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Using Algebra Tiles to teach for Understanding MDTP Conference January 15, 2009 2 I. Adding Integers Steps: a. Model the number of positive and negative units in the expression using tiles or symbols. b. Combine pairs of a positive and a negative to make zero or neutral pairs. c. Record the number and sign of remaining units. d. Write your steps in mathematical form. Examples: 1. 5 + (-3) = ________ 2. -4 + -5 = _________ 3. -7 + 2 = _________ 4. 2 + 8 = _________ 5. 6 + (-7) = ________ 6. 3 + (-3) = ________ Think About It 7. When did you end up with fewer tiles than you began with (when could you remove zero pairs)? 8. Can you predict when your answer will be positive (yellow) or negative (red) without doing the problem? How? 3 II. Subtracting Integers Steps: a. Model the number of positive or negative units in the first term using tiles or symbols. b. Add enough zero pairs so that the amount being subtracted exists in your model. c. Take away the units to be subtracted. d. Record the number and sign of the remaining units. e. Write your steps in mathematical form. Examples: 9. 4 – 6 = _________ 10. 2 – ( -4) = _________ 11. -3 – 5 = ___________ 12. 8 – 5 = _________ 13. -4 – (-7) = _________ 14. -3 – (-2) = __________ Think About It 15. When did you end up with fewer tiles than you began with (when could you remove zero pairs)? 16. Can you predict when your answer will be positive (yellow) or negative (red) without doing the problem? How? 17. Write down some rules you could use to solve addition and subtraction integer problems without using the tiles. 18. Create 3 new problems that you solve with your rules. Use a calculator or tiles to verify that your rules work. 4 III. Multiplying Integers: Steps: a. To multiply by a positive integer n, make n rows of your modeled number. b. To multiply by a negative integer n, take away n rows of your modeled number. You may need to add n rows of zero pairs in order to take away n rows. c. Record the number and sign of the remaining units. d. Write your steps in mathematical form. Examples: 19. 3 x (-4) = _____________ 20. 5 x 2 = _________ 21. (-2) x 3 = _____________ 22. (-3) x 4 = ____________ 23. (-4) x (-2) = ________ 24. –(-5) = _______________ Think about it 17. Write some rules for multiply integers. 26. Write 3 new problems, apply your rules and verify with a calculator or tiles. 5 IV. Dividing Integers Steps: a. To divide by a positive integer n, separate the tiles into n rows or groups. b. To divide by a negative integer n, change the sign of your number by turning over all tiles or replacing the tiles with opposite signed tiles. Then separate the tiles into |n| groups. c. Record the number and sign of the units per group. d. Write your steps in mathematical form. Examples: 27. 15/3= ___________ 28. -8/4 = ______________ 29. -10/5 = _________________ 30. 12/-6 = _________ 31. -9/-3 = ____________ 32. 8/-2 = _________________ Think about it 33. Write some rules for multiply integers. 34. Write 3 new problems, apply your rules and verify with a calculator or tiles. 6 V. Equations: Steps: a. To solve a first degree equation, place the models on the equation mat. b. Add an equivalent number of unit tiles of opposite sign to form zero pairs on the variable side of the equation to each side of the equation. c. Remove the zero pairs created from each side. d. Separate the tiles on each side into rows. The number of rows is equal to the coefficient of x. e. Remove duplicate rows from each side. f. Record the number and sign of the units equivalent to the x row. g. Write your steps in mathematical form. 35. 2x + 3 = 11 36. 4x - 8 = 8 37. 3x - 6 = 12 38. 3a - 5 = 7 39. 5 – 2x = 13 40. 2(x+1) = 10 7 VI. Equations with variables on both sides: Steps: a. Place the models on the equation mat. b. Add an equivalent number of x tiles of opposite sign to each side of the equation to form zero pairs of x tiles on one side of the equation. c. Remove the zero pairs created from each side. d. Use the process steps of equations above to solve for an x = row. e. Write your steps in mathematical form. Examples: 41. 2x + 3 = x + 9 42. 3x – 5 = 2x – 1 43. 5 – 3x = 15 + 2x Think About It 44. What mathematical properties did you use in your steps of solving the equations? 8 Examples: 45. ( x + 2 )( x + 3 ) 46. ( 2x + 1 )( x + 4 ) 47. ( x – 4) ( x + 2 ) 48. (x – 4)2 VII. Factoring Trinomials and Binomials Steps: a. Place the models to form a rectangle in the t-bar. Zero pairs may be added to complete the rectangle, if needed. b. Use the x and unit tiles on the top and left of the t-bar to reflect the dimensions. c. Record the dimensions as factors in a product. d. Draw and complete a generic rectangle to check your work. 49. x2 + 8x + 7 50. 3x + 6 51. x2 + x – 6 52. 2x2 + 5x -3 9 10 11

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Algebra Tiles, University of Arkansas at Monticello, algebra and geometry, geometry teachers, math teachers, Math and Science, UAM School of Education, Test Taking Strategies, text attachment, Summer Workshops

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posted: | 2/19/2010 |

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