1. Pamela Leutwyler

2. Examine the familiar base 10 algorithm. Multiplication in other bases works the same way.

3. 26 x34

4. hundreds tens ones 26 x34

5. hundreds tens ones 26 x34 ones times ones = ones 6x4 = 24

6. hundreds tens ones 26 x34 ones times ones = ones 6x4 = 24 Each set of 10 “ones” is replaced by 1 “ten”

7. hundreds tens ones 26 x34 4 ones times ones = ones 6x4 = 24 Each set of 10 “ones” is replaced by 1 “ten” 2 Put down 4 and carry 2

8. hundreds tens ones 26 x34 4 2

9. hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 2

10. hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 2 plus the 2 carried from the last step puts ten pebbles In the tens pile

11. hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2

12. hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2

13. hundreds tens ones 26 x34 04 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2 Put down 0 and carry one 1

14. hundreds tens ones 26 x34 104 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2 Put down 0 and carry one 1

15. hundreds tens ones 26 x34 104

16. hundreds tens ones 26 x34 104

17. hundreds tens ones 26 x34 104 tens times ones = tens 3x6 = 18

18. hundreds tens ones 26 x34 104 tens times ones = tens 3x6 = 18 Each set of 10 “tens” is replaced by 1 “hundred”

19. hundreds tens ones 26 x34 104 8 tens times ones = tens 3x6 = 18 Each set of 10 “tens” is replaced by 1 “hundred” Put down 8 and carry one 1

20. hundreds tens ones 26 x34 104 8 1

21. hundreds tens ones 26 x34 104 8 1 tens times tens = hundreds 3x2 = 6

22. hundreds tens ones 26 x34 104 8 1 tens times tens = hundreds 3x2 = 6 plus the 1 carried from the last step

23. hundreds tens ones 26 x34 104 78 1 tens times tens = hundreds 3x2 = 6 plus the 1 carried from the last step Put down 7

24. hundreds tens ones 26 x34 104 78 1 tens times tens = hundreds 3x2 = 6 plus the 1 carried from the last step Put down 7

25. hundreds tens ones 26 x34 104 78

26. hundreds tens ones 26 x34 104 78 884 Add

28. 24 5 x13 5

29. twenty fives fives ones 24 5 x13 5

30. twenty fives fives ones 24 5 x13 5 3 x 4

31. twenty fives fives ones 24 5 x13 5 2 3 x 4 Base 10 Base 5 3x4= 122 2

32. twenty fives fives ones 24 5 x13 5 2 3 x 4 Base 10 Base 5 3x4= 122 2 Put down 2 and carry 2

33. twenty fives fives ones 24 5 x13 5 2 Base 10 Base 5 3x4= 1222 2

34. twenty fives fives ones 24 5 x13 5 2 Base 10 Base 5 3x4= 1222 2 3 x 2

35. twenty fives fives ones 24 5 x13 5 2 Base 10 Base 5 3x4= 1222 2 3 x 2

36. twenty fives fives ones 24 5 x13 5 2 Base 10 Base 5 3x4= 1222 (3x2) +2 8 2 3 x 2

37. twenty fives fives ones 24 5 x13 5 2 2 Base 10 Base 5 3x4= 1222 (3x2) +2 81313

38. twenty fives fives ones 24 5 x13 5 32 2 Base 10 Base 5 3x4= 1222 (3x2) +2 81313 1 Put down 3 and carry 1

39. twenty fives fives ones 24 5 x13 5 132 2 Base 10 Base 5 3x4= 1222 (3x2) +2 813 1

40. twenty fives fives ones 24 5 x13 5 132 Base 10 Base 5 3x4= 1222 (3x2) +2 813

41. twenty fives fives ones 24 5 x13 5 132 Base 10 Base 5 3x4= 1222 (3x2) +2 813

42. twenty fives fives ones 24 5 x13 5 132 4 Base 10 Base 5 3x4= 1222 (3x2) +2 813 1 x 4

43. twenty fives fives ones 24 5 x13 5 132 24 Base 10 Base 5 3x4= 1222 (3x2) +2 813 1 x 2 fives times fives = twenty fives

44. fives ones 24 5 x13 5 132 24 Base 10 Base 5 3x4= 1222 (3x2) +2 813 Add in the base 5

45. twenty fives fives ones 24 5 x13 5 132 24 2 Base 10 Base 5 3x4= 1222 (3x2) +2 813

46. twenty fives fives ones 24 5 x13 5 132 24 2 Base 10 Base 5 3x4= 1222 (3x2) +2 813 3+4= 7

47. twenty fives fives ones 24 5 x13 5 132 24 22 Base 10 Base 5 3x4= 1222 (3x2) +2 813 3+4= 71212 1

48. twenty fives fives ones 24 5 x13 5 132 24 422 Base 10 Base 5 3x4= 1222 (3x2) +2 813 3+4= 712 1

49. twenty fives fives ones 24 5 x13 5 132 24 422 Base 10 Base 5 3x4= 1222 (3x2) +2 813 3+4= 712 1

50. another example This time we will not bother with the pebble board. As you work the familiar algorithm, it helps if you think in the base ten and then switch to the base 5.

51. fives ones 43 5 x32 5 Base 10 Base 5

52. fives ones 43 53 5 x32 52 5 1 Base 10 Base 5 2x3= 61 1

53. fives ones 43 5 x32 52 5 1 Base 10 Base 5 2x3= 61 (2x4) +1 9 1

54. fives ones 43 5 x32 5 41 1 1 Base 10 Base 5 2x3= 611 (2x4) +1 91414

55. fives ones 43 5 x32 5 141 1 Base 10 Base 5 2x3= 611 (2x4) +1 91414

56. fives ones 43 5 x32 5 141 1 Base 10 Base 5 2x3= 611 (2x4) +1 914

57. fives ones 43 53 5 x32 5 141 4 Base 10 Base 5 2x3= 611 2x4 813 3x33x3 91414 1

58. fives ones 43 5 x32 5 141 4 Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) + 1 13 1

59. fives ones 43 5 x32 5 141 2 34 Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) + 1 132323 1

60. fives ones 43 5 x32 5 141 2 34 31 Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) + 1 1323 4+4= 81313 Add in the base 5 1

61. fives ones 43 5 x32 5 141 2 34 031 Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) + 1 1323 3+4= 712 1+1+ 3= 51010 Add in the base 5 1 1

62. fives ones 43 5 x32 5 141 2 34 3 031 Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) + 1 1323 3+4= 712 1+1+ 3= 510 1 1