Progression in addition and subtraction

1. Progression in addition and subtraction

2. Readiness for written calculations (+/−) • In order to prepare the children for written calculations, we do lots of work on mental strategies and number facts. This includes: • Knowledge of their number bonds to 10 and 20 (+and-) • A sound understand of place value and partitioning numbers into H, T and U • Being able to add at least three single-digit numbers mentally • Being able to add and subtract any pair of two-digit numbers mentally Children also need to be able to explain their mental strategies orally and record them using informal jottings

3. Methods of Addition +10 +2 34 36 24 +40 +7 76 116 123 • Children need to know their number bonds to 10 and 20. • Next step is to use number lines e.g 24 + 12 24 + 12 = 36 • Then progress onto recording with partitioning: • 76 + 47 = 76 + 40 + 7 • = 116 + 7 • = 123

4. Methods of Addition (continued…) 47 +76 123 1 47 +76 13 (7+6) 110(40+70) 123 • + 70 = 110 • 7 + 6 = 13 • 123 166 +129 295 1 • Then children move on to vertical addition, through partitioning using expanded working, before moving on to the standard short method. • 47 + 76 = (40 + 70) + (7 + 6) or 40 + 7 70 + 6 110 + 13 • An example using larger numbers e.g. 166 + 129 166 + 129 15 (9+6) 80 (60 + 20) 200 (100 + 100) 295

5. Methods of Subtraction +10 +8 +1 29 30 40 48 • Children will then continue this method, but without the help of the number line and using larger numbers e.g. 783-356 • 356 360 = + 4 • 360 400 = + 40 • 400 700 = + 300 • 700 783 = + 83 • 427 • Again, children need to know their number bonds to 10 and 20! • Next step is to use number lines to COUNT UP eg 48 - 29

6. Methods of Subtraction……..(continued) • The next step is to begin recording vertically, using partitioning e.g. 81 – 57 = • 81 = 80 + 1 = 70 + 11 • - 57 = 50 + 7 = 50 + 7 • 20 + 4 = 24 • This then leads to the standard written method and will involve larger numbers . • 81 754 • - 57 - 236 • 24 518 7 4 1

7. Readiness for written calculations (x/÷) • As with + and –, in order to prepare the children for formal written calculations using x and ÷, we do lots of work on mental strategies. This includes: • A SOUND knowledge of their times tables and the corresponding division facts. • A thorough understanding of place value • Multiplying 2 and 3 digit numbers by 10 and 100 • Doubling and halving 2 digit numbers mentally • An ability to use multiplication facts they know to derive mentally other multiplication facts that they do not know e.g. 3 x 4 = 12, so 30 x 4 = 120 • Understanding that multiplication and division are inverses Again, children need to be able to explain their mental strategies orally and record them using informal jottings • Children also need to be able to explain their mental strategies orally and record them using informal jottings

8. Multiplication and Division “At whatever stage in their learning, and whatever method is being used, it must still be underpinned by a secure and appropriate knowledge of number facts, along with those mental skills that are needed to carry out the process and judge if it was successful.”

9. Why teach them different methods and not just one? • The aim is that by the end of Key Stage 2, the great majority of children should be able to use an efficient written method for each operation with confidence and understanding. • At Warden Hill Primary School, we want our children to know that they have such a reliable, written method to which they can turn when the need arises.

10. Multiplication 15 x 9=??? How many different ways can we work this out? When faced with a calculation, no matter how large or how difficult the numbers may appear to be, pupils should ask themselves: • ‘Can I do this in my head?’ then • ‘Do I know the approximate size of the answer?’ and more importantly, • ‘What do I already know that will help me solve this?’

11. 15 x 9=??? We can look at approximation. 15 x 9 is nearly 15 x 10 which is 150. In turn, we can use this information to solve the answer… 15 x 9 is the same as 15 x 10 (150)and then subtract 1 lot of 15.(150-15=135)

12. 15 x 9=??? We can use partitioning. 15 10 5 X 9 90 + 45 = 135

13. The Grid Method Links need to be made to the expanded short multiplication

14. Short Multiplication

15. Two-digit by two-digit multiplication Links need to be made to the expanded short multiplication

16. Division The main point to realise is that children’s mental methods are practised and secured alongside their learning and use of an efficient written method of division. Children also need to be able to: • Understand divison as repeated subtraction. • Understand that divison is the inverse operation of multiplication. • Estimate how many times one number divides into another.

17. Subtracting groups of ‘5’ 72 ÷ 5 72 • 50 10 x 5 22 - 20 4 x 5 2 Answer 14 remainder 2

18. Chunking • The previous method is called chunking. It is based on subtracting chunks of the divisor. It is useful in reminding children about the link between division and repeated subtraction.

19. 196 ÷ 6

20. A greater understanding of multiples will allow this…

21. Multiplication and Division The Last Word… With both these operations, children who have a secure knowledge of multiplication facts and place value will be able to move on quickly to more efficient paper and pencil recordings.