles. To use algebra tiles to model 3 + (2x + 4) represent each addend with tiles. 3+2x + 4 111 x x 1111 = 2x + 7 x x 1111 111 + = Combine the tiles

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Find the sum: Find the sum: 2x + (5x + 4) 2x + (5x + 4) ALGEBRAIC ADDITION ANSWER xx + xxxxx 1111 = xx xxxxx 1111 2x + (5x + 4) = 7x + 4

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ALGEBRAIC ADDITION Find the sum: Find the sum: (x + 3) + (2x + 4) (x + 3) + (2x + 4) ANSWER x 111 + xx 1111 = xxx 1111 111 (x + 3) + (2x + 4) = 3x + 7

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Find the sum: Find the sum: (x 2 + 3) + (2x 2 + x + 2) (x 2 + 3) + (2x 2 + x + 2) ALGEBRAIC ADDITION ANSWER x2x2 111 + x2x2 x2x2 x 11 = x2x2 x2x2 x2x2 x 11 111 (x 2 + 3) + (2x 2 + x +2) = 3x 2 + x + 5

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To use algebra tiles to model subtraction, represent each expression with tiles. Put the second expression under the first. To use algebra tiles to model subtraction, represent each expression with tiles. Put the second expression under the first. (5x + 4) – (2x + 3) (5x + 4) – (2x + 3) ALGEBRAIC SUBTRACTION xxxxx 1111 xx 111 5x + 4 2x + 3 Now remove the tiles which match in each expression. The answer is the expression that is left. (5x + 4) – (2x + 3)= 3x +1

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Use algebra tiles to find the difference. Use algebra tiles to find the difference. (8x + 5) – (6x + 1) (8x + 5) – (6x + 1) ALGEBRAIC SUBTRACTION ANSWER xxxxxxxx 11111 - xxxxxx 1 8x + 5 6x + 1 (8x + 5) – (6x + 1) = 2x + 4

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Find the difference. Find the difference. (6x + 1) – (3x) (6x + 1) – (3x) ALGEBRAIC SUBTRACTION xxxx 1 - x xx 6x + 1 3x (6x + 1) – (3x) = 3x +1 xx ANSWER

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Find the difference. Find the difference. (5x + 6) – (5x) (5x + 6) – (5x) ALGEBRAIC SUBTRACTION xxxx 1 - xxx 5x + 6 5x (5x + 6) – (5x) = 6 x ANSWER 11111 xx

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Use algebra tiles to find the difference. Use algebra tiles to find the difference. (3x 2 + 4x + 5) – (x 2 + 3x + 4) (3x 2 + 4x + 5) – (x 2 + 3x + 4) ALGEBRAIC SUBTRACTION ANSWER xxxx 11111 - xxx 1 3x 2 + 4x + 5 x 2 + 3x + 4 (3x 2 + 4x + 5) – (x 2 + 3x + 4) (3x 2 + 4x + 5) – (x 2 + 3x + 4) = 2x 2 + x + 1 x2x2 x2x2 x2x2 x2x2 111

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Lets Practice!

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