1. The New Curriculum and calculation methods in KS2 Tuesday 17 th November 2015

2. The New Curriculum Five-year-olds will be expected to learn to count up to 100 (compared to 20 under the old curriculum) and learn number bonds to 20 (old was up to 10) Fractions (1/4 and 1/2) will be taught from KS1, and by the end of primary school, children should be able to convert decimal fractions to simple fractions (e.g. 0.375 = 3/8) By the age of nine, children will be expected to know times tables up to 12×12 (old curriculum 10×10 by the end of primary school) Calculators will not be introduced until near the end of KS2, to encourage mental arithmetic.

3. A child working confidently in mathematics: Has a sense of the size of a number Knows where numbers fit in the number system Knows number facts Knows how to use what they know to work out new information Uses a range of methods of calculating in their head and on paper Makes sense of a problem and knows how to start to solve it Checks their answers Knows if their answers are reasonable Talks about how they work things out Suggests suitable units for measuring Justifies and proves answers Can explain and make predictions from data in graphs tables and charts

4. Addition

5. Resources to help children with addition

6. Stages in addition 1) Informal counting strategies e.g. counting songs, rhymes and games 2) Practical and pictorial addition – (a) count all (b) count on 3) Use of number lines to count on from one number to another

7. 4) Blank number lines: 8 + 6 = 14 (counting on in ones) 5) Blank number lines: 8 + 6 = 14 (chunking) Progressing :

8. 6) Partitioning Horizontal expansion T U + T U = 76 + 4 7 = 70 + 40 = 110 6 + 7 = 13 110 + 13 = 123 4 7 = 40 + 7 7 6 = 70 + 6 110 + 13 = 123 Vertical layout 7 6 + 4 7 1 3 + 1 1 0 1 2 3

9. Compacted Method or leading to 9

10. 7) Vertical layout Contracting the working out into a compact efficient form: T U H T U 7 6 3 4 6 + 1 4 7 + 1 1 9 3 1 2 3 5 3 9

11. Decimals 3.6 + 4.8 = 8.4 5.34 + 12.77 = 18.11 0.07 + 0.04 = 0.11 6. 8 9 0.7 + 0.3 = 1.0 1. 5 6 12 + 5 = 17.00 8. 4 5 1 0.11 + 1.0 + 17.0 = 18.11 + 3.0 + 0.6 4.8 7.8 8.4

12. Subtraction

13. Resources to help children with subtraction 1.

14. Stages in subtraction 1) Informal counting strategies e.g. counting songs, rhymes and games 2) Practical and pictorial subtraction 3) Use of number lines to count back or on from one number to another

15. 4) Finding the difference between groups of objects or numbers 5) Using an empty number line to count up 1.

16. 6) Stages in subtraction by decomposition 67 - 32 = 35 60 - 30 = 30 7 - 2 = 5 30 + 5 = 35 61 - 27 = 34 50 – 20 = 30 11 – 7 = 4 30 + 4 = 34 7) Expanded layout 563 – 241 = 863 – 346 = 50 13 500 + 60 + 3 800 + 60 + 3 - 200 + 40 + 1- 300 + 40 + 6 300 + 20 + 2 = 322 500 + 10 + 7 = 517

17. leading to or Compacted method 17 2 612 6

18. 8) Compact Method 563 – 271 = H T U 4 1 5 63 -2 71 2 92

19. Decimals 5.3 – 3.9 = 0.1 + 1 + 0.3 = 1.4 4 1 5. 3 3. 9 1 4 0.1 1 0.3 3.9 4 5 5.3

20. Multiplication

21. Resources to help children with multiplication

22. 10 20 30 4050 5 50 60 55 45 35 40 30 25 20 15 10 2 4 6 1) Counting groups of objects

23. 2) Grouping objects Repeated addition 3 x 2 2 + 2 + 2 = 6

24. 3) Arrays in real life 5 x 3 or 3 x 5 6 x 4 or 4 x 6 7 x 6 or 6 x 7 4 x 6 or 6 x 4 4 x 3 or 3 x 4

25. Solving multiplication problems How many legs on 6 spiders? Notation: 8 x 6 = Repeated addition: 8 + 8 + 8 + 8 + 8 + 8 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = Array: Using known facts: I know that 5 x 8 = 40, so 6 x 8 = 48 Jottings: 816 24 32 40 48

26. 4) Number line + 70 +21 10 x 7 3 x 7 0 70 91 13 x 7 = 91

27. 5) Grid Method 13 x 7 X103 7 70 21 70 + 21 = 91

28. Grid Method 123 x 13 = X100203 10100020030 3 300 60 9 1230 + 369 = 1000 + 200 + 300 + 30 + 60 + 9 = 1000 + 500 + 90 + 9 = 1230 369

29. Grid Method Decimals 7 x 3.3 = X30.3 7 21 2.1 21 + 2.1 = 23.1

30. 6) Expanded Short Multiplication 38 x 7 = 266 30 + 8 x 7 5 6 (8 X 7) 2 1 0 (30 X 7) 2 6 6 56 x 27 = 1512 50 + 6 20 + 7 4 2 (6 X 7) 3 5 0 (50 X 7) 1 2 0 (6 X 20) 1 0 0 0 (50 X 20) 1 5 1 2

31. 7) Compact Multiplication 2 3 x 1 2 4 6 (2 x 23) 2 3 0 (10 x 23) 2 7 6 1 2 3 1 2 2 4 6 ( 2 x 123) 1 2 3 0 (10 x 123) 1 4 7 6

32. Division

33. Resources to help children with division ½

34. 1) Sharing objects Share these six biscuits between three teddies. How many biscuits does each teddy get each?

