Algebra Tiles Workshop

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Algebra Tiles Workshop Powered By Docstoc
					 Using Algebra Tiles to
teach for Understanding

    MDTP Conference
       January 15, 2009
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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?




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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.



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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.




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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.




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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




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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?




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   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




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