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Using Algebra Tiles for Modeling Expressions - The Basics

Learn about algebra tiles as a visual model for algebraic expressions. Understand using tiles for addition, subtraction, and multiplication. Explore examples and evaluations with variables.

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Using Algebra Tiles for Modeling Expressions - The Basics

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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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