Written Calculation A whole school approach

1. Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Written CalculationA whole school approach Sacred Heart Catholic Primary SchoolByermoor

2. Sacred Heart Byermoor Written Calculation Policy The purpose of this calculation policy is to ensure consistency in teaching throughout Sacred Heart Catholic Primary School. This policy will give an overview of the different strategies used in our school to teach maths throughout the Primary Maths Curriculum. As children progress at different rates, some may need to use the strategies from previous or future year groups.

3. Sacred Heart Byermoor The introduction of calculation strategies At Sacred Heart Catholic Primary School, children are introduced to the processes of calculation through practical, oral and mental activities. As children begin to understand the underlying ideas they develop ways of recording to support their thinking and calculation methods, use particular methods that apply to special cases, and learn to interpret and use the signs and symbols involved. Over time children learn how to use models and images, such as empty number lines, to support their mental and informal written methods of calculation. There is a considerable emphasis on teaching mental calculation strategies. Informal written recording takes place regularly and is an important part of learning and understanding. More formal written methods follow only when the child is able to use a wide range of mental calculation strategies. As children’s mental methods are strengthened and refined, so too are their informal written methods. Some recording takes the form of jottings, which are used to support children’s thinking. This may be done on scrap paper and whiteboards and is not always retained as it is for the children’s own personal use.

4. Sacred Heart Byermoor This policy contains the key pencil and paper procedures that will be taught within our school. It has been written to ensure consistency and progression throughout the school and reflects a whole school agreement. This policy concentrates on the introduction of standard symbols, the use of the empty number line as a jotting to aid mental calculation and on the introduction of pencil and paper procedures. It is important that children do not abandon jottings and mental methods once pencil and paper procedures are introduced. Therefore children will always be encouraged to look at a calculation/problem and then decide which is the best method to choose – pictures, mental calculation with or without jottings, structured recording or a calculator. Our long-term aim is for children to be able to select an efficient method of their choice (whether this be mental, written or in upper Key Stage 2 using a calculator) that is appropriate for a given task. They will do this by always asking themselves: ‘Can I do this in my head?’ ‘Can I do this in my head using drawings or jottings?’ ‘Do I need to use a pencil and paper procedure?’ ‘Do I need a calculator?’

5. Sacred Heart Byermoor Although the focus of the policy is on pencil and paper procedures it is important to recognise that the ability to calculate mentally lies at the heart of the Primary National Strategy for mathematics. The mental methods in the Primary Framework for teaching mathematics will be taught systematically from Reception onwards and pupils will be given regular opportunities to develop the necessary skills. However mental calculation is not at the exclusion of written recording and should be seen as complementary to and not as separate from it. In every written method there is an element of mental processing. Sharing written methods with the teacher encourages children to think about the mental strategies that underpin them and to develop new ideas. Therefore written recording both helps children to clarify their thinking and supports and extends the development of more fluent and sophisticated mental strategies.

6. Our Aims • The overall aim is that when children leave primary school they: • Have a secure knowledge of number facts and a good understanding of the four operations; • Are able to use this knowledge and understanding to carry out calculations mentally and to apply general strategies when using one-digit and two-digit numbers and particular strategies to special cases involving bigger numbers; • Make use of diagrams and informal notes to help record steps and part answers when using mental methods that generate more information than can be kept in their heads; • Have an efficient, reliable, compact written method of calculation for each operation that children can apply with confidence when undertaking calculations that they cannot carry out mentally; • Use a calculator effectively, using their mental skills to monitor the • process, check the steps involved and decide if the numbers displayed • make sense. Sacred Heart Byermoor

7. Objectives The objectives in the revised Framework show the progression in children’s use of written methods of calculation in the strands ‘Using and applying mathematics’ and ‘Calculating’. Sacred Heart Byermoor

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14. Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Addition

15. Sacred Heart Byermoor Reception How many? Add 1 more How many now? Lots of practical first. Could be then used as a recording activity.

