1. HEATHERSIDE JUNIOR SCHOOL PROGRESSION IN SUBTRACTION Parents’ Information Evening

2. Progression towards a short column method for subtraction Establish mental methods, based on a knowledge of number bonds and an understanding of place value. With more difficult calculations, approximate first, using mental methods. Show children how to set out written calculations using jottings and expanded layouts. Gradually refine their written recording into a more compact and efficient formal method. Extend to larger numbers and to decimals.

3. What does your child need to know? Mental Skills recognise the size and position of numbers count back in steps of different sizes know number facts for all numbers to 20 subtract multiples of 10 from any number partition and recombine numbers bridge through multiples of 10 Key Vocabulary subtract take away minus count back / up less than fewer difference

4. Step 1 Using everyday objects children will: begin to count backwards in familiar contexts such as number rhymes or stories; count back in ones from any given number; begin to relate subtraction to ‘ taking away ’; find one less than a number; count back in larger steps, (tens, then twos and fives). I can subtract 5 – 1 = 4

5. Using pictures and marks There were five monkeys. Three ran away. How many monkeys were left? 5 – 3 = 2

6. Step 2 Progression in the use of number lines Firstly, children will count backwards in steps along a number track to ‘take away’.

7. Children will then use a numbered number line, counting back in steps of one, then ten, two and five. 10 – 5 = 5

8. Children will then begin to use a number line with regular interval markings and some or no numbers marked. 24 – 5 = 15 20 19

9. Children will then use an empty number line to count back by partitioning a number 35 – 7 = 28 30 35 - 5- 2 5 + 2 28

10. Step 3 Next children begin to find the difference by counting up from the smallest number

11. Step 4 Next they use a number line to ‘take-away’ and find the difference by counting back and up using the nearest multiple of 10 and adjusting. 36 – 19 = - 20 1 6 17 36 + 1 17

12. Step 5 Children then partition numbers to be subtracted mentally. (linked to counting back on a number line) 83 – 53 = 83 – 50 – 3 = 83 – 50 = 33 33 – 3 = 30

13. Partitioning then leads to the start of the expanded column method 52 - 87 35 50 2 - 80 7 30 5 87 - 35 = The numbers do not need to be adjusted.

14. Step 6 Expanded short column method The numbers are then adjusted when necessary. 40 + 3 - 20 + 7 10 + 6 3010+ 43 - 27 = 16 to subtract 7 units we need to exchange a ten for ten units This method enables children to see what happens to numbers in the short column method.

15. This is then extended to subtracting three digit numbers and decimals 563 – 141 with no adjustment 563 – 227 with adjustment from the tens to the units 561 – 272 with adjustment from the hundreds to the tens and then the units 503 – 278 dealing with zeros when adjusting, first in the units then the tens and hundreds

16. Step 7 Short column method The previous stages reinforce what happens to numbers when they are subtracted using more formal written methods. This is then extended to using larger numbers and decimals. 3 4 3 - 1 2 7 2 1 6 31