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ALGEBRA TILES

ALGEBRA TILES. The University of Texas at Dallas. INTRODUCTION. Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions. There are three types of tiles: 1. Large square with x as its length and width.

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ALGEBRA TILES

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  1. ALGEBRA TILES The University of Texas at Dallas

  2. INTRODUCTION • Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions. • There 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 1 x The University of Texas at Dallas

  3. 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 The University of Texas at Dallas

  4. 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 FOR TUTOR The University of Texas at Dallas

  5. ALGEBRAIC EXPRESSIONS • To model 2x2, you need 2 large squares x2 x2 The University of Texas at Dallas

  6. AGEBRAIC EXPRESSIONS • To model x2 + 3x, you need 1 large square and 3 rectangles x2 x x x The University of Texas at Dallas

  7. ALGEBRAIC EXPRESSIONS • How would you model 2x2 + x + 4? ANSWER x2 x2 x 1 1 1 1 The University of Texas at Dallas

  8. ALGEBRAIC EXPRESSIONS • What algebraic expression is modeled below? ANSWER 2x + 3 The University of Texas at Dallas

  9. ALGEBRAIC EVALUATION • Suppose x is standing for 4. What is the value of 2x +3 ? (2x means 2 times x). • 2x +3 = 2 (4) +3 = 8 +3 = 11 The University of Texas at Dallas

  10. ALGEBRAIC EVALUATION • What is the value of 2x + 3 if x = 8? ANSWER • 2 (8) + 3 • 16 + 3 • 19 2x + 3 =19 if x = 8 The University of Texas at Dallas

  11. ALGEBRAIC EVALUATION • Remember that a variable can represent many number. The University of Texas at Dallas

  12. ALGEBRAIC EVALUATION • Find the value of this expression using these values of x. • x = 2 • x = 5 • x = 10 X X X 1 1 1 1 1 ANSWER The University of Texas at Dallas

  13. ALGEBRAIC EVALUATION • The algebraic expression for the tiles is 3x + 5 • If x = 2 • 3 (2) + 5 • 6 + 5 = 11 • 2) If x = 5 • 3 (5) + 5 • 15 + 5 = 20 3) If x = 10 3 (10) + 5 30 + 5 = 35 The University of Texas at Dallas

  14. ALGEBRAIC OPERATIONS • We can use algebra tiles to model adding, subtracting, multiplying, and dividing algebraic expressions The University of Texas at Dallas

  15. ALGEBRAIC ADDITION • 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 The University of Texas at Dallas

  16. ALGEBRAIC ADDITION • Find the sum: • 2x + (5x + 4) 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 The University of Texas at Dallas

  17. ALGEBRAIC ADDITION • Find the sum: • (x + 3) + (2x + 4) 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 The University of Texas at Dallas

  18. ALGEBRAIC ADDITION • 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 The University of Texas at Dallas

  19. 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 The University of Texas at Dallas

  20. 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 The University of Texas at Dallas

  21. ALGEBRAIC SUBTRACTION • Find the difference. • (6x + 1) – (3x) ANSWER 6x + 1 x x x x x x 1 3x x - x x (6x + 1) – (3x) = 3x +1 The University of Texas at Dallas

  22. 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 The University of Texas at Dallas

  23. 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 The University of Texas at Dallas

  24. ALGEBRAIC MULTIPLICATION • To multiply using algebra tiles, lay the factors in a rectangular array. • Ex: 2 (x + 3) x + 3 2 x Fill in this space to form a rectangle. And the result is your answer 1 1 1 x x 1 1 1 1 1 1 1 1 2 (x + 3) = 2x + 6 The University of Texas at Dallas

  25. ALGEBRAIC MULTIPLICATION • Find the product. • x (x + 2) ANSWER (x + 2) x x 1 1 x2 x x x x (x + 2) = x2 + 2x The University of Texas at Dallas

  26. ALGEBRAIC MULTIPLICATION • Find the product. • 2x (x + 3) ANSWER (x + 3) 2x x 1 1 1 x2 x x x x x x2 x x x 2x (x + 3) = 2x2 + 6x The University of Texas at Dallas

  27. ALGEBRAIC MULTIPLICATION • Find the product. • (x+2) (x + 4) ANSWER (x + 4) x +2 x 1 1 1 1 x2 x x x x x x x 1 1 1 1 1 1 1 1 1 1 (x+2) (x + 4) = 2x2 + 6x + 8 The University of Texas at Dallas

  28. ALGEBRAIC MULTIPLICATION • Find the product. • (x+3) (2x + 1) ANSWER (2x + 1) x +3 x x 1 x2 x2 x x x x x x 1 1 x x 1 1 1 1 (x+3) (2x + 1) = 2x2 + 7x + 3 The University of Texas at Dallas

  29. ALGEBRAIC DIVISION • To model division using algebra tiles, use a rectangular array like you did for multiplication except the dividend (the numerator) goes where your multiplication answer was The University of Texas at Dallas

  30. ALGEBRAIC DIVISION • Ex: Fill in this space to complete the array. This is your answer! 2 x x 1 1 1 x x x x 1 1 1 1 4x + 6 1 1 1 1 The University of Texas at Dallas

  31. ALGEBRAIC DIVISION • Find the quotient: ANSWER 3 x x x 1 (9x + 3) x x x x x x 1 1 x x x 1 1 1 1 The University of Texas at Dallas

  32. ALGEBRAIC DIVISION 6x2 + 3x 3x • Find the quotient: ANSWER 3x x x 1 (6x2 + 3x) x x2 x2 x x x2 x2 x 6x2 + 3x 3x = 2x + 1 x x2 x2 x The University of Texas at Dallas

  33. ALGEBRAIC DIVISION 2x2 + 6x + 4 x + 2 • Find the quotient: ANSWER x+ 2 x x 1 1 (2x2 + 6x + 4) x x2 x2 x x x x x x 1 1 1 1 1 1 2x2 + 6x + 4 x + 2 = 2x + 2 The University of Texas at Dallas

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