1. Subtraction progression of methods June 2015

2. Reception - Subtraction 1 less than 5 is? 2 less than 5 is? 1 less than 7? 4 4,3 6 7 Say which is one or two less than a given number 6

3. Reception - Subtraction Use objects to take a single digit away. “Six take away two is four” “What is six take away two?”

4. Year 1 - Subtraction Repeat using a bead string 1234567891011121314151617181920 Repeat using a number line 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Use a number track to subtract a single digit number from 20 17 – 3 = 14

5. Year 1 - Subtraction Understand subtraction as finding the difference using objects and visual representations The model would be introduced with concrete objects which children can move (including cards with pictures) before progressing to pictorial representation. The use of other images is also valuable for modelling subtraction e.g. Numicon, bundles of straws, Dienes apparatus, multi-link cubes, bead strings

6. Missing numbers – using multilink 7 - = 5 Use Numicon to overlap the corresponding numbers to find the difference Year 1 - Subtraction

7. 26 – 4 = Using a 100 square to count back 22

8. Year 2 - Subtraction 47 – 23 = Use (empty) number lines by counting back including jumping in tens -10 37 38 39 40 41 42 43 44 45 46 4724 25 26 27 28 29 30 31 32 33 34 35 36 -10 24 -10 37 47 24 27 -10

9. Year 2 - Subtraction 47 – 23 = Use 100 squares by counting back including jumping in tens 24

10. Year 2 - Subtraction Working towards written methods with concrete support (no decomposition) 75 – 42 =33

11. Year 3 - Subtraction Expanded column subtraction (abstract representation) using place value counters with no decomposition 98 – 35 = Dienes could be used, as in year 2, for those pupils who need a less abstract representation 63

12. Year 3 - Subtraction Exchanging through expanded method using place value counters (or dienes for those needing less abstract models) 72 - 47=25

13. Year 4 - Subtraction Expanded column subtraction with decomposition, modelled with place value counters, progressing to calculations with 4-digit numbers.

14. Year 4, 5 & 6 - Subtraction If understanding of the expanded method is secure, children will move on to the formal method of decomposition, which again can be initially modelled with place value counters.