Overview of Strategies and Methods KS1 – Subtraction
Year 1
NC Objectives
Year 2
NC Objectives
Through regular practice and rote learning, with access to number lines and number
squares, children are taught to count back in 1s and 10s to 100. This moves onto
children knowing 53 – 20 without counting back in 1s
Using number lines and number squares to reinforce, children should be able to
calculate 1 less than any number, or 10 less without counting back in ones.
e.g. 1 less than 74
e.g. 10 less than 82
Through regular practice, children are also taught to subtract multiples of 10
mentally
e.g. Know 53 – 20 as 53, 43, 33
To subtract 10, the spider goes up the square.
e.g. 76 – 20 as 76, 66, 56 or in one hop: 76 – 20 = 56
Using number facts
Using a range of concrete equipment including pegs, cubes and Numicon, children are
taught to use their number bonds to 10 to generate subtraction facts
Subtraction
e.g. 10 – 1 = 9, 10 – 2 = 8, 10 – 3 = 7
Using Intelligent Practice, children are taught to subtract using
patterns of known facts e.g. 7 – 3 = 4
so 27 – 3 = 24,
47 – 3 = 44 etc
Understanding
Using concrete resources, children are taught to
understand subtraction as take-away and as finding
the difference.
Taking away
Children use concrete apparatus, moving
onto a number square when ready, to
subtract two 2-digit numbers by counting
back in 10s, then in 1s
e.g. using diennes for 75 – 42
Children are taught to subtract near multiples
of 10 by subtracting ten and then adjusting
by one.
e.g. 74 – 21
e.g. 57 − 19
Using number facts
Children know pairs of numbers which make the numbers up to and including 12
and derive related subtraction facts
Once children are confident with subtraction using concrete resources, they progress to
pictorial representation including tens model, part/whole model and bar model.
e.g. 10 – 6 = 4, 8 – 3 = 5, 5 – 2 = 3
Finding the difference
Recording:
Children should be confident with using the – sign. Missing numbers need to be
placed in all possible places.
4-3=
7-=4
=4–3
7=-4
Children continue to use the bar
model to visualise finding the
difference. They use number lines to
calculate the difference between two
numbers that are close together, by
counting up from the smaller
number. e.g. 42 – 39
Overview of Strategies and Methods LKS2 – Subtraction
NC Objectives
Year 3
NC Objectives
Mental methods continue to be developed, supported by a range of concrete
resources, models and visual images. Children should be supported to make choices
about whether to use complementary addition or counting back, depending on the
numbers involved.
Children should:
Know pairs which total each number to 20
Video
-
Recall number bonds to 100
-
Subtract by bridging back through a 10 e.g. 42 – 5 = 42 – 2 (40) – 3 = 37
Subtraction
Taking away
Children are taught to:
-
use place value to subtract e.g. 348 - 300, 348 – 40, 348 – 8
-
take away multiples of 10, 100 and £1 e.g. 476 – 300 = 176,
-
partition numbers e.g. 68 – 42 as 60 – 40 and 8 – 2 and to count back in 100s,
Video
10s then 1s e.g. 763 – 121 as 763 – 100 (663) – 20 (643) – 1 = 642
-
Year 4
Mental methods
Children should know:
-
derived facts from number bonds to 10 and 100 e.g. 100 – 76 = 24
-
Number bonds to £1 and £10 e.g. £1·00 – 86p = 14, £10·00 – £3·40 = £6·60
Taking away
Children develop their use of place value and partitioning from Year 3, moving
onto numbers with 4 digits. Children are taught to take away multiples of 1000, 10p
and 0·1 e.g. 6723 – 3000,
Children are taught to subtract near multiples of 1000 or £1 e.g. 3522 – 1999
Counting up
Children continue to find a difference between two numbers by counting up from
the smaller to the larger e.g. 506 – 387, 4000 – 2693. They use counting up
subtraction to find change from £10, £20, £50 and £100 e.g. Buy a computer
game for £34·75 using £50
subtract near multiples of 10 and 100 e.g. 648 – 19, 86 – 39
Finding the difference / counting up
Children find a difference between two numbers by counting up from the smaller
to the larger e.g. 121 – 87. They use counting up subtraction to find change from
£1, £5 and £10
They use the bar model to support their problem solving skills when finding the
difference.
Written methods (progressing to 4-digits)
Children are introduced to the expanded column subtraction with no decomposition,
modelled with equipment. A number line and expanded column method may be
compared next to each other. If understanding of the expanded method is secure,
children can move on to the formal method of decomposition, which again can be
initially modelled with equipment and introduced alongside the expanded method. The
formal method should be seen as a more streamlined version of the expanded method,
not a new method.
Overview of Strategies and Methods UKS2 – Subtraction
Subtraction
NC Objectives
Year 5
NC Objectives
Year 6
Mental methods
Children continue to refine their mental subtraction, using increasingly difficult
Mental methods
numbers, including decimals, and supported by a range of models and images. The
numbers, including decimals, and supported by a range of models and images. The bar
bar model should continue to be used to help with problem solving.
model should continue to be used to help with problem solving.
Taking away
Children should:
Taking away
-
Use place value to subtract decimals e.g. 4·58 – 0·08, 6·26 – 0·2
-
Take away multiples of powers of 10 e.g. 15 672 – 300
-
Partition or count back to subtract decimals e.g. 5·72 – 2·01
-
Subtract near multiples of 10 000
Counting up
Children continue to use counting up for subtractions involving money, including
finding change e.g. £50 − £28·76
Children continue to refine their mental subtraction, using increasingly difficult
Children are taught to subtract near multiples of powers of 10 e.g. 360 078 – 99
998
Counting up
Children continue to use counting up for subtractions where the larger number
is a multiple or near multiple of 1000 or 10 000, when dealing with money e.g.
£100 – £78·56 and to subtract decimal numbers e.g. 13·1 – 2·3.
Written methods
Children refine their use of compact column subtraction for large numbers,
developing fluency, accuracy and conceptual understanding.
Written methods (progressing to more than 4-digits)
When understanding of the expanded method is secure, children move on to the
formal method of decomposition, which is initially modelled with equipment. Children
progress to calculating with decimals, including those with different numbers of
decimal places.
e.g. 34 685 – 16 458
Year 1:
Year 2:
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Year 3:
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Year 4:
Year 5:
Year 6:
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