1. LATTICE MULTIPLICATION
Tutorial 12

2. At the end of Tutorial I gave you a problem to work on independently. Watch as I use LATTICE MULTIPLICATION to solve that problem.

3. Tutorial 11’s On Your Own Problem:
68 x 9 =

4. First, write the larger number down.

5. 6 8

6. Draw a rectangle below this number.

7. 6 8

8. The larger number is made up of 2 digits, so cut the rectangle into two boxes.

9. 6 8

10. Write the other problem number on the right of the rectangle.

11. 6 8 9

12. Cut the boxes diagonally
Cut the boxes diagonally. For each box draw a line from the bottom left to the top right.

13. 6 8 9

14. Now we do basic multiplication. Start with the 6
Now we do basic multiplication. Start with the 6. If we go down from the 6 and across from the 9, they “meet” in that first box.

15. 6 8 9

16. 6 x 9 = 5 4 Write 5 in the top half of the box and write 4 in the bottom half of the box.

17. 6 8 5 9 4

18. Move on to the 8. If we go down from the 8 and across from the 9, they “meet” in that second box.

19. 6 8 5 9 4

20. 8 x 9 = 7 2 Write 7 in the top half of the box and write 2 in the bottom half of the box.

21. 6 8 5 7 9 4 2

22. Extend your diagonal lines down.

23. 6 8 5 7 9 4 2

24. Add the numbers inside the boxes. Use the diagonal lines to guide you
Add the numbers inside the boxes. Use the diagonal lines to guide you. Start on the right with the 2 then move to the left nothing = 2. So put a 2 on the right of the diagonal lines.

25. 6 8 5 7 9 4 2 2

26. NEW CONCEPT ALERT!! = You can only write down one digit between the diagonal lines. So what do you do?!

27. NEW CONCEPT ALERT!! Write a 1 between the diagonal lines, then regroup the other 1 above the I like to put a plus (+) sign with it to remind me it’s a regrouped number.

28. 6 8 +1 5 7 9 4 2 1 2

29. 1 + 5 = 6. So put a 6 to the left of the diagonal lines.

30. 6 8 +1 5 7 9 4 2 6 1 2

31. That’s it! 612 is your answer. 6 8 x 9 = 6 1 2

32. NEW CONCEPT ALERT!! It’s time to practice 2 digit x 2 digit multiplication!

33. EXAMPLE
73 x 40 =

34. First, write the larger number down.

35. 7 3

36. Draw a rectangle below this number.

37. 7 3

38. The larger number is made up of 2 digits, so cut the rectangle into two boxes.

39. 7 3

40. NEW CONCEPT On the right side write the second number, 40, up and down.

41. 7 3 4

42. NEW CONCEPT Draw another rectangle below the first one.

43. 7 3 4

44. NEW CONCEPT Cut the second rectangle into two pieces, just like the first one.

45. 7 3 4

46. Cut ALL the boxes diagonally
Cut ALL the boxes diagonally. For each box draw a line from the bottom left to the top right.

47. 7 3 4

48. Now we do basic multiplication. Start with the 7
Now we do basic multiplication. Start with the 7. If we go down from the 7 and across from the 4, they “meet” in that first box.

49. 7 3 4

50. 7 x 4 = 2 8 Write 2 in the top half of the box and write 8 in the bottom half of the box.

51. 7 3 2 4 8

52. Move on to the 3. If we go down from the 3 and across from the 4, they “meet” in that second box.

53. 7 3 2 4 8

54. 3 x 4 = 1 2 Write 1 in the top half of the box and write 2 in the bottom half of the box.

55. 7 3 2 1 4 8 2

56. We have multiplied 73 by the 4 on the right.

57. But, there is another number on the right. Below the 4, there is a 0
But, there is another number on the right. Below the 4, there is a 0. We need to multiply 73 by 0.

58. Start with the 7. If we go down from the 7 and across from the 0, they “meet” in the bottom left box.

59. 7 3 2 1 4 8 2

60. 7 x 0 = 0 Write 0 in the top half of the box and write second 0 in the bottom half of the box.

61. 7 3 2 1 4 8 2

62. Move on to the 3. If we go down from the 3 and across from the 0, they “meet” in the bottom right box.

63. 7 3 2 1 4 8 2

64. 3 x 0 = 0 Write 0 in the top half of the box and write second 0 in the bottom half of the box.

65. 7 3 2 1 4 8 2

66. Extend your diagonal lines down.

67. 7 3 2 1 4 8 2

68. Add the numbers inside the boxes. Use the diagonal lines to guide you
Add the numbers inside the boxes. Use the diagonal lines to guide you. Start on the right with the 0 then move to the left nothing = 0. So put a 0 on the right of the diagonal lines.

69. 7 3 2 1 4 8 2

70. Move on to the next set of diagonal numbers (2, 0, and 0)
Move on to the next set of diagonal numbers (2, 0, and 0) = 2. So put a 2 between the diagonal lines.

71. 7 3 2 1 4 8 2 2

72. Move on to the next set of diagonal numbers (1, 8, and 0)
Move on to the next set of diagonal numbers (1, 8, and 0) = 9. So put a 9 between the diagonal lines.

73. 7 3 2 1 4 8 2 9 2

74. 2 + nothing = 2. So put a 2 to the left of the diagonal lines.

75. 7 3 2 1 4 8 2 2 9 2

76. That’s it! 2,920 is your answer. 7 3 x 4 0 = 2, 9 2 0

77. ON YOUR OWN
Try the following problem using the rules from today’s work. The answer will be the first thing given in TUTORIAL 13.

78. On Your Own Problem:
54 x 80 =