Frances Olive Anderson Primary School Subtraction Calculation Policy
Year 1
Read, write and
interpret
mathematical
statements
involving
subtraction (-)
and equals
(=) signs
Given a number, identify one less
Progress from objects/ Numicon to bead string to number track to number line.
Count back on
ones from any
given number
Vocabulary:
Number bonds,
number line
Inverse
Half, halve
Equals, is the same as
(including equals sign)
Difference between
Subtract, take away,
minus
How many fewer
is…than..?, how much
less is..?
Number
Zero, one, two, three
to twenty, and beyond
None
Count
(on/up/to/from/down
)
Before, after
Progression:
Given a
number,
identify one
less
Count back in ones from any given number
Children need to be able to confidently count back from any given number. Counting
practice needed. Use mental oral starters.
Read, write
and interpret
mathematical
statements
involving
subtraction (-)
and the equals
(=) sign
-concrete
objects
-number track
-marked
number line
-empty number
line (only if
children are
secure)
Counting on to
find the
diiference.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
More, less, many, few,
fewer, least, fewest,
smallest, greater,
lesser
Equal to, the same as
Odd, even
Pair
Units, ones, tens
One less, two less/
three less/ Ten less
Digit
Numeral
Figure(s)
Value
Between, halfway
between
Above, below
Read, write and interpret mathematical statements involving subtraction (-) and the
equals (=) sign
Make sure that children understand that subtraction cannot be done in any order.
Subtract onedigit and twodigit numbers
within 20,
including zero
Revision from foundation stage:
Solve missing
number
problems eg
20 = 15
Initially use the number track to count back for subtraction
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Progress onto marked number line:
Children must be confident using a marked number line before moving onto an
empty number line (see year two guidance)
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Counting onto find the difference (complementary addition).
The use of models is extremely important. This should only be used for small differences.
Count up from the smallest number to find the difference. Use resources such as
Numicon, cubes, bead strings, number tracks and number lines.
Solve missing number problems eg 20 -
= 15
Year 2
Subtract any single digit number to or from a multiple of 10.
Subtract numbers
using concrete
objects, pictorial
representations,
and
mentally,
including:
A two digit
number and ones
Progression:
Subtract any
single digit
number to or
from a multiple
of 10 (80 – 7).
Subtract a
single-digit
number to or
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Frances Olive Anderson Primary School Subtraction Calculation Policy
A two digit
number and tens
Two two-digit
numbers
Subtract a single-digit number from a two-digit number, including crossing the tens
boundary
Marked number line
Vocabulary:
Number bonds,
number line
Inverse
Half, halve
Equals, is the same as
(including equals sign)
Difference between
Subtract, take away,
minus, find the
difference,
How many fewer
is…than..?, how much
less is..? Hundred less,
counting back,
Number
Zero, one, two, three
to twenty, and beyond
None
Count
(on/up/to/from/down
)
Before, after
More, less, many, few,
fewer, least, fewest,
from a twodigit number,
including
crossing the
tens boundary
(57 – 3
progressing to
52 – 7) –
marked
number line
progressing to
empty number
line.
Subtract a
multiple of 10
from any 2digit number
(27 + 60, 72 –
50)
Progressing to counting back using an empty number line (within 100) in ones.
Subtract two 2digit numbers
(68 – 35)
Counting on to
find
differences.
Further
develop with
subtraction
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Frances Olive Anderson Primary School Subtraction Calculation Policy
smallest, greater,
lesser
Equal to, the same as
Odd, even
Pair
Units, ones, tens
One less, two less/
three less/ Ten less
Digit
Numeral
Figure(s)
Value
Between, halfway
between
Above, below
Subtract a multiple of 10 from any 2-digit number
that bridges
100.
Subtract two 2-digit numbers
Subtraction using partitioning on an empty number line (used marked number line initially
if children need to):
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Encourage children to begin to use more efficient jumps:
Counting on to find differences – children may be more successful at this than
taking away on the number line.
Consolidate complementary addition by counting on from the smallest number to the
largest (small differences).
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Frances Olive Anderson Primary School Subtraction Calculation Policy
If children are confident, further develop this method
Further develop subtraction with numbers that bridge 100
Year 3
Subtract
numbers with up to
three digits, using
formal written
methods
of columnar
subtraction
Vocabulary:
Expanded written
method, partition,
Ensure children are confident in previous year’s guidance before moving on.
Develop the use of the empty number line
Bridging 100
Progression:
Develop the
use of the
empty number
line
-bridging 100
-making more
efficient jumps
-extend onto
larger numbers
by counting
back
-find the
difference by
counting on.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Column subtraction,
Number bonds,
number line
Inverse
Half, halve
Equals, is the same as
(including equals sign)
Difference between
Subtract, take away,
minus, find the
difference,
How many fewer
is…than..?, how much
less is..? Hundred less,
counting back,
Number
Zero, one, two, three
to twenty, and beyond
None, efficient jumps,
Count
(on/up/to/from/down
)
Before, after
More, less, many, few,
fewer, least, fewest,
smallest, greater,
lesser
Equal to, the same as
Odd, even
Pair, Units, ones, tens
One less, two less/
three less/ Ten less
Digit
Making more efficient jumps
-Expanded
written method
leading to
formal written
method – two
digits (no
decomposition
)
Extend onto larger numbers by counting back
Counting on to find the difference
-Expanded
written method
leading to
formal written
method – two
digits (with
decomposition
)
-Expanded
written method
– numbers
over 100.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Numeral
Figure(s)
Value
Between, halfway
between
Above, below,
exchange,
decomposition,
Expanded written method leading to formal written method – 2 digit numbers (no
decomposition)
Introduce the expanded written method showing the children the calculation written
horizontally and then laid out in columns vertically. Use two-digit numbers when initially
introducing this method.
