1. Addition and Subtraction Calculating efficiently and accurately

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

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 in knowledge and understanding for + / - 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

10. 374 374 + 248 + 248 12 622 110 500 622 1 Column addition Extend to: 1247 + 367£2.36 + £6.483.5 + 4.8 7.48 + 2.612.5 km + 6.08 km 1

11. 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

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

13. 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

14. 74 4850 54 − 2 − 4 − 20 taking away Number lines - taking away 74 – 26 = 48

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

16. 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.

17. Subtraction by decomposition No breaking down needed: 563 − 241 500 + 60 + 3 −200 + 40 + 1 300 + 20 + 2 Leading to: 563 −241 322 Using red alerts: 563 − 248 500 and 60 and 3 −200 and 40 and 8 Re-written as: 500 and 50 and 13 −200 and 40 and 8 300 and 10 and 5 Leading to:5 6 3 −2 4 8 3 1 5 5 1