Broadwater Down Primary School
Calculations Policy
Division
Reception
Mental calculations
Working at a practical
level to gain experience
of sharing and to
become familiar with
appropriate language.
‘Can you share the 6
apples between 2
children?’
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Recall and use doubles
of all numbers to 10 and
corresponding halves.
Recall and use
multiplication and
division facts for the 2,
5 and 10 multiplication
tables, including
recognising odd and
even numbers
Recall and use
multiplication and
division facts for the 3,
4 and 8 multiplication
tables.
Recall multiplication and
division facts for
multiplication tables up
to 12 × 12
Continue to recall
multiplication and
division facts for
multiplication tables up
to 12 × 12.
Continue to recall
multiplication and
division facts for
multiplication tables up
to 12 × 12.
Use partitioning to
double or halve
numbers , including
decimals to two decimal
places.
Use partitioning to
double or halve any
number.
Practical work involving
sharing into and sharing
by.
Derive and use halves
of two digit numbers to
50.
Understand division as
sharing and grouping.
Know that division
calculations can have a
remainder.
Derive and use doubles
of all numbers to 100
and the corresponding
halves.
Write and calculate
mathematical
statements for division
using the multiplication
tables that they know,
including for two-digit
numbers times one-digit
numbers, using mental
methods .
Understand division is
the inverse of
multiplication.
Understand how
multiplication and
division can be shown
using an array.
Understand division as
sharing and grouping.
Use partitioning to
double or halve
numbers, including
decimals to one decimal
place.
Use place value, known
and derived facts to
multiply and divide
mentally, including:
dividing by 1.
Divide numbers
mentally drawing upon
known facts.
Divide whole numbers
and those involving
decimals by 10, 100 and
1000.
Perform mental
calculations, including
with mixed operations
and large numbers.
Associate a fraction
with division and
calculate decimal
fraction equivalents
(e.g. 0.375) for a simple
fraction (e.g. 3/8).
Divide by 0.1 and 0.01.
Written methods
Can you share the 12
bananas between 3
children?
Calculate mathematical
statements for division
within the multiplication
tables and write them
using the, division (÷)
and equals (=) signs.
Repeated subtraction
using a number line to
support the subtraction
of each number.
Write and calculate
mathematical
statements for division
using the multiplication
tables that they know,
including for two-digit
numbers by a one-digit
numbers, using mental
and progressing to
formal written methods.
Divide numbers up to
three digits by a onedigit number
progressing to formal
written layout.
Informal recording,
Divide numbers up to 4
digits by a one-digit
number using the
formal written method
of short division and
interpret remainders
appropriately for the
context.
Continue to divide
numbers up to 4-digits
by a two-digit whole
number using the
formal written method
of short division.
Divide numbers up to 4
digits by a two-digit
whole number using
chunking if needed.
e.g.
a)
Children also learn how
to use grouping to find
the answers to division
questions.
12 jumps of 4 with 2
left over,
50 ÷ 4 = 12 r 2
Chunking –
b) Carry the remainder
in front of the next
digit, then how many 4s
in 18?
4 remainder 2
c) Carry the remainder
in front of the next
digit, then how many 4s
in 24?
6
There are 3 groups of 3
in 9.
d) How many
4s in 584?
12 ÷ 4
How many 4s in 12?
Moving to:
12 ÷ 4 = is the same as
how many groups of 4
are there in 12?
How many 4s in 5?
1 remainder 1
Find out ‘How many
36s are in 972?’ by
subtracting „chunks‟
of 36, until zero is
reached (or until
there is a
remainder). Teach
pupils to write a
‘useful list‘ first at
the side that will
help them decide
what chunks to use,
e.g. Useful list:
1x = 36
10x = 360
100x = 3600
Moving on to the formal
written method of long
division, and interpret
remainders as whole
number remainders,
fractions, or by
rounding, as appropriate
for the context.
e.g. To calculate 748
divided by 51,
First, set the sum out
as shown:
We work out 74 divided
by 51, and write the
answer (1) above the 4.
1 × 51 = 51, so we write
this underneath 74.
Subtract 51 from 74 to
get the remainder (23).
We now bring down the
next digit (8) and write
it on the end of the 23.
We now work out 238
divided by 51, and write
the answer (4) above
the 8. You use
estimation skills here:
51 is roughly 50 and 4 ×
50 = 200. You can work
out 51 × 4 = 204
separately.
We write 204
underneath the 238 and
subtract to find the
remainder. There are
no more digits to bring
down, so we have our
answer:
Use written division
methods in cases where
the answer has up to
two decimal places.
Multiplication
Reception
Mental calculations
Working at a practical
level
to
gain
