1. Westfield Middle School Visual Calculation Policy

2. Choosing a method
Addition methods
Subtraction methods
Multiplication methods
Division methods
About this policy

3. Choosing a method Can I use a mental strategy?
Can drawings or objects help me?
Should I use a written method?

4. Use this technique when answering word problems

5. Addition
Sum
Total
Add
Plus
Count on
Altogether
More
Increase

6. Addition – Counting
Divisor =

7. 1. Addition – Counting on 0 1 2 3 4 5 6 7 8 9 10 6 + 3 = 9
Use numbered number lines to add, by counting on in ones.
Start with the larger number and count on.
+ 1
+ 1
+ 1
6 + 3 = 9

8. 2. Addition – Leaping Further
Use empty number lines and hundred squares to build confidence when adding 2 digit numbers.
+ 10
+ 6
= 79

9. 3 . Addition – Partitioning
= 39
= 39

10. 4. Addition – Expanded Column
T U
+ 2 3
1 7
1 0
3 0
4 0
H T U
7 3 9
1 0 0
2 0 0
3 0 9
Add the units first in preparation for the compact method

11. 5 . Addition – Compact Column
Move from expanded addition to the compact column method, adding units first, and ‘carrying’ numbers
underneath the calculation.
Th H T U
3 9 6
1 1
Remember this number is 500 not 5.
Start with the units
Carry any numbers underneath.

12. 6. Addition – Compact Column
Including decimals
The decimal point should be aligned in the same way as
the other place value columns, and must be in the same
column in the answer

13. Subtraction Take away Minus Count back Fewer Subtract Less
Difference between

14. Subtraction – Take away=
Divisor =

15. 1. Subtraction – Finding the difference
7 is 3 more than 4

16. 2. Subtraction – Counting back
Model subtraction using hundred squares, numbered number lines and practically.
7 – 3 = 4

17. 3. Subtraction – Leaping Back-1 -1 -1
-10
Partition the second number and subtract the tens first
47 – 23 = 24

18. 3. Subtraction – Counting On
Start at the smaller number and count on in tens first, then count on in units to find the rest of the difference +3
+10
Continue to reinforce counting on as a strategy for close together numbers and also for numbers that are nearly multiples of 10, 100, 1000 or £s
102 – 89 = 13

19. 4. Subtraction – Expanded column =
100
Once pupils are secure
with the understanding of‘
‘exchanging’, they can use the partitioned column method to subtract any 2 and 3-digit numbers. 1
Use vocabulary ‘steal’ or ‘take’ not ‘borrow’.
238 – 146 = 92

20. 5. Subtraction – Compact Column
Th H T U
Children who are still not secure with number facts and place value will need to remain on the partitioned column method until ready for the compact method. 6 1

21. 6 . Subtraction – Compact Column with decimals 9 1 3 1 1
Empty decimal places can be
filled with zero to show the
place value in each column.

22. Multiplication
Multiple
Groups of
Repeated addition
Multiply
Lots of
Product
Times

23. Spiders have 8 legs. How many legs do 3 spiders have altogether?
Multiplication - Repeated Addition
= 24
Spiders have 8 legs. How many legs do 3 spiders have altogether?

24. 1. Multiplication - Repeated Addition
There are 3 sweets in a bag and 3 bags of sweets. How many sweets altogether?

25. 2. Multiplication - Arrays
3 X 7 = 21 or 7 X 3 = 21

26. 3 .Multiplication – The Grid Method4
Make sure you do not add the 4 in the total
300
1200
Partition the number into the grid 20 80 7 28
1308

27. 4. Multiplication – Expanded Column Method
3 2 7
X 4
2 8
8 0
Short Multiplication

28. 5. Multiplication – The Grid Method
Long Multiplication 10 8 10
100 80
1 8 0 3 30 24
+ 5 4
2 3 4
18 X 13 = 234

29. 5. Multiplication – Expanded Column Method
2 6
X 1 4
2 4
8 0
6 0
Long Multiplication 1

30. 6. Multiplication – Decimals .
Include multiplying more complex numbers and decimals. x 8
Remember place value, make sure numbers are in the correct column. 1 7

31. Division Share Divide Quotient Remainder Halve Equal groups of Factor
Divisor

32. 1 . Division –Sharing
15 ÷ 3 = ÷ 5 = 3

33. Division - Arrays
2. Division - Arrays
12 ÷ 4 = ÷ 3 = 4

34. 3. Division – On a number line
This helps to see the link between division and grouping
12 ÷ 3 as ‘How many groups of 3 are in 12?’

35. 4 / 5. Division - Short Division
Remind children of correct place value, that 96 is equal to 90 and
6, but in short division, pose:
How many 3’s in 9? = 3 3 5
Start with one digit numbers without remainders

36. 5/6 . Division – Chunking 2 2 3 6 7 9 2 - 3 6 0 4 3 2 0 7 2 - 0 7 2
2 2
Circle the groups of 36 you have ‘chunked’ off the total.
3 6
0 0
3 6 x 10 = 3 6 0
3 6 x 2 = 7 2 3 1
Keep chunking until there is less than 36 left

37. Calculation Policy
This policy aims to clearly show strategies for calculating whilst meeting the expectations set out in the New Curriculum The policy is for use of all pupils, parents and staff in the Westfield community.
The strategies have been organised to show the progression from early calculation methods such as counting through to written methods involving decimals. The age expectations have been added to the calculations as a guide of where children should be working however decisions about when to progress should be based on the security of pupils understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new
content.
It is important that any type of calculation is given a real life context or problem solving approach to help build children's understanding of the purpose of calculation, and to help them recognise when to use certain operations and methods when faced with problems. This must be a priority within calculation lessons.
The Maths department will be offering Maths support for parents. Please contact the office for more information.

38. Westfield Middle School Visual Calculation Policy