1. Maths the Modern Way!! Multiplication and Division St Teresa’s Primary School Paul Hargreaves Primary Strategy Consultant – Mathematics Essex County Council

2. Mental Starter – Bunny Ears

3. Total Recall! Select pairs of numbers from the target board on your table. Add these using one of the methods from last session. Will you use a number line? Will you partition and add mentally? Do you need to make jottings? BE BRAVE – try to avoid using the standard method! Now try with three numbers! Or try pairs of numbers and carry out a subtraction!

4. The Primary National Strategy Basis of teaching since 1999 – based on extensive research and proven success Basis of teaching since 1999 – based on extensive research and proven success Daily entitlement to maths lesson Daily entitlement to maths lesson Key features Key features Progression carefully set out Progression carefully set out Interactivity – use of models, images, games, practical activities Interactivity – use of models, images, games, practical activities Focus on mental skills as well as written Focus on mental skills as well as written Vocabulary, problem solving, communication, explanation and reasoning Vocabulary, problem solving, communication, explanation and reasoning

5. There is no “right way” to work!! Children exposed to a range of methods. Children exposed to a range of methods. Methods selected will depend upon the situation and the numbers involved, including when to use calculators. Methods selected will depend upon the situation and the numbers involved, including when to use calculators. Children make decisions about methods and draw on a range of strategies and approaches when applying Maths is context. Children make decisions about methods and draw on a range of strategies and approaches when applying Maths is context. Children in same class could be using different methods to others depending on their ability, confidence and stage of mathematical development. Children in same class could be using different methods to others depending on their ability, confidence and stage of mathematical development.

6. Describing Shapes

7. The Importance of Vocabulary Key to success in mathematics Key to success in mathematics Can be confusion between school and home Can be confusion between school and home Children need opportunities in class and in homework to use mathematical vocabulary – games, collaborative work, open ended investigations Children need opportunities in class and in homework to use mathematical vocabulary – games, collaborative work, open ended investigations

8. Mathematical Vocabulary Booklet Guide to which words and phrases are introduced to each year group Guide to which words and phrases are introduced to each year group Schools many make decisions regarding vocabulary Schools many make decisions regarding vocabulary It is not a checklist It is not a checklist Check with children and teachers if there are unfamiliar words Check with children and teachers if there are unfamiliar words

9. Multiplication Calculate the answer to this… Calculate the answer to this… 5 6 x 3 x 3

10. Did you do this? 5 6 x 3 x 3 16 8 16 81 Or did you use a mental method? Why did you choose the method you used?

11. Repeated Addition (Year 2/3) 5 added to 5 added to 5 5 + 5 + 5 3 lots of 5 5 x 3 3 x 5 Lots of practical experiences and use of number lines. Children will begin to use x and = signs.

12. Multiplication as an Array 4 x 2 = 8 2 lots of 4 = 8 2 x 4 = 8 4 lots of 2 = 8 Arrays are quite common – ice cube trays, egg boxes, chocolate boxes, medicine wrapping, tiles etc.

13. Multiplication by 10 7 x 10 = 70

14. Multiplication by 10 7 x 10 = 70

15. Multiplication by 10 7 x 10 = 70 BUT WE DIDN’T JUST ADD A 0!

16. Multiplication by 10 7 x 10 = 70 BUT WE DIDN’T JUST ADD A 0! 77.0 Both of these numbers are worth the same! 7 add a 0 is 7 + 0 = 7 We haven’t multiplied here!

