1. Addition and Subtraction Calculating efficiently and accurately [KS1]

2. Objectives To explore the knowledge, skills and understanding required for children to add, subtract, multiply and divide efficiently and accurately To explore the progression in recording and (some of) the teaching approaches used

3. The Four Rules Understanding Mental calculations Rapid recall Efficient written methods Models, images & concrete materials Stories / rhymes Problem solving and role play Use of ICT

4. Progression for addition and subtraction Counting One more / less Addition as combining two groups, then counting on Subtraction as take away or difference (eg how many more is … than …?) Ten more/less Recall of addition/subtraction facts to 10, 20 and beyond Understand that subtraction and addition are inverses

5. Counting and estimation There are 5 principles of counting: 1. The stable order principle - understanding that the number names must be used in that particular order when counting 2. The one-to-one principle - understanding and ensuring that the next item in a count corresponds to the next number 3. The cardinal principle - knowing that the final number represents the size of the set 4. The abstraction principle - knowing that counting can be applied to any collection, real or imagined 5. The order irrelevance principle - knowing that the order in which the items are counted is not relevant to the total value

6. 9465483071 2836569732 1224518219 7763445328 6096751743

7. 2 + 3 = I buy 2 cakes and my friend buys 3 cakes. How many cakes did we buy altogether? (Children could draw a picture to help them work out the answer) 8 + 5 = 8 people are on the bus. 5 more get on at the next stop. How many people are on the bus now? (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Addition pictures symbols

8. Counting on – jumps of 1 (modelled using bead strings) 18 + 5 = 23 18 19 20 21 22 23 24 +1 +1 +1 +1 +1

9. 47 77 80 82 (+ 2) (+ 3) (+ 30) 35 + 47 = 47 + 30 + 5 = 77 + (3 + 2) = 82 35 + 47 = 82 No number line

10. 374 + 248 Addition by partitioning 70 + 40 = 110 4 + 8 = 12 300 + 200 = 500 622

11. 1 Column addition Extend to: 1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km 1 + 248 374 622

12. 31142016 246525 30291836 117131 14 20 21 34 39 45 50 Three in a row Choose two numbers from the row of numbers above the grid. Find the difference between these numbers. If the answer is on the grid, cover that number with a counter.

13. 5 – 2 = I have five cakes. I eat two of them. How many do I have left? A teddy bear costs £5 and a doll costs £2. How much more does the bear cost? (Take away) (Find the difference) 13 – 5 = Mum baked 13 biscuits. I ate 5. How many were left? Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have? Drawing a picture helps children to visualise the problem Using dots or tally marks is quicker than drawing a detailed picture (Take away) (Find the difference) Subtraction

14. Taking away – jumps of 1 (modelled using bead strings) 13 – 5 = 8 8 9 10 11 12 13 -1 -1 -1 -1 -1

15. Counting on – jumps of 1 (modelled using bead strings) 11 – 8 = 3 0 1 2 3 4 5 6 7 8 9 10 11 +1 +1 +1

16. 74 4850 54 − 2 − 4 − 20 Number lines - taking away 74 – 26 = 48

17. Number lines - counting on 74 – 26 = 48 0 26 30 70 74 + 4 + 40

18. Subtraction by partitioning 754 - 186 754 – 100 = 654 654 – 80 = 574 574 – 6 = 568

19. Subtraction by decomposition