2. Efficient written methods for calculating addition, subtraction, multiplication and division by the end of year 6.

4. Partition into tens and units and recombine 12 +15 + 21 = 12 = 10 + 2 15 = 10 + 5 21 = 20 + 1 Recombine 10 + 10 + 20 =40 2 + 5 + 1 = 8, 40+ 8 = 48

5. Partition into tens and units and recombine 12 +15 + 21 = 36 + 42 =

6. Use informal pencil and paper methods to support, record or explain addition and subtraction. 227 + 312 = ? 200 300 500 20 10 30 + 729729 + = 539

7. 36 + 42 = Use informal pencil and paper methods to support, record or explain addition 227 + 312 = 227 + 315 =

8. 227 315 500 030 012 542 Using a standard written method + 227 315 542 + 1 Most significant digits first Least significant digits first + Prepares for carrying 227 315 012 030 500 542

9. 227 + 315 = Using a standard written method 4567 + 315 =

10. Using a standard written method; carrying 4567 315 4882 + 1 4567 + 315 =421.36 + 25.7 = + 1 421.36 25.70 447.06

11. Using a standard written method; carrying 4567 + 315 =421.36 + 25.7 =

13. Counting up from the smaller to larger number (complementary addition) 56 + 4 +20 6080 + 4 84 84 – 56 = 56 + 4 + 20 + 4 = 84 84 56 4 to 60 20 to 80 4 to 84 28 -

14. 84 – 56 = 84 56 4 to 60 20 to 80 4 to 84 28 - Apply partitioning skills 84 = 80 + 4 = 70 + 14 56 50 + 6 = 50 + 6 20 + 8 = 28 - Begin to record calculations in preparation for an efficient standard method; decomposition

15. 84 – 56 =84 – 52 = 46 – 25 = Counting up from the smaller to larger number (complementary addition)

16. 84 – 56 =84 – 52 = 46 – 25 = Begin to record calculations in preparation for an efficient standard method; decomposition

17. Record calculations in preparation for an efficient standard method; decomposition 89 = 80 + 9 57 50 + 7 30 + 2 = 32 - - 81 = 80 + 1 = 70 + 11 57 50 + 7 = 50 + 7 20 + 4 = 24 No decomposition Decomposition

18. 89 – 57 =84 – 57 = 284 – 57 = Record calculations in preparation for an efficient standard method; decomposition

19. Continue to develop an efficient standard method; decomposition 754 = 700 + 50 + 4 leading to 286 200 + 80 + 6 = 700 + 40 + 14 744 200 + 80 + 6 286 = 600 +140 + 14 644 754 200 + 80 + 6 286 286 400 + 60 + 8 468 468 - - -- 1 11 6 14 14

20. 754 – 286 = 5821 – 764 =4567 – 893 = Continue to develop an efficient standard method; decomposition

21. Develop and use an efficient standard written method; decomposition 6467 2684 3783 - 5 16 13 12467 84 12383 16 3 -

22. Develop and use an efficient standard written method; decomposition 6467 – 2684 = 782 175 – 4387 =324.9 – 7.25 =

24. Understand multiplication as repeated addition and as an array. 3 5 3 rows of 5 = 15 3 x 5 = 15 5 + 5 + 5 = 15 5 rows of 3 = 15 5 x 3 = 15 3 + 3 + 3 + 3 + 3 = 15 (rows are always mentioned before columns)

25. Modelling the number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials, but it can also assist the children to form useful mental pictures to support memory and reasoning.

26. Commutative property The commutative property of multiplication can be neatly illustrated using an array. For example, the array above could be read as 2 rows of 6, or as 6 columns of 2. Or the array could be physically turned around to show that 2 rows of 6 has the same number as 6 rows of 2. Regardless of the way you look at it, there remain 12 objects. Therefore, the array illustrates that 2 x 6 = 6 x 2, which is an example of the commutative property for multiplication. Being able to apply the commutative property means that the number of multiplication facts that have to be memorised is halved.

27. 4 x 3 =6 x 3 = Understand multiplication as repeated addition and as an array. 5 x 6 =

28. Use informal pencil and paper methods to support, record or explain multiplication. 23 x 3 23 x 3 = (20 x 3) + (3 x 3) 609 = 69 20 3 3 x Times tables Partitioning Array Grid method

29. 12 x 9 =26 x 3 = 35 x 16 = Use informal pencil and paper methods to support, record or explain multiplication

30. Grid method 346 x 9 270036054 x 9 300406 = 2700 360 54 3114 +

31. Continue to develop an efficient standard written method Short multiplication 346 x 9 leading to 346 9 2700 360 54 3114 300 x 9 40 x 9 6 x 9 x 346 9 3114 x 4 5

32. 346 x 9 Use informal pencil and paper methods to support, record or explain multiplication Grid method Short multiplication 543 x 7 Develop an efficient standard written method

33. Continue to develop an efficient standard written method Long multiplication 72 x 38 72 38 2160 576 2736 x 72 x 30 72 x 8

34. 72 x 38 Continue to develop an efficient standard written method Long multiplication

36. Use informal pencil and paper methods to support, record or explain divisions Chunking! Division made easy! 42 ÷ 3 = ? –12–-30 12 0 42 4 groups of 3 10 groups of 3 0 - 30 - 12 12 Chunks 10 chunks + 4 chunks = 14

