Addition and Subtraction

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

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

7. Addition 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) pictures 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) symbols

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

9. (+ 30) (+ 3) (+ 2) 47 77 80 82 35 + 47 = 82 35 + 47 = 47 + 30 + 5 = 77 + (3 + 2) = 82

10. Column addition 374 374 + 248 + 248 12 622 110 500 622 1 1 Extend to: 1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km

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? Subtraction (Take away) Drawing a picture helps children to visualise the problem (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? Using dots or tally marks is quicker than drawing a detailed picture (Take away) (Find the difference)

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

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

14. Number lines - taking away 74 – 26 = 48 − 20 − 4 − 2 48 50 54 74

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

16. 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. 14 20 21 34 39 45 50

17. 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 Subtraction by decomposition 5 1