1. St Paul’s Calculation Policy

2. Aim: To share the progression in the teaching of written calculation strategies

3. How did you learn maths? ‘Don’t ask, just copy what I am doing’
‘8+7=15 so write 5 carry 1’ (addition method)
‘We can’t do 6-8 so borrow 1 from the tens which makes 16-8=8’
‘Now write a zero’ (long multiplication method)
How successful was everyone in the class? How many were left behind?

4. Key Points
We aim for children to be using the standard written calculation methods by the end of year 6
We have a focus on securing a good understanding of number and mental calculation strategies before learning written methods
Our calculation policy ensures a consistent approach to the teaching and learning of calculation methods as children move up the school
We believe that children must use a method they understand, therefore different members of the class may be using different methods. We do not believe in ‘one size fits all.’

5. Fun with counting
For all children their calculation journey begins with counting – forwards, backwards, in groups, starting at different numbers
We also like learning by playing with things – counters, mini teddy bears, pegs, beads, unifix, pencils – anything close to hand! We give our children lots of hands on experience with equipment to help them become familiar with what each operation means before using ‘abstract’ written calculation methods.
Eg. Start with 7 counters then take three away:

6. Fun with counting
For all children their calculation journey begins with counting – forwards, backwards, in groups, starting at different numbers
We also like learning by playing with things – counters, mini teddy bears, pegs, beads, unifix, pencils – anything close to hand! We give our children lots of hands on experience with equipment to help them become familiar with what each operation means before using ‘abstract’ written calculation methods.
Eg. Start with 7 counters then take three away:

7. The next steps …
Children use equipment to help them explore number facts. These will them become ‘known facts’ :
Bonds to 10 eg. 7+3=10
Subtraction facts up to 10 eg. 7-3=4
Times tables
Division facts
These can then all be used to derive new facts eg =100

8. Addition Methods Partitioning and using jottings (stage 2) 34 + 63=
= = =97
= 97
Vertical partitioning – learning to start at the ones. =
= 425

9. Addition Methods
Standard written method with carried numbers (stage 3)

10. Subtraction Methods
Using Number lines to count backwards and forwards (stage 2 and 3)
eg. 97 – 15 =
eg. 84 – 56 =
As children become more confident they can use larger numbers and make fewer jumps on the number line. 82 97 82 87 -5
-10 28 +4
+20 +4 56 60 80 84

11. Subtraction Methods Expanded / Partitioning Method (stage 3)
Eg. 734 – 286 =
= 448
600 1 20 1
400 40 8

12. Subtraction Methods
Standard written method with carried numbers (stage 3 and 4)

13. Multiplication Methods
Understanding arrays
Grid method eg. 275 x 4 =
4 x 2 = 8
2 x 4 = 8
1100
800
280
+ 20
1100 1 x
200 70 5 4
800
280 20

14. Multiplication Methods
Short Multiplication (stage 5)
456 x
1368
1 1
Long Multiplication (stage 6)
158
X 67
 1106 (x7)
9480 (x 60)
10586 45 34

15. Division Methods Using a numberline Eg 30 ÷ 6 = 5 Eg. 61 ÷ 4 = 15 R130
15 R1
+40
10groups
+20
5groups R1 40 60 61

16. Division Methods
Short division (stage 5) only works when the divisor is a single digit, 11 or 12.
Quick recall of division facts is now really important!

17. Division Methods
Long division (stage 5 and 6) can be used when dividing by a 2-digit number
It requires a good understanding of division and subtraction
Before starting we write down the 15x table to help us:
1x15 = 15
2x15= 30
3x15 = 45
4x15 = 60
5x15 = 75
6x15 = 90
7x15 = 105
8x15 = 120
9x15 = 135
10x15 = 150

18. How can you help? Number facts
Partition numbers – this works from 2-digit numbers to decimals to huge numbers and supports your child’s understanding of number
Build up mental calculation strategies – these are crucial if your child is to be successful with written calculation
Check your child understands what each operation means and the language associated with it – particularly for subtraction and division
Encouragement – it is ok to be stuck, that is part of the learning process.

19. And finally …