35. 2) Linking with halving and quartering shapes Splitting into equal groups/parts ½ ¼

36. 3) Using tens and units to solve division problems 48 48 ÷ 2 = 24 12 ÷ 4 = 3 15 ÷ 3 = 5

37. 4) Division as grouping – Repeated Addition 15 ÷ 3 = 5 + 3 + 3 + 3 + 3 + 3 0 3 6 9 12 15

38. 5) Arrays to find answers with a remainder 13 ÷ 4 = 3 r1 + 4 + 4 + 4 +1 0 4 8 12 13

39. Finding remainders 39 How many fives in 37? 7 and two fifths! 7 r 2

40. Solving division problems How many boxes of 6 eggs do I have if I have 36 eggs altogether? Notation: 36 ÷ 6 = Array: Using known facts (grouping) : I know that 6 x 6 = 36, so 36 ÷ 6 = 6 Jottings: 612 18 24 30 36

41. 6) Long Division 560 ÷ 24 = How many packs of 24 biscuits can we make with 560 cookies? 23 r 8 24 5 6 0 4 8 0 (20 packs 20 x 24) 8 0 7 2 (3 packs 3 x 24) 8

42. 7) Counting on by chunking 100 ÷ 7 = 14 r2 8) Compact Bus Stop when dividing by a single digit 10x7 = 70 4x7 = 28 r 2 10 4 0 70 98 100 2 3 1 3 6 9 3 3 1 2 r1 3 9 3 7

43. Any questions? If you have any questions please feel free to ask.

44. Fractions Fraction of shape: Total number of equal parts (denominator). How many of those parts are coloured / shaded / eaten (numerator) Fraction of number using sharing/division Fraction of number using grouping/division 1.2/5 of 25 How many parts can be made from denominator 2.25÷5 (this gives the value of each part) 3.5 x 2 = 10 (value times numerator) Simplification: thinking about the common factor between the numerator and the denominator and dividing each. 3/12 - ¼5/10 - ½

45. Decimals Introduced in terms of money and half (0.5) £1.2113.5cm Number line to show decimals between whole numbers. 11.251.51.752 Place Value and Fractions H T U 1/10 1/100 1/1000 8 3 1. 2 7 4 Measure (converting measures) E.g.1534g = 1.534kg 250ml = 0.25l

46. Percentages and their equivalents % per hundred Ten and a unit value (upper KS2) For example 16% 100%50%25%75%10% Whole½¼¾1/10 10.50.250.750.1 Knowing halves Halve and halve again Halve and a quarter Whole less a quarter Divide by 10

47. Equivalence (Beg KS2) knowing basic equivalents: 0.25 = ¼= 25% 0.5 = ½ = 50% 0.75 = ¾ = 75% (Later KS2) Progress in ks2 Using calculation to go from fraction to decimals etc e.g. 4/5 = 4÷5 = 0.8 Percentages to fractions e.g. 32% = 32/100 = 16/50 = 8/25

48. Any questions? If you have any questions please feel free to ask.

49. Word Problems Simple 1 step problems These often involve 1 operation +-x÷ addtake awaytimesshare Totalsubtractmultiplydivide Plusminusproductgroups of Altogetherhow many more thanlots ofeach More thandifference Sum ofleft

50. Word Problems Multi-Step problems These often involve 2 or more operations

51. Word Problems Advanced Multi-Step problems Involve percentages/fractions/decimals/Unit conversion Jennifer earns £624 per month. She pays 6% to her mum. How much does she have left. There were 300 children at Hogwarts school of Witchcraft and Wizardry. 1/10 had a toad at their pet, ½ had an owl and 4/10 had a cat. How many of each pet were in the school. Laura had spent 2 and a half hours reading her book. She read 10 pages every 5 minutes. How many pages did she read? Cows travel at 15m per minute. How far in km will it travel in 2 hours. Jenna has a bag of flour that weighs 1.5kg and some butter that weights 250g and some sugar that weights 1.07kg. How much her ingredients weight altogether in grams.

52. Finding all possibilities Have a system for finding all possibilities E.g. Start with the smallest number, keeping something the same. Check for repeats Know and reason when all possibilities have been found. Organise results in an ordered list, tables or sections

53. Logic Problems Identify given facts and prioritise them. Look for relationships and patterns. Use one piece of information in the problem and see what effect it has. Choose a recording system to organise given information. Check the answer fits the criteria.

54. Diagram and visual puzzles Use a systematic approach to solve and record problem. Use drawings and annotations. Try possibilities to check the solution. Visualise problem using familiar shapes and patterns.

55. Vocabulary Add, addition, plus, more, increase Score, total, altogether, equals Sum Number sentence Record, draw, show me, jottings Place Value (Thousands, Hundreds, Tens and units) Count on, jump on

56. Vocabulary Subtract, subtraction, minus, take away, less, leave, fewer, decrease, left, difference, grouping and re- grouping Equals Number sentence Record, draw, show me, jottings Sum! Count on/count back Place Value-Thousands, Hundreds, Tens and Units

57. Vocabulary Lots of, groups of, ‘x’, times, multiply, multiplied by Multiple of Once, twice, three times… ten times… Times as (big, long, wide… and so on) Repeated addition Array, row, column Double One each, two each, three each… Group in pairs, threes… tens Number sentence Record, draw, show me, jottings

58. Vocabulary Share, share equally One each, two each, three each… Group in pairs, threes… tens Equal groups ÷, divide, division, divided by, divided into Halve, quarter, ½, ¼, One each, two each, three each… Group in pairs, threes… tens Left, left over, remainder Grouping and chunking Number sentence Record, draw, show me, jottings