Progression in Calculations

1. Progression in Calculations

2. Welcome to Year 4 INSPIRE Workshop

3. Which of these words would you useto describe mathematics? fun • Maths is …….. uncomfortable frightening scary boring easy important hard exciting useful challenging

4. Maths is like RICE PUDDING …you love it or hate it, …depending on how it was served up to you at school!

5. We all use Maths all day everyday!

6. Understanding and Using Calculations For all calculations, children need to: Understand the = sign as is the same as, as well asmakes. See calculations where the equals sign is in different positions and what these number sentences represent, e.g. 3 + 2 = 5 and 5 = 7 - 2. Decide on the most appropriate method i.e. mental, mental with jottings, written method or calculator Approximate before calculating and check whether their answer is reasonable.

7. Addition Children need to understand the concept of addition, that it is: Combining two or more groups to give a total or sum Increasing an amount They also need to understand and work with certain principles: Inverse of subtraction Commutative i.e. 5 + 3 = 3 + 5 Associative i.e. 5 + 3 + 7 = 5 + (3 + 7)

8. Adding Two Digit Numbers Children can use base 10 equipment to support their addition strategies by basing them on counting, e.g. 34 + 29 Children need to be able to count on in 1s and 10s from any number and be confident when crossing tens boundaries.

9. Adding Three Digit Numbers Children can support their own calculations by using jottings, e.g. 122 + 217

10. T U 6 7 Beginning Column Addition 2 4 + 1 1 8 0 9 1

11. U H T Continuing Column Addition e.g. 164 + 257

12. HT U 1 6 4 Efficient Column Addition 2 7 5 + 4 2 1 1 1

13. Subtraction Children need to understand the concept of subtraction, that it is: Removal of an amount from a larger group (take away) Comparison of two amounts (difference) They also need to understand and work with certain principles: Inverse of addition Not commutative i.e. 5 - 3 ≠ 3 - 5 Not associative i.e. (9 – 3) – 2 ≠ 9 – (3-2)

14. Taking Away Two Digit Numbers 31 Children can support their own calculations by using jottings, e.g. 54 - 23

15. Taking Away Two Digit Numbers (Exchange) 26 Children can use base 10 equipment to support their subtraction strategies by basing them on counting, e.g. 54 - 28

16. Taking Away Two Digit Numbers (Exchange) 26 Children can support their own calculations by using jottings, e.g. 54 - 28

17. Continuing Column Subtraction U H T 200 10 1 1 300 20 1 e.g. 321 - 157 - 100 50 7 100 60 4 = 164

18. HT U 1 2 1 1 3 2 1 Efficient Decomposition 1 7 5 - 6 4 1

19. Moving on to Number lines 52 61 61 - 52

20. Consolidating Number Lines

21. Multiplication Children need to understand the concept of multiplication, that it is: Repeated addition Can be represented as an array They also need to understand and work with certain principles: Inverse of division Is commutative i.e. 3 x 5 = 5 x 3 Is associative i.e. 2 x (3 x 5) = (2 x 3) x 5

22. Grid Method 10 6 42 70 70 42 112 7 +

23. Grid Method 600 100 90 15 805 + Children have to develop their understanding of related facts. e.g. 23 x 35

24. Division Children need to understand the concept of division, that it is: Repeated subtraction They also need to understand and work with certain principles: Inverse of multiplication Is not commutative i.e. 15 ÷3 ≠ 3 ÷ 15 Is not associative i.e. 30 ÷ (5 ÷ 2) ≠ (30 ÷ 5) ÷ 2

25. 48 ÷ 4 = 12 48 -4 44 -4 40 -4 36 -4 32 -4 10 groups 28 -4 24 -4 20 -4 16 -4 12 -4 8 -4 2 groups 4 -4 0

26. Division by Chunking Recall of multiplication tables helps make this method more efficient, e.g. 72 ÷ 3.

27. Division by Chunking e.g. 196 ÷ 6

28. Key Messages For written calculations it is essential that there is a progression which culminates in one method. The individual steps within the progression are important in scaffolding children’s understanding and should not be rushed through. Practical equipment, models and images are crucial in supporting children’s understanding.