1. Nonsuch Primary School Progression through Calculations Y4-6 Can I do it in my head? Do I need jottings ? Do I need to use a calculator? Shall I use a pencil and paper method?

2. Starter Mental mathematics test! Get your pencils ready

3. Aims To look at the ways that we teach mathematics To look at how children learn and calculate To look at ways in which parents can help their children

4. How has mathematics changed? Emphasis on mental calculations; Interactive whole class and group teaching; Enjoyable practical approaches; Mathematics with understanding Mathematics through problem solving to develop real life links and higher order thinking skills

5. Skills of mental calculation Remembering number facts and recalling them without hesitation. Using facts that are known by heart to figure out new facts. Applying understanding of place value and ability to partition numbers into parts Understanding and using the laws of arithmetic and relationships between the four operations to find answers and check results Having a repertoire of mental strategies to do calculations with some thinking time Solving word problems

6. Calculations Ways to help children to remember… Practice with just one fact a day, or try a ‘fact of the week’ Practice ‘fact families’, e.g. 6+8=14, 8+6+14, 14-6=8, 14-8=6 Work from answers back to facts – how many facts do you know with an answer of 12? Make an addition or multiplication table and cross out all those facts you already know. Now focus on those you need to learn. Encourage children to work out their own ways to remember facts Draw pictures to accompany particular facts. Repeat it and repeat it!

7. Mental gymnastics Think of a number and keep doubling it. How far can you go? Face the person next to you and alternate! In twos – one person recites all the numbers from 1 to 100 The other person raises their hand at any number that can be divided by 3 or … Divided by 4 or … Divided by 3 and 4 or … Divided by 5 You can use your number square to help you!

8. Mental calculations Children are encouraged to count in different ways and to calculate mentally. Number lines – Bead strings / number stick / individual number lines / Number ladders

9. Calculations The aim is that children will always be able to recognise when calculations can be done ‘ in their heads’ and choose effective and efficient strategies to work out the answers.

10. Overview Up to Year 3 the emphasis is on: oworking mentally, ocalculations recorded in horizontal number sentences osome jottings for more challenging numbers oModels and Images In Year 3-6 children will be gradually taught more formal written methods of calculation but they will still use mental methods, models and images and jottings where appropriate.

11. Developing children’s mental picture of number system oDEMONSTRATE on a number line children’s response to a calculation. oDISPLAY number lines and washing lines around the room for the children to access. oMODEL the use of number lines and tracks to aid calculation and empty number lines from Y2 oCONTINUE to demonstrate, display and model use of a number line all the way to Y6!

12. So - how can we give children the best foundations for success with written calculations? o We need to encourage children to use mental calculation strategies for mental calculation strategies for smaller/ simpler numbers. smaller/ simpler numbers. o We need to encourage children to ask the question “Can I do it in my ask the question “Can I do it in my head?” or “Can I do it in my head with head?” or “Can I do it in my head with jottings/ a number line?” jottings/ a number line?”

13. Laying the foundations for addition and subtraction oPartitioning oRounding oCounting on oBridging through 10s, 100s, 1000s boundaries oAddition and subtraction facts

14. Laying the foundations for multiplication and division oDoubling/ Halving oGrouping/ equal groups/ equal jumps oRepeated addition/ subtraction oArrays oMultiplication and division facts

15. Multiply Slap, clap, click (not as violent as it sounds!) ‘Show me’ – 1. The product of a multiplication 2. A multiple of 2, 3, 5, 10, 4, etc 3. A number that is exactly divisible by 3, 5, 2, 10, 4. A common multiple of 2 and 3, 3 and 5, 3 and 10

16. Secure understanding so we avoid such calculation errors! 158 + 184 612 4 1 945 - 237 712

17. Addition- Progression oY1-3 oMental calculation supported by: Modelling of method by teacher Modelling of method by teacher Jottings Jottings Number lines Number lines oExpanded method using partitioning oCompact ‘carrying’ method

18. When do children use jottings / number lines? When they can calculate mentally and need a little support.When they can calculate mentally and need a little support. When they are not completely secure with ‘carrying’.When they are not completely secure with ‘carrying’. When they are dealing with addition of decimals, negative numbers, time, measurement scales, etc.When they are dealing with addition of decimals, negative numbers, time, measurement scales, etc.

19. Extend to expanded horizontal method (partitioning both numbers and adding the units first.) 40 + 8 30 + 6 70 + 14 = 84

20. Move from horizontal to vertical layout, adding the units first: 352 + 43 = 395 352 + 43 5 90 300 395

21. Expanded method - crossing the units boundary (This is called ‘carrying’ in the standard written form) It is important for children to have a good understanding of place value and partitioning using resources and images to support calculations. This method enables children to see what happens to numbers in the standard written method. VideoVideo 48 +36 14 +70 84 T U 4 8 + 3 6 8 4 1 “Carry one ten”

22. Standard written method The previous stages reinforce what happens to the numbers when they are added together using more formal written methods. VideoVideo 3 5 8 7 + 6 7 5 4 2 6 2 1 1 1

23. Subtraction - Progression Mental calculations supported by:Mental calculations supported by: Modelling of method by teacher Modelling of method by teacher Jottings Jottings Number line Number line Expanded decomposition using partitioningExpanded decomposition using partitioning Compact decompositionCompact decomposition

24. Subtraction Children are taught to understand subtraction as: taking away (counting back) and finding the difference (counting up).

