Recording Subtraction Calculations

A guide to the progression and written methods for subtraction used at:

•Verwood CE VA First School

•Trinity First School

•Hillside First School

•Emmanuel CE VA Middle School

Here’s some key vocabulary that can be used when talking about subtraction with your child

count back

takeaway difference

subtract less than

minus

Subtraction vocabulary+

number sentence/calculation

Making the link…

• It is really important that we all help children to make the link between addition and subtraction.

• You can help them with this understanding in many different ways Eg, If I have 7 objects and add 3 more I make 10. What number do you think I would have left if I took the 3 away?

Progression of written methods

Once your child has grasped basic counting back of objects and ordering of numbers, using practical equipment, they will move onto

taking away using a basic number line as a more formal way of recording

The basic number line is one where all the numbers are marked on the line

e.g calculate 8 - 3 = ?

0 1 2 3 4 5 6 7 8 9 10 11 12

We can see from this that the answer = 5.Using this method your child has to mark all the numbers

on the number line.

-1 -1 -1

15-7=

So we start at the biggest number…15 (at the other end of the number line)

And count down 7 places

The number we end on is our answer!

8

-1 -1 -1 -1 -1 -1 -1

9 10 11 12 13 14 15

Once your child has grasped this concept the next step is to use a blank number line

23-12=

So we start at the biggest number…23

And make one jump back of 10

Then takeaway the smaller jumps

23

-10-1-1

1312

Once your child has is confident subtracting on a blank number line using jumps of 1, they may progress to

counting back in bigger jumps by partitioning the smaller number

11

67-23=

So we start at the biggest number…67

And make two jumps of 10

Then subtract our smaller jumps

44

-1 -1 -1

45 46 47

-10 -10

57 67

44

Have a go….

• Have a look at the four number lines which shows common errors a child could make.

• Use pink and green to mark them. Spot the one that’s right and underline it in pink.

• On the three that are wrong can you spot the place where the person has gone wrong and underline that part in green?

• Why do you think they have made these errors? Is it a misconception with place value? Counting back? Partitioning? Understanding?

Counting on as a strategy…

• 65 – 49 = 16

So we start at the smallest number….49

And count up to the biggest number 65

Then add our jumps together to get the answer

49

+1

61 6259

+10

60 63 64 65

+1+1 +1 +1 +1

28 - 9 =

So we start at the biggest number…28

And make one jump back of 10

Then readjust by adding 1

-10

18

+1

19 28

Sometimes you may need to subtract a near multiple of 10 (such as 9 or 19) The quickest way

to do this is by subtracting a multiple of 10 and readjusting.

19

99 – 43 =

So we start at the biggest number…99

And make one jump back of 40

Then make one jump of 3

-40

56

-3

The next step in using a number line to add is to partition the numbers according to their place

value

59 99

56

The next step is partitioning when subtracting numbers

Partitioning involves breaking numbers down according to the ‘value’ of each individual digit.

e.g calculate 25 - 12

10 2

25 – 10 = 15

15 – 2 = 13

So, 25 – 12 = 13

Eventually the children will progress to Column Subtraction and the first step in doing this is to partition in vertical

columns.

e.g calculate 77 - 46

77 – 46 =

70 + 7

- 40 + 6

+ 130 = 31

Column Subtraction is where the numbers are placed vertically according to their place value.

You ALWAYS start subtracting the numbers in the far right hand column FIRST (units in this case) and then work across to the left.

e.g calculate 68 - 34

T U

6 8

- 3 4

4

Take away the 8 from the 4 first which gives you an answer

of 4

Then subtract the 3 from the 6

(remembering these are tens!)

Answer = 34

3

We would always start this where the top units number is bigger than the bottom units number, so that the children become familiar with the

process. We would model this using cubes

68-34=

Sometimes when doing column subtraction, if the tops units number is smaller than the bottom units number, you have

to exchange a 10.

At Verwood First we call this visiting the swap shop!

Remember if the top units is a smaller number than the bottom units you need to visit the swap

shop

At the Swap Shop you can swap one ten for ten units

How can we record this?

63-38=

-6 3

3 8

T U 5

1

Try this one:

42-28=

4 2

2 8

T U

-

31

41