experience of doubling
and become familiar
with
appropriate
language.
‘How many eyes does
one person have?’
‘How many pairs of
eyes can you see?’
Lining up in 2s
Finding a partner in
P.E.
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Count forwards and
backwards in multiples
of twos, fives and
tens.
Count in steps of 2, 3,
and 5 from 0, and in
tens from any number,
forward or backward.
Count from 0 in
multiples of 4, 8, 50
and 100.
Count in multiples of 6,
7, 9, 25 and 1 000.
Count forwards or backwards
in steps of powers of 10 for
any given number up to
1 000 000.
Recall and use doubles
of all numbers to 10
and corresponding
halves .
Recall and use
multiplication facts for
the 2, 5 and 10
multiplication tables,
including recognising
odd and even numbers.
Count forwards or
backwards in steps of
powers of 10 for any
given number up to
1 000 000.
Use the vocabulary
associated with
multiplication.
Introduce odd and
even numbers.
Practical work
involving lots of.
Practical work to show
link between 2 lots of
4 and 4 lots of 2.
Recall and use
multiplication facts for
the 3, 4 and 8
multiplication tables.
Derive and use doubles
of all numbers to 100.
Calculate mathematical
statements for
multiplication.
Derive and use doubles
of all multiples of 50 to
500.
Understand
multiplication as
repeated addition.
Write and calculate
mathematical
statements for
multiplication using the
multiplication tables
that they know,
including for two-digit
numbers times onedigit numbers, using
mental and progressing
to formal written
methods.
Understand how
multiplication can be
shown using an array.
Recall multiplication
facts for multiplication
tables up to 12 × 12
Use partitioning to
double numbers,
including decimals to
one decimal place.
Use place value, known
and derived facts to
multiply mentally,
including: multiplying
by 0 and 1 and
multiplying together
three numbers.
Recognise and use
factor pairs and
commutativity in
mental calculations.
Continue to recall
multiplication facts for
multiplication tables up to 12 ×
12.
Use partitioning to double
numbers , including decimals
to two decimal places.
Multiply numbers mentally
drawing upon known facts.
Multiply whole numbers and
those involving decimals by 10,
100 and 1000.
Continue to recall
multiplication facts
for multiplication
tables up to 12 × 12.
Use partitioning to
double any number.
Perform mental
calculations, including
with mixed operations
and large numbers.
Multiply and divide 0.1
and 0.01.
Written Calculations
Calculate mathematical
statements for
multiplication within
the multiplication
tables and write them
using the multiplication
(×) and equals (=) signs.
Children will begin
repeated addition on a
given number line and
move on to using a
blank number line.
3x5 =
Children may use
arrays as visual
prompts.
Write and calculate
mathematical
statements for
multiplication using
the multiplication
tables that they know,
including for two-digit
numbers times onedigit numbers, using
mental and progressing
to formal written
methods.
13 x 7 =
10 x 7 =
3x7=
On a number line
38 x 7 =
Multiply two-digit (and
three-digit numbers)
by a one-digit number
or two-digit number
using the grid method,
extend to bigger
numbers.
Multiply numbers up to 4
digits by a one- or two-digit
numbers using a formal
written method, including long
multiplication for two-digit
numbers.
56 × 27 is approximately
60 × 30 = 1800.
Introduction of
vertical format linked
to grid method.
38
x 7
210 (30 x 7)
56 (8 x 7)
266
56
 27
1000
120
350
42
1512
50  20  1000
6  20  120
50  7  350
6  7  42
Multiply multi-digit
numbers up to 4 digits
by a two-digit whole
number using the
formal written
method of long
multiplication.
e.g. To calculate
158 × 67:
First, multiply by 7
(units):
158
x 67
____
1106
1
Moving to,
Then add a zero on
the right-hand side
of the next row.
This is because we
want to multiply by
60 (6 tens), which
is the same as
multiplying by 10
and by 6.
Now multiply by 6:
158
x 67
____
1106
9480
Now add your two
rows together, and
write your answer.
158
x 67
_____
1106
9480
_____
10586
So the answer is
10586.
Addition
Reception
Mental calculations
Practical
activities
discussions.
and
Finding one more than a
number from 1 to 10.
Using vocabulary associated
with addition.
Questions should be real
life and related to children’s
experiences.
How many bears are there
altogether?
(adult
asks
orally)
I have 4 bears and I add 2
more bears. How many do I
have now?
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Represent and use number
bonds and related
subtraction facts within 20.
Recall and use addition and
subtraction facts to 20
fluently, and derive and use
related facts up to 100.
Recall and use
addition and
subtraction facts for
100.
Recall and use
addition and
subtraction facts for
100.
Add and subtract numbers
using concrete objects,
pictorial representations,
and mentally, including:

