1. Aim To explain some of the strategies that we use to teach +, -, x and ÷.

2. Concrete/practical/objects Pictorial Abstract (‘writing it down’)

3. We always try to relate calculations to real-life and to solving problems Mental as well as pencil-and-paper methods Develop rapid, confident recall of number facts and Times Tables

4. Addition Add Add Plus Plus More than More than Count on Count on

5. Laying the foundations…… Number lines Practical equipment Multilink cubes Real life contexts Number bonds Patterns

6. 12345678910111213 6+5= Use of a 100 square 34+14 = Use of a number line

7. Partitioning…….. Place value Partitioning Recombining

8. Children use their knowledge to move towards the ‘standard’ written method: Continue to use partitioning 58 + 43 50 + 8 40 + 3 90 + 11 = 101

9. Column addition…. The final step, when the children have a sound grasp of place value & of the whole process… 364 + 54 418 1

10. Subtraction

11. 3-2= Taking away practically.

12. Use of a number line/100 square 12-6=6 12345678910111213

13. Written methods for Subtraction Partitioning Subtraction can be recorded using partitioning to write equivalent calculations that are easier to carry out mentally. For 74 - 28 this involves partitioning the 28 into 20 and 8, then subtracting 20 and 8 in turn. 74 – 28 is the same as 74 – 20 – 8 74 – 20 = 54 54 – 8 = 46

14. Written methods for Subtraction Stage 4: Column method The expanded method is eventually reduced to:

15. Multiplication

16. Multiplication- repeated addition xx x 3x5= (3 groups of 5) xx x xx x 5 +5 +5= 15

17. Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method. 3 x 5 5 x 3

18. Grid Method Using partitioning, we can look at 8 x 13 = 104 as 8 x 10 plus 8x3: 80 + 24 = 104

19. Standard Written Method

20. Division ÷

21. Written methods for Division Initially division is introduced as ‘sharing’ using real objects or pictures. Share 10 apples equally between 2 children which eventually becomes 10 ÷ 2 = 5

22. Remainders:

23. Written Methods for Division ‘Short’ division

24. Written methods for Division Long division for HTU ÷ TU The next step is to tackle HTU ÷ TU. This is the 'long division' method. The 20, or 2 tens, and the 3 ones forming the answer are recorded above the line, as in the second version.