16. Sacred Heart Byermoor Recording Simple Calculations in Reception 5 + 1 =

17. Sacred Heart Byermoor Year One 15 + 3 = Begin with all numbers identified. Move onto having just markers.

18. Sacred Heart Byermoor Adding 9 7 + 9 = 7 + 10 = 17 – 1 = 16 Use a number line to record + 10 -1 - 7 16 17

19. Sacred Heart Byermoor 14 + 25 = Year Two

20. Sacred Heart Byermoor + 30 + 30 + 5 74 104 134 139 74 + 65 = Year Three Use an empty number line

21. Sacred Heart Byermoor Vertical Strategy (Spring / Summer Term) 2 7 4 + 3 4 9 1 3 1 1 0 5 0 0 6 2 3

22. Sacred Heart Byermoor Year Four, Year Five and Year Six 2 5 4 7 £5 . 6 8 + 6 7 6+£4 . 8 7 3 2 2 3£1 0 . 5 5 1 1 1 1 1 1

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24. Sacred Heart Byermoor Compensation Addition + £1.00 -4 - 75p £1.71 £1.75 75p + 96p 75p + £1.00 = £1.75 £1.75 – 4p = £1.71 Use a number line to record Informal strategies such as this one can still be used in Y4, Y5 and Y6 to help the children arrive at the correct answer,

25. Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Subtraction

26. Sacred Heart Byermoor Reception How many? Take 1 away How many now? Lots of practical first. Could be then used as a recording activity.

27. Sacred Heart Byermoor Recording Simple Calculations in Reception 5 - 1 = 5 - 1 =

28. Sacred Heart Byermoor Year One 17 - 6 = Use a counter, then count back. Begin with all numbers identified. 9 - 6 =

29. Sacred Heart Byermoor 9 - 6 = 3 4 5 6 7 8 Move onto just having the start number and then just markers for other numbers. 19 – 3 = 16 17 18 19 Depending on how children cope, you could move onto no markers.

30. Sacred Heart Byermoor Year Two Counting back on an empty number line 65 – 34 = -10 -10 -10 - 4 31 35 45 55 65

31. Sacred Heart Byermoor 145 – 64 = -20 -20 -20 - 4 81 85 105 125 145 Year Three Counting back on an empty number line 357 – 132 = -2 -30 -100 225 227 257 357

32. Sacred Heart Byermoor Year Three Counting up 153 – 84 = +6 +10 +50 +3 84 90 100 150 153 Vertical Counting up (Summer term)

33. Sacred Heart Byermoor Year Four Counting up 353 – 184 = +6 +10 +100 +53 184 190 200 300 353

34. Sacred Heart Byermoor Year Five and Year Six Decomposition strategy (Could be introduced at end of Year 4 with MA pupils) 6 12 4 1 1 • 7 3 8 • 5 7 9 • 1 5 9 • 3 5 2 • 2 3 7 • 1 1 5

35. Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Multiplication

36. Sacred Heart Byermoor Multiplication Facts Using multiplication facts Tables should be taught everyday from Y2 onwards, either as part of the mental oral starter or other times as appropriate within the day. Year 2 2 times table 5 times table 10 times table Year 3 2 times table 3 times table 4 times table 5 times table 6 times table 10 times table Year 4, 5 & 6 Derive and recall all multiplication facts up to 10 x 10

37. Sacred Heart Byermoor Year One Children will experience equal groups of objects and will count in 2s and 10s and begin to count in 5s.

38. Sacred Heart Byermoor Year Two and Three Multiplication as array patterns. The calculation can be done in any order and you still have the same answer.

39. Sacred Heart Byermoor Year Two and Three

40. Year Four, Year Five and Year Six The Grid Method of Multiplication This is introduced in Year 4 and developed and progressed throughout Year 5 and Year 6. This can even be extended to decimals in Year 6

41. Year Four, Year Five and Year Six Year 4 Year 5 and Year 6

42. Year Five and Year Six

43. Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Sacred Heart Byermoor Division

44. Sacred Heart Byermoor Year Two and Three Division as array patterns. The calculation can be done in any order and you still have the same answer.

45. Sacred Heart Byermoor Year Two and Three Division as repeated subtraction. This is usually a question on Key Stage 1 SATs.

46. Sacred Heart Byermoor Year Two and Three

47. Year Four, Year Five and Year Six

48. Year Six