25. 78 – 12? 74 – 57? How do you work out….

26. Using a Number line for Subtraction Counting Back - videovideo 78 – 12 -10 -2 66 68 78 Counting on to find the Difference 74 – 57 +10 +3 +4 57 67 70 74

27. When do children still use jottings/ number lines?? oWhen they can calculate mentally and need a little support. oWhen they are calculating the difference between two numbers relatively close together. oWhen not completely secure with decomposition oWhen calculating with decimals. oWhen decomposition is made difficult by ‘trapped zeroes’.

29. Expanded subtraction (no exchanging) Partition both numbers, and subtract, starting with the units. 93 – 32 = 61 90 + 3 -30 + 2 60 + 1 = 61

30. Expanded subtraction (with exchanging) It is important that children have a good understanding of place value and partitioning using resources and images to support calculations. The expanded method enables children to see what happens to numbers in the standard written method.

31. Standard written method The previous stages reinforce what happens to numbers when they are subtracted using more formal written methods. It is important that children have a good understanding of place value and partitioning. Video using Apparatus Video

32. Multiplication - Progression oMental calculation supported by: Jottings Jottings Number lines Number lines Modelling of method by teacher Modelling of method by teacher oUnderstanding of multiplication as: an array an array repeated addition repeated addition scaling scaling oGrid method oStandard written method Multiplication facts ITP

33. 4 x 7 = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 + 7 1 234

34. Using a number line - video video

35. Use place value apparatus to support the multiplication of U x TU 4 x 13

36. Use place value apparatus to support the multiplication of U x TU alongside the grid method 4 x 13 Video

37. Expanded multiplication Remember to multiply the units first 8 7 x 6 4 2 (6 x 7) 4 8 0 (6 x 80) 5 2 2 5 6 x 2 7 4 2 (7 x 6) 3 5 0 (7 x 50) 1 2 0 (20 x 6) 1 0 0 0 (20 x 50) 1 5 1 2

38. 8 7 x 6 5 2 2 4 Standard written method Remember to start from the units and ‘carry’ numbers underneath

39. Long multiplication - video video

40. Division - Progression oMental calculations supported by: Jottings Jottings Number lines Number lines Modelling of method by teacher Modelling of method by teacher oUnderstanding division as sharing and grouping. oVisualising division using: arrays arrays repeated subtraction repeated subtraction

41. Division - Progression Chunking Step 1: Demonstrate practically by repeatedly subtracting groups of objects and keeping count Step 2: Model on a number line Step 3: Model vertical method

42. Chunking along a number line - videovideo

43. Chunking with 6x table 93 ÷ 6 93 -60 (x10) 33 - 30 (x5) 3 Count up the lots of 6 Answer - 15 r 3 Video

44. Stage 3 Long division (HTU ÷ TU) 15 432 15 432 - 150 x 10 - 300 x 20 282 132 - 150 x 10 - 120 x 8 132 12 - 60 x 4 72 Answer = 28 r 12 - 60 x 4 12 Answer = 28 r 12

45. Move on to short division or the ‘bus stop method’ (HTU ÷ U)

46. How to help your child with mathematics!

47. Sorting Socks Cars Shoes

48. Measures Keep a record of your child's growth; Scales and balances e.g. see-saws Capacity – different containers to play with in the sink or bath;

49. Shape and space Recognising shapes around them e.g. doors, windows, cans, boxes etc Construction sets, Lego, Shapes of cakes, biscuits, sandwiches.

50. How can parents help? Count with their child Play number games Involve children in shopping activities Involve children when taking measurements or weighing items Take note of numbers in real life e.g. telephone numbers, bus numbers, lottery numbers etc Give children opportunities to use money to shop, check change etc Talking about the mathematics in football e.g.. How many points does your favourite team need to catch the next team in the division? When helping children calculate use the method that they have been taught (not straight to a standard written method as this is what you use!)

51. Key Messages To develop written calculation strategies, children need: oSecure mental strategies from YR. oA solid understanding of the number system. oPractical, hands on experience including counters and base 10 apparatus. oVisual images including number lines and arrays. oExperience of expanded methods to develop understanding and avoid rote learning. oSecure understanding of each stage before moving onto the next. oThe questions at the forefront of their minds: ‘Can I do it in my head? If not which method will help me?’ ‘Can I do it in my head? If not which method will help me?’