HEATHERSIDE JUNIOR SCHOOL

PROGRESSION IN SUBTRACTION

Parents’ Information

Evening

Progression towards a short column method for

subtraction• Establish mental methods, based on a knowledge of

number bonds and an understanding of place value.

• With more difficult calculations, approximate first, using mental methods.

• Show children how to set out written calculations using jottings and expanded layouts.

• Gradually refine their written recording into a more compact and efficient formal method.

• Extend to larger numbers and to decimals.

What does your child need to know?

Mental Skills

• recognise the size and position of numbers

• count back in steps of different sizes

• know number facts for all numbers to 20

• subtract multiples of 10 from any number

• partition and recombine numbers

• bridge through multiples of 10

Key Vocabulary

• subtract

• take away

• minus

• count back / up

• less than

• fewer

• difference

Step 1Using everyday objects children

will:

• begin to count backwards in familiar contexts such as number rhymes or stories;

• count back in ones from any given number;

• begin to relate subtraction to ‘ taking away ’;

• find one less than a number;

• count back in larger steps, (tens, then twos and fives).

I cansubtrac

t 5 – 1

= 4

Using pictures and marks

There were five monkeys. Three ran away.

How many monkeys were left?

5 – 3 =2

Step 2

Progression in the use of number lines

Firstly, children will count backwards in steps along a number track to ‘take

away’.

Children will then use a numbered number

line, counting back in steps of one, then ten, two and five.

10 – 5 = 5

Children will then begin to use a number line with regular interval

markings and some or no numbers marked.

24 – 5 =

15 20

19

Children will then use an empty number line

to count back by partitioning a number

35 – 7 =

28 30 35

- 5- 2

5 + 2

28

Step 3

Next children begin to find the difference by counting up from the smallest number

Step 4Next they use a number line to ‘take-away’ and

find the difference by counting back and up using

the nearest multiple of 10 and adjusting.

36 – 19 =

- 20

16 17 36 + 1

17

Step 5

Children then partition numbers to be subtracted mentally.

(linked to counting back on a number line)

83 – 53 = 83 – 50 – 3 =

83 – 50 = 33

33 – 3 = 30

Partitioning then leads to the start of the expanded column method

5 2

-

8 7

3 5

50 2

-

80 7

30 5

87 - 35 =

The numbers do not need to be adjusted.

Step 6

Expanded short column method

The numbers are then adjusted when necessary.

40 + 3- 20 + 7 10 + 6

30 10+

43 - 27 = 16

to subtract 7 units we need to exchange

a ten for ten units

This method enables children to see what happens to numbers in the short column

method.

This is then extended to

subtracting three digit numbers and decimals

563 – 141 with no adjustment

563 – 227 with adjustment from the tens to the units

561 – 272 with adjustment from the hundreds to the tens and then

the units

503 – 278 dealing with zeros when adjusting, first in the

units then the tens and hundreds

Step 7Short column method

The previous stages reinforce what happens to numbers when they are subtracted using more

formal written methods.

This is then extended to usinglarger numbers and decimals.

3 4 3- 1 2 7 2 1 6

3 1