1. 1 Addition

2. 57 Models for addition Combining two sets of objects (aggregation) 2

3. 57 Models for addition Combining two sets of objects (aggregation) 3

4. 57 Models for addition Combining two sets of objects (aggregation) 4

5. 57 Models for addition Combining two sets of objects (aggregation) 5

6. 57 Models for addition Adding on to a set (augmentation) Counting on with a bead bar/number line Combining two sets of objects (aggregation) 12 Issue: Tend to count one set, count the other and then count all. 5 6 7 8 9101112 Issue: Requires fluency with counting from any number. 12 5 0 + 7 Issues: Bead bar is a useful bridge from cardinal to ordinal. Number line helps to stop counting all Also: Bead bar and number line (showing 10s) encourages use of number bonds and place value for added efficiency. 10 +2+5 6

7. More than single digits? 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13

14. 14

15. 10 TensOnes 74 + 1111 11 1 1 1 1 11 52 10

16. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

17. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

18. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

19. TensOnes 74 + 111111111111 52 10 12

20. 10 TensOnes 74 + 111111111111 52 10 2 1

21. TensOnes 74 + 111111111111 52 10 2 1

22. TensOnes 74 + 111111111111 52 10 2 1

23. TensOnes 74 + 111111111111 52 10 2 1

24. TensOnes 74 + 111111111111 52 10 2 1 7

25. 25 Subtraction

26. 12 Models for subtraction Removing items from a set (reduction or take-away) - 1- 2- 3- 4- 5= 7 Issue: Relies on ‘counting all’, again. Comparing two sets (comparison or difference) Issue: Useful when two numbers are ‘close together’, where ‘take-away’ image can be cumbersome Seeing one set as partitioned Seeing 12 as made up of 5 and 7 Issue: Helps to see the related calculations; 5+7=12, 7+5=12, 12-7 = 5 and 12-5=7 as all in the same diagram N.B. When this is done on a bead bar, there are links with both counting back and difference on a number line 26

27. Models for subtraction Counting back on a number line Finding the difference on a number line 12 0 - 5 7 Issue: Number line helps to stop ‘counting all’. Also: Knowledge of place value and number bonds can support more efficient calculating 12 0 5 7 Issue: Useful when two numbers are ‘close together’, use of number bonds and place value can help. 52 10 -2-3 27

28. 72 - 47 More than single digits? 28

29. 72 - 47 29

30. 72 - 47 This is now “Sixty- twelve” 7 1 2 6 30

31. 72 - 47 31

32. 72 - 47 32

33. 72 - 47= 25 33

34. 10 1 TensOnes 1 72 74 - 10 1 6 1 1 1 1 1 11 1 1 1

35. TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

36. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

37. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

38. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

39. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5

40. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5

41. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5 10

42. TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5 10

43. TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 52 10

44. Addition and Subtraction: Both Ways

45. 10 1 TensOnes 1 72 74 - 10 1 6 1 1 1 1 1 11 1 1 1

46. TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

47. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

48. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

49. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6

50. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5

51. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5

52. 10 TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5 10

53. TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 5 10

54. TensOnes 72 74 - 1111 11 1 1 1 1 11 1 6 52 10

55. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

56. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

57. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

58. TensOnes 74 + 1111 11 1 1 1 1 11 52 10

59. TensOnes 74 + 111111111111 52 10 12

60. 10 TensOnes 74 + 111111111111 52 10 2 1

61. TensOnes 74 + 111111111111 52 10 2 1

62. TensOnes 74 + 111111111111 52 10 2 1

63. TensOnes 74 + 111111111111 52 10 2 1

64. TensOnes 74 + 111111111111 52 10 2 1 7