17. Multiplication by 10 HTUHTUHTUHTU

18. HTU 7

19. Multiplication by 10 HTU 77

20. Multiplication by 10 HTU 7 7 0 7 0

21. Partitioning 15 x 5

22. Partitioning This is 10 x 5 and 5 x 5 added together. 10 x 5 = 50 5 x 5 = 25 50 + 25 = 75

23. Partitioning 36 x 4

24. Partitioning 36 x 4 is 30 x 4 and 6 x 4 added together. I know that 30 is three lots of 10, so 30 x 4 is 10 x 4 added to 10 x 4 added to 10 x 4. 10 x 4 = 40 6 x 4 = 24 40 + 40 + 40 + 24 = 144

25. Partitioning 36 x 4 36 x 4 is 30 x 4 added to 6 x 4 I know that 30 x 4 is 10 times bigger than 3 x 4 3 x 4 = 12, so 30 x 4 = 120 6 x 4 = 24 120 + 24 = 144

26. Grid Method 23 x 8

27. Grid Method 23 x 8 20 8 3x

28. Grid Method 23 x 8 20 8 3x 160

29. Grid Method 23 x 8 20 8 3x 16024

30. Grid Method 23 x 8 20 8 3x 16024 + 24 160 184

31. Have a Go!! 26 x 5 32 x 4

32. Grid Method 26 x 5 20 5 6x 10030 + 30 100 130

33. Grid Method 32 x 4 30 4 2x 120 8 + 8 120 128

34. Grid Method 346 x 4 x 4 300406

35. Grid Method 346 x 4 x 4 300406 1200

36. Grid Method 346 x 4 x 4 300406 1200160

37. Grid Method 346 x 4 x 4 300406 241601200

38. Grid Method 346 x 4 x 4 300406 241601200 1200 160 + 24 1384

39. Grid Method 72 x 38 x 8 30 702

40. Grid Method 72 x 38 x 8 30 702 560 210060 16 2100 560 60 60 + 16 2736

41. Standard Method 23 x 8 20 8 3x 16024 + 24 160 184

42. Standard Method 23 x 8 1 8 4 3 x 8 3 x 8 2 4 20 x 8 1 6 0 x 8 2 3

43. Standard Method 23 x 8 1 8 4 3 x 8 3 x 8 2 4 20 x 8 1 6 0 x 8 2 3 x 8 2 3 4 2

44. Standard Method 23 x 8 1 8 4 3 x 8 3 x 8 2 4 20 x 8 1 6 0 x 8 2 3 x 8 2 3 1 8 4 2

45. Why Not Just Teach the Standard Method? 1 0 0 0 7 x 3 x 4 2 5 6

46. Why Not Just Teach the Standard Method? 1 0 0 0 7 x 3 x 4 2 5 6 0 0 0 2 1

47. Why Not Just Teach the Standard Method? 1 0 0 0 7 x 3 x 4 2 5 6 0 0 0 2 112 2 0 3 2

48. Squashy Boxes

49. Division Share 8 sweets between two children.

50. Division

51. Division

52. Division

53. Division

54. Division

55. Division

56. Division

57. Division

58. Division 4 sweets in each pile

59. Repeated Subtraction (Grouping) 8  2 can be thought of as 8 – 2 = 6 6 – 2 = 4 4 – 2 = 2 2 – 2 = 0 I’ve taken 2 away 4 times, so the answer is 4!! 02468 -2

60. 13  3 13 – 3 = 10 10 – 3 = 7 7 – 3 = 4 7 – 3 = 4 4 – 3 = 1 4 – 3 = 1 I cannot make anymore groups of 3 out of 1, so there is one left over.

61. 13  3 = 4 r 1 13 – 3 = 10 10 – 3 = 7 7 – 3 = 4 7 – 3 = 4 4 – 3 = 1 4 – 3 = 1 I cannot make any more groups of 3 out of 1, so there is one left over.

62. 72  5 72 – 5 = 6737 – 5 = 32 67 – 5 = 6232 – 5 = 27 62 – 5 = 5727 – 5 = 22 57 – 5 = 5222 – 5 = 17 52 – 5 = 4717 – 5 = 12 47 – 5 = 4212 – 5 = 7 42 – 5 = 37 7 – 5 = 2

63. 72  5 72 – 5 = 6737 – 5 = 32 67 – 5 = 6232 – 5 = 27 62 – 5 = 5727 – 5 = 22 57 – 5 = 5222 – 5 = 17 52 – 5 = 4717 – 5 = 12 47 – 5 = 4212 – 5 = 7 42 – 5 = 37 7 – 5 = 2 Too long winded!!!!

