1. Year 5/6 Mathematical Strategies Progression in written calculation methods.

2. Aims 1. Increase knowledge of how we teach written methods for addition, subtraction, multiplication and division. 2. Share helpful ideas and resources that will allow you to support your child at home.

3. Our approach at Hillside  Develop children’s understanding of number and give them a firm basis to build on.  Constant reinforcement of key skills.  Ensure the children receive daily mental maths strategies to help build confidence and knowledge.

4. Vocabulary includes; add, addition, more, plus, increase, make, sum, altogether, score, how many more…..? How many more is … than ….?

5. 4325 + 9568 =

6. Horizontal Method

7. Either partition both numbers or just the second number. 126 + 51 = 100 + 20 + 50 + 6 + 1 = 100 + 70 + 7 = 177 OR 126 + 51 = 126 + 50 + 1 = 176 + 1 = = 177

8. Expanded Vertical Method

9. Can be done using either the largest or the smallest digit first. Partial sums are added mentally. Year 5 Year 6

10. Compact Method

11. Vertical layout, contracting the working to a compact efficient form: First without any carrying: HTU 355 + 243 598

12. Vertical layout, contracting the working to a compact efficient form: ThHTU 5871 + 3475 9346 1 1 Then including carrying: Emphasis is always on place value… 140 not 14

13. Vocabulary includes; subtract, subtraction, take away, minus, leave, how many are left/left over? Difference between, how many fewer is… than….? How much less is….? Difference between.

14. 9 7 3 4 - 8 8 6 3=

15. 23 – 14 is not the same as 14 – 23!! Never swap your numbers around! All ages need to be reminded:

16. Complimentary Addition - Subtraction by adding on

17. . 502 - 198 198 +2 200500 +300 502 +2 = 304 502 - 198 2(to 200) 300 (to 500) (to 502)2 304

18. Compact Method

19. Year 5 HTU 349 - 228 121 Year 6 ThHTU 3768 - 2336 1432 Method 1 -Without decomposition

20. Method 2: with decomposition Year 5 HTU 7 1 823 - 582 241 Year 6 ThHTU 1 131 2346 - 827 1519

21. Decimals – Compact method Year 5 Year 6 H T U. t Th H T U. t h 8 13 1 3 1 - 3 9 4. 6 - 6 8 9 4. 3 6 2 8 7. 7 4 5 9 3. 4 5 1 0 6. 9 2 3 0 0. 9 1

22. Vocabulary includes; lots of, groups of, times, multiply, multiplication, multiplied by, multiple of, product, repeated addition, array.

23. 734 x 23=

24. Grid Method

25. 10 7 10 5 100 50 70 35 1 0 0 + 7 0 5 0 3 5 2 5 5 Year 5 18 600 90 200 30 6 3 600 + 90 18 708 15 x 17 236 x 3

26. 200 70 4 20 5 4000 1000 1400 350 4 0 0 0 + 1 4 0 0 1 0 0 0 3 5 0 8 0 2 0 6 8 5 0 Year 6 As for Year 5 plus 3 digit x 2 digit. 20 80 274 x 25

27. Expanded Method

28. 1 3 4 x 7 2 8 2 1 0 7 0 0 9 3 8 1 7 x 1 5 3 5 5 0 7 0 1 0 0 2 5 5 1 3 5 x 2 4 2 0 1 2 0 4 0 0 1 0 0 6 0 0 2 0 0 0 3 2 4 0 Year 6 Year 5

29. Decimal Expanded method – Year 6 3.6 4 x 7 0.2 8 4.2 0 2 1.0 0 2 5.4 8

30. Compact Method

31. 1 7 x 1 5 8 5 1 7 0 2 5 5 2 1 7 x 5 1 0 8 5 Year 6 1 3 4 x 2 4 5 3 6 2 6 8 0 3 2 1 6 Year 5

32. Decimal Compact method – Year 6 3.6 4 x 7 2 5.4 8 4 2

33. Vocabulary includes; halve, share, share equally, group in pairs, equal groups of, divide, division, factor, quotient, divisible by.

34. 357 divided by 17 =

35. Vertical Chunking Method

36. 256 - 70 (10 x 7) 186 - 70 (10 x 7) 116 70 (10 x 7) 46 35 (5 x 7) 11 7 (1 x 7) 4 256 - 210 (30 x 7) 46 - 42 (6 x 7) 4 256 divided by 7 = 36 r 4 256 divided by 7 = 36 r 4 Year 5 division – 3 digit divided by 1 digit. Year 6 division – 3 digit divided by 2 digit

37. Compact Method

38. 5)9 5 1 4 45 divided by 5 is 9. 9 There are 4 tens left over. There is no remainder. 9 tens divided by 5 is 1 ten. Year 5:

39. 4)9 4 2 1 14 divided by 4 is 3. 3 There is 1 ten left over. There is a remainder of 2. 9 tens divided by 4 is 2 tens. 2.0 2 units divided by 4 is 0.5..5 Year 6:

40. Long Division

41. 839 ÷ 27= Method 1 8 3 9 - 2 7 0(27 x 10 = 270) 5 6 9 2 9 9 2 9 - 2 7 (27 x 1 = 27) 2 10 + 10 + 10 + 1 = 31

42. 839 ÷ 27 Method 2 27 ) 8 3 9 - 8 1 0 2 9 Don’t forget the remainder! - 2 7 3 1r 2