37. 42 ÷ 321 ÷ 3 54 ÷ 6 Use informal pencil and paper methods to support, record or explain divisions

38. Use informal pencil and paper methods to support, record or explain division Using multiples of the divisor (CHUNKING) 725 50 10 x 5 22 20 4 x 5 2 Answer: 14 remainder 2 - - ÷

39. 72 ÷ 3 = 72 ÷ 5 =72 ÷ 4 = Use informal pencil and paper methods to support, record or explain division

40. Develop an efficient standard written method Short division 196 ÷ 6 ) 6 32 R 4 196 18 (30 x 6 = 180) 16 12 (2 x 6 = 12) 4 (remainder)

41. 196 ÷ 6 Develop an efficient standard written method Short division 256 ÷ 7

42. Continue to develop an efficient standard written method Short division (thousands) 2196 ÷ 6 ) 6 366 2196 1800 (300 x 6 = 1800) 396 360 (60 x 6 = 360) 36 (6 x 6= 36)

43. Continue to develop an efficient standard written method Short division (Bus Stop Method!) 2196 ÷ 6 ) 6 366 2196 332 6 into 2 doesn’t go – carry the 2 over. 6 into 21 goes 3 remainder 3 – carry the 3 over. 6 into 39 goes 6 remainder 3 – carry the 3 over. 6 into 36 goes 6 exactly. 2196 divided by 6 = 366!

44. 2196 ÷ 6 Continue to develop an efficient standard written method Short division (thousands) 4321 ÷ 68104 ÷ 6

45. Know what each digit represents and partition three-digit numbers into a multiple of 100, a multiple of 10, and ones. Understand multiplication as repeated addition and as an array. Partition into tens and units and recombine. Add three two-digit numbers using apparatus or informal methods. Add or subtract a near multiple of 10 to a two-digit number, by adding or subtracting the nearest multiple of 10, and adjusting. Choose appropriate number operations and calculation methods to solve word problems.

46. Know what each digit represents and partition three-digit numbers into a multiple of 100, a multiple of 10, and ones. 243 200 40 3 What is partitioning?

47. What is an array? Understand multiplication as repeated addition and as an array. 3 x 5 = 15 5 + 5 + 5 = 15 3 5

48. Add three two-digit numbers using apparatus or informal methods. What does it mean by informal method? 12 +15 + 21 = 21 + 20+7 41 48 10 + 10 + 20 =40 2 + 5 + 1 = 8, 40+ 8 = 48

49. Partition into tens and units and recombine. Why is partitioning so useful? 10 + 10 + 20 =40 2 + 5 + 1 = 8, 40+ 8 = 48 12 +15 + 21 = It’s one of those informal methods!

50. Add or subtract a near multiple of 10 to a two-digit number, by adding or subtracting the nearest multiple of 10, and adjusting. What does it mean by adjusting 39 + 34 = ? 40 + 34 = 74 74 – 1 = 73 Round up 39 to 40 40 + 30 = 70 70 + 4 = 74 Partitioning Recombine A clearly written answer

51. Choose appropriate number operations and calculation methods to solve word problems. Use informal pencil and paper methods to support, record or explain addition and subtraction. To add/subtract by counting on or back in repeated steps of 1, 10, 100. Use informal pencil and paper methods to support, record or explain multiplication. Use informal pencil and paper methods to support, record or explain divisions.

52. 227 + 300 To add/subtract by counting on or back in repeated steps of 1, 10, 100. What is counting on and back on a number line? 227 + 100 337 537 + 100 437

53. Use informal pencil and paper methods to support, record or explain addition and subtraction. What does it mean by informal method? 227 + 312 = ? 200 300 500 20 10 30 + 729729 + = 539

54. Use informal pencil and paper methods to support, record or explain addition and subtraction. What does it mean by informal method? £5.20 - £3.60 = ? Demonstrate the need to re-partition the numbers as: £5.20 - £3.60 = £4 + 120p subtract £3 + 60p = £4 - £3 and 120p – 60p = £1 and 60p = £1.60

55. Use informal pencil and paper methods to support, record or explain multiplication. What another informal method? 23 x 3 23 x 3 = (20 x 3) + (3 x 3) 609 = 69 20 3 3 x Times tables Partitioning

56. Use informal pencil and paper methods to support, record or explain divisions. Division made easy! 42 ÷ 3 = ? –12–-30 12 0 42 4 groups of 3 10 groups of 3 0 - 30 - 12 12 Chunks 4 chunks + 10 chunks = 14

57. Choose appropriate number operations and calculation methods to solve word problems. Understand and use the principle of the associative law. Extend written methods to short division of HTU by U

58. Establish 5 x 16 is the same as 10 x 8 etc. Understand and use the principle of the associative law. What is associative law and do the majority of children care? GRID! 5 x 10 = 50 5 x 6 = 30 = 80

59. Extend written methods to short division of HTU by U Chunking! 183 ÷ 5 = ? 183 – 150 (30 x 5) = 33 33 – 30 (6 x 5) = 3 Answer 36 r 3

60. Choose appropriate number operations and calculation methods to solve word problems. Use informal pencil and paper methods to support, record or explain addition and subtraction. To add/subtract by counting on or back in repeated steps of 1, 10, 100. Use informal pencil and paper methods to support, record or explain multiplication. Use informal pencil and paper methods to support, record or explain divisions.