1. MULTIPLICATION Egyptian and Chinese and more

2. Pre requisite skills ■Can you double a number? ■Can you add? ■If you can do these things you can do Egyptian multiplication

3. Lets start with something easy. 21 x 5 ■You start by making a table

4. Lets start with something easy. 21 x 5 ■You start by making a table 215

5. Lets start with something easy. 21 x 5 ■You start by making a table 215 15

6. Lets start with something easy. 21 x 5 ■You start by making a table 215 15 210

7. Lets start with something easy. 21 x 5 ■You start by making a table 215 15 210 420

8. Lets start with something easy. 21 x 5 ■You start by making a table 215 15 210 420 840

9. Lets start with something easy. 21 x 5 ■You start by making a table 215 15 210 420 840 1680

10. PAUSE ■How long do we need to make the table? ■The table needs to have all the powers of two that are smaller then the first number (in our case 21) ■This means we can stop at 16 because our next power of 2 is larger than 21.

11. So we have a table now what? ■Now we need to look at our table and decide how we can make our first number (21) by adding powers of two together. 215 15 210 420 840 1680

12. So we have a table now what? ■Now we need to look at our table and decide how we can make our first number (21) by adding powers of two together. 215 15 210 420 840 1680 21 = 16+4+1

13. So we have a table now what? ■Once we have identified which powers of two we need all we have to do is add up the corresponding doubles. 215 15 210 420 840 1680 21 = 16+4+180+20+5 =

14. So we have a table now what? ■Once we have identified which powers of two we need all we have to do is add up the corresponding doubles. 215 15 210 420 840 1680 21 = 16+4+180+20+5 = 105

15. Lets practice representing numbers as sums of powers of 2. ■9 ■14 ■23 ■44

16. Lets do another problem 23 x 132 ■First make our table

17. Lets do another problem 23 x 132 ■First make our table 23132 1 2264 4528 81056 162112

18. Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 23132 1 2264 4528 81056 162112

19. Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 23132 1 2264 4528 81056 162112 23 = 16+4+2+1

20. Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 23132 1 2264 4528 81056 162112 23 = 16+4+2+1

21. Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 ■Third: Add corresponding doubles 23132 1 2264 4528 81056 162112 23 = 16+4+2+12112+528+264+132

22. Lets do another problem 23 x 132 ■First make our table ■Second: identify numbers that add to 23 ■Third: Add corresponding doubles 23132 1 2264 4528 81056 162112 23 = 16+4+2+12112+528+264+132 3036

23. With your teams try these: ■25 x 31 ■38 x 45 ■12 x 63

24. Lets try another one 14 x 1962

25. Chinese Multiplication ■Chinese multiplication involves drawing pictures to help solve multiplication problems. ■We look at where line segments intersect and count those.

26. Chinese Multiplication ■Lets start with an easy problem 12 x 11 ■What is this going to look like?

27. Chinese Multiplication ■So how does this picture help us?

28. Chinese Multiplication ■We have to remember what the different lines represent 10 2 1

29. Chinese Multiplication ■We have to remember what the different lines represent 10 2 1 The stuff in the red circle represents 1 x 2

30. Chinese Multiplication ■We have to remember what the different lines represent 10 2 1 The stuff in the grey circles are 1x10 and 2x10

31. Chinese Multiplication ■We have to remember what the different lines represent 10 2 1 The stuff in the green circle is 10 x 10

32. Chinese Multiplication ■We have to remember what the different lines represent 10 2 1 So all together we have: 2 x 1 10 x 1 10 x 2 10 x 10

33. Chinese Multiplication ■We have to remember what the different lines represent 10 2 1 So all together we have: 2 x 1 = 2 10 x 1 = 10 10 x 2 = 20 10 x 10 = 100

34. Now what? ■So all together we have: ■2 x 1 = 2 ■10 x 1 = 10 ■10 x 2 = 20 ■10 x 10 = 100 ■Now all we do is add. ■2 + 10+ 20+ 100 ■132

35. Lets try another one ■Using the Chinese method multiply 23 x 111

36. And another one 121 x 121

37. Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92

38. Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92 ■Draw a rectangle and divide it up like so

39. Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92 ■Draw a rectangle and divide it up like so

40. Lattice Multiplication (coms from 10 th century India) ■First we need a problem: 43 x 92 ■Draw a rectangle and divide it up like so

41. Lattice Multiplication (coms from 10 th century India) ■Now we label the rectangle with our numbers. 4 3 9 2

42. Lattice Multiplication (coms from 10 th century India) ■Then multiply all the mini problems 4 3 9 2

43. Lattice Method

44. And another one 7219 x 341

45. Which do you like best?

46. Which do you like best? Using your favorite method do the following ■173 x 59 ■341 x 27 ■1563 x 11