# Algebra Tiles Workshop

Document Sample

```					 Using Algebra Tiles to
teach for Understanding

MDTP Conference
January 15, 2009
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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) = ________

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) = __________

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

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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) = _______________

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 = _________________

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

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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