1. Making Math WorkAlgebra Tiles Visualizing algebra

2. Algebra Tiles • Manipulative tool kit for solving linear equations • Multiplying two linear equations to form a quadratic • Factoring quadratic equations into their linear roots

3. Tool Kit • 5-inch square tiles = x2 • 5-in by 1-in rectangle = x • Unit squares = 1 • Green tiles = + • Red tiles = –

4. Algebra tiles illustrate • Solving linear equations • Building quadratic equations from linear equations • Factoring quadratic equations into their linear roots

5. x + 4 = • Tiles needed • 1 green x rectangle • 4 green unit tiles =

6. x + 4 = • Place 4 red unit tiles on each side of the equation (What you do to one side, you have to do to the other side) =

7. x + 4 = • Remove pairs of red and green tiles =

8. x + 4 = • Remove pairs of red and green tiles =

9. x + 4 = • Remove pairs of red and green tiles =

10. x + 4 = • Remove pairs of red and green tiles =

11. x + 4 = • Remove pairs of red and green tiles =

12. x = -4 =

13. How to choose a red or green tile • If the tiles are the same color, use a green tile • If the tiles are different colors, use a red tile • A positive times a positive is a positive • A positive times a negative is a negative • A negative times a negative is a positive

14. (x+2)(x+3) Place x+2 down the sidePlace x+3 across the top

15. (x+2)(x+3) Place x2

16. (x+2)(x+3) Place 3 x’s on the right

17. (x+2)(x+3) Place 2 x’s on the bottom

18. (x+2)(x+3) Fill in with unit squares

19. (x+2)(x+3) Count up partsx2+5x+6

20. (x+2)(x-3) Place x-3 on topPlace x+2 on the side

21. (x+2)(x-3) We have a green x on the top and a green x on the side, use a green x2

22. (x+2)(x-3) We have red units on the top and a green x on the side, use red x’s

23. (x+2)(x-3) We have a green x on top and green units down the side, use green x’s

24. (x+2)(x-3) We have red units on the top and green units on the side, use red units

25. (x+2)(x-3) Remove pairs of green x’s and red x’s

26. (x+2)(x-3) Remove pairs of green x’s and red x’s

27. (x+2)(x-3) Remove pairs of green x’s and red x’s

28. (x+2)(x-3) Count up partsx2-x-6

29. (x+2)(3-x) Place x+2 down the sidePlace 3-x across the top

30. (x+2)(3-x) We have a red x on the top and a green x on the side, use a red x2

31. (x+2)(3-x) We have green units on the top and a green x on the side, use green x’s

32. (x+2)(3-x) We have a red x on the top and green units on the side, use red x’s

33. (x+2)(3-x) We have green units on the top and green units on the side, use green units

34. (x+2)(3-x) Remove pairs of green and red x’s

35. (x+2)(3-x) Remove pairs of green and red x’s

36. (x+2)(3-x) Remove pairs of green and red x’s

37. (x+2)(3-x) Count up parts -x2+x+6

38. Factoring • Determine factorization of constant term x2 –x – 12 12 1 6 4 2 3

39. x2-x-12 Pick and place a factorization of -12

40. x2-x-12 Red units mean we have a positive and a negative, so use red x’s

41. x2-x-12 Red units mean we have a positive and a negative, so use green x’s

42. x2-x-12 Check for –x by removing pairs of green and red x’s

43. x2-x-12 Check for –x by removing pairs of green and red x’s

44. x2-x-12 Too many red x’s left, try another factorization of 12

45. x2-x-12 Pick and place a factorization of -12

46. x2-x-12 Place red x’s

47. x2-x-12 Place green x’s

48. x2-x-12 Check for –x by removing pairs of green and red x’s

49. x2-x-12 Check for –x by removing pairs of green and red x’s

50. x2-x-12 Check for –x by removing pairs of green and red x’s