This will lead to the formal written method:
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Expanded written method where exchange/ decomposition is required.
Use dienes to consolidate children’s understanding of this.
Only move onto the formal written method when children can confidently use the
expanded column method without error.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Formal written method using numbers over 100.
Only if children are confident.
It may be necessary to return to the expanded written method first.
If at any time the children are making significant errors, return to the previous stage
in calculation.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Year 4
Subtract
numbers with up
to 4
digits using the
formal
written methods
of
columnar
addition and
subtraction
where
appropriate
Continue to use empty number lines to subtract three and four-digit numbers.
Revisit the expanded column method first.
Consider using
‘and’ instead of + if
this confuses the
children.
Extend to the formal method, including decomposition.
Revisit
expanded
written
method.
Extend onto
formal written
method,
including
decomposition.
Vocabulary:
Expanded written
method, partition,
Column subtraction,
Number bonds,
number line
Inverse
Half, halve
Equals, is the same as
(including equals sign)
Difference between
Subtract, take away,
minus, find the
difference,
How many fewer
is…than..?, how much
less is..? Hundred less,
Progression:
Continue to
use the empty
number line to
subtract three
and four-digit
numbers.
Subtracting 3-digit numbers from 3 digit numbers.
Subtracting 3digit from 3digit numbers
– expanded
method
leading to
formal written
method.
Extend onto 4digit numbers
and decimal
numbers.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
counting back,
Number
Zero, one, two, three
to twenty, and beyond
None, efficient jumps,
Count
(on/up/to/from/down
)
Before, after
More, less, many, few,
fewer, least, fewest,
smallest, greater,
lesser
Equal to, the same as
Odd, even
Pair, Units, ones, tens
One less, two less/
three less/ Ten less
Digit
Numeral
Figure(s)
Value
Between, halfway
between
Above, below,
exchange,
decomposition,
decimial numbers,
Extend onto 4-digit numbers and decimal numbers.
Only if the children are confident.
Use a number line where appropriate with money.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Year 5
Subtract whole
numbers with
more than 4
digits, including
using
formal written
method
(columnar
subtraction)
Continue to use empty number lines with larger numbers and decimals
Consider appropriate numbers i.e. when finding change it may be easier to use the
number line.
Develop the formal written method for subtraction with three or four-digit numbers
Return to the expanded method if necessary (use year 4 guidance).
Vocabulary:
Expanded written
method, partition,
Column subtraction,
Number bonds,
number line
Inverse
Half, halve
Equals, is the same as
(including equals sign)
Difference between
Subtract, take away,
minus, find the
difference,
How many fewer
is…than..?, how much
less is..? Hundred less,
counting back,
Number
Zero, one, two, three
to twenty, and beyond
This leads to the formal written method.
Take care. There is potential for error in this example and children must have a secure
understanding of place value.
Progression:
Continue to
use empty
number lines
with larger
numbers and
decimals as
appropriate.
Develop
formal written
method for
subtraction
with three or
four digit
numbers.
(discuss
where the
number line
might be
more
appropriate)
Extend onto
larger
numbers,
including
decimals.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
None, efficient jumps,
Count
(on/up/to/from/down
)
Before, after
More, less, many, few,
fewer, least, fewest,
smallest, greater,
lesser
Equal to, the same as
Odd, even
Pair, Units, ones, tens
One less, two less/
three less/ Ten less
Digit
Numeral
Figure(s)
Value
Between, halfway
between
Above, below,
exchange,
decomposition,
decimial numbers,
Ensure that discussions are had about the efficiency of the method – would an
empty number line be a more efficient method with these numbers?
Extend onto larger numbers, including decimals.
Only if the children are confident.
Introduce subtraction of decimals, initially in the context of money and measures
Ensure that the decimal points line up.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
Year 6
Vocabulary:
Expanded written
method, partition,
Column subtraction,
Number bonds,
number line
Inverse
Half, halve
Equals, is the same as
(including equals sign)
Difference between
Subtract, take away,
minus, find the
difference,
How many fewer
is…than..?, how much
less is..? Hundred less,
counting back,
Number
Zero, one, two, three
to twenty, and beyond
None, efficient jumps,
Count
(on/up/to/from/down
)
Before, after
More, less, many, few,
fewer, least, fewest,
No objectives have been included in the programmes of study explicitly related to written
methods for subtraction in Y6. However, there is an expectation that children will continue
to practice and use the formal written method for larger numbers and decimals and use
these methods when solving problems, when appropriate (see previous years’ guidance
for methods).
Our aim is that by the end of Y6 children use mental methods (with jottings) when
appropriate, but for calculations that they cannot do in their heads, they use an
efficient formal written method accurately and with confidence.
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Frances Olive Anderson Primary School Subtraction Calculation Policy
smallest, greater,
lesser
Equal to, the same as
Odd, even
Pair, Units, ones, tens
One less, two less/
three less/ Ten less
Digit
Numeral
Figure(s)
Value
Between, halfway
between
Above, below,
exchange,
decomposition,
decimial numbers,
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