64. 72 -50 (10 x 5) 22 - 5(1 x 5) 17 12 7 5 (1 x 5) 5 (1 x 5) 2 72  5 = 14 r 2

65. 72 -50 (10 x 5) 22 - 5(1 x 5) 17 12 7 5 (1 x 5) 5 (1 x 5) 2 72  5 = 14 r 2 5 ) 14 r 2

66. 72 -50 (10 x 5) 22 -20( 4 x 5) 2 72  5 = 14 r 2 5 ) 14 r 2

67. Try it!!! 93  4256  7

68. Why not use the way that we were taught?

69. The method that we are used to looks like this… 6 ) 1 3 3

70. The method that we are used to looks like this… 6 ) 1 3 3 0 1

71. The method that we are used to looks like this… 6 ) 1 3 3 0 2 11

72. The method that we are used to looks like this… 6 ) 1 3 3 0 2 2 r 1 11 It does work, but many children make the following errors…

73. The method that we are used to looks like this… 6 ) 1 3 3 Hmmm! I can’t make any groups of 6 out of 1, so…

74. The method that we are used to looks like this… 6 ) 1 3 3 Hmmm! I can’t make any groups of 6 out of 3, so… 0

75. The method that we are used to looks like this… 6 ) 1 3 3 Hmmm! I can’t make any groups of 6 out of 3, so… 0

76. The method that we are used to looks like this… 6 ) 1 3 3 Hmmm! I can’t make any groups of 6 out of 3, so… 0 0 0

77. The method that we are used to looks like this… 6 ) 1 3 3 Great! The answer is 0! 0 0 0

78. The method that we are used to looks like this… 6 ) 1 3 3 OK – 6s into 1 don’t go, so…..

79. The method that we are used to looks like this… 6 ) 1 3 3 1

80. The method that we are used to looks like this… 6 ) 1 3 3 1 Now, 6s into 13. I know that two 6s are 12 and I’ll have 1 left over.

81. The method that we are used to looks like this… 6 ) 1 3 3 1 12 1

82. The method that we are used to looks like this… 6 ) 1 3 3 1 12 1 Oh, look! 6s into 13 again! I know that!

83. The method that we are used to looks like this… 6 ) 1 3 3 1 12 1 12 r 1

84. The method that we are used to looks like this… 6 ) 1 3 3 1 12 1 12 r 1 The answer is 1212 r 1!

85. The method that we are used to looks like this… 18 )1 1 0

86. The method that we are used to looks like this… 18 )1 1 0 0 1

87. The method that we are used to looks like this… 18 )1 1 0 0 111

88. The method that we are used to looks like this… 18 )1 1 0 0 111 Back to square one! Lots more learning and understanding is needed here. To successfully tackle this problem, you need to know how to use repeated subtraction!

89. Multiplication Tables Year 1 – begin to learn 2x, 5x and 10x Year 1 – begin to learn 2x, 5x and 10x Year 2 – know 2x, 5x and 10x. Year 2 – know 2x, 5x and 10x. Year 3 – know 2x, 3x, 4x, 5x, 6x and 10x. Year 3 – know 2x, 3x, 4x, 5x, 6x and 10x. Year 4 – know all facts to 10 x 10 Year 4 – know all facts to 10 x 10

90. Multiplication Tables Three for free! If you know 3 x 5 = 15, you also know 5 x 3 = 15 15  5 = 3 15  3 = 5

91. Maths the Modern Way!! Multiplication and Division St Teresa’s Primary School Paul Hargreaves Primary Strategy Consultant – Mathematics Essex County Council