a two-digit number and
ones

a two-digit number and
tens

two two-digit numbers

adding three one-digit
numbers
Add and subtract
numbers mentally,
including:

a three-digit
number and ones

a three-digit
number and tens

a three-digit
number and
hundreds
Derive and use
addition and
subtraction facts for
1 and 10 (with
decimal numbers to
one place).
Recall and use
addition and
subtraction facts
for 1 and 10 (with
decimal numbers to
one place).
Recall and use
addition and
subtraction facts
for 1 and 10 (with
decimal numbers to
two places).
Derive and use
addition and
subtraction facts
for 1 and 10 (with
decimal numbers to
two places).
Perform mental
calculations,
including with mixed
operations and large
numbers and
decimals.
Add and subtract one-digit
and two-digit numbers to
20, including zero.
Use knowledge that
addition can be done in any
order to do mental
calculations more
efficiently.
Use partitioning to reflect
mental methods.
Recall and use
addition and
subtraction facts for
multiples of 100
totalling 1000.
Add and subtract
numbers mentally
combinations of one,
two and three digit
numbers and
decimals to one
decimal place
numbers.
Use their knowledge
of the order of
operations to carry
out calculations
involving the four
operations.
Written calculations
Read, write and interpret
mathematical statements
involving addition (+) and
equals (=) signs.
Use a number track to
count on for addition,
counting on from the
largest number:
5+4=9
‘Put your finger on number
five. Count on (count
forwards) four.’
Use a given number line to
make jottings.
Draw a number line to make
informal jottings.
Blank number lines, bridging
through 10 8 + 7 = 15
48 + 36 = 84
Using informal pencil
and paper methods
(jottings) and
introducing vertical
addition.
Adding TU and TU
moving into HTU
using jottings (most
significant digit
first).
Add numbers with up
to 4 digits using a
vertical format, least
significant digit
first, extended to
bigger number.
Add whole numbers
with more than 4
digits, including
using formal written
methods (columnar
addition)
Leading on to,
children using the
compact layout,
involving carrying.
Add numbers with
two decimal places
using the formal
written methods of
columnar addition
where appropriate.
83 + 42 =
2368
+5493
11
+150
+700
+7000
7861
80 + 3
40 + 2
120 + 5 = 125
or:
Then progress to a marked
number line:
6 + 6 = 12
Partitioning 47+78=
40+70 = 120
7+8 = 15
120+15 = 135
83
+42
120
+ 5
125
Add numbers with
decimals to one
decimal places using
the formal written
methods of columnar
addition where
appropriate.
123.8
+ 79.4
203.2
111
Add whole numbers
and decimals using
formal written
methods.
Subtraction
Reception
Mental calculations
Practical
activities
and discussions.
Finding one less than
a number from 1 to 10.
Using
vocabulary
associated
with
subtraction.
Questions should be
real life and related
to
children’s
experiences.
Begin to relate
subtraction to ‘taking
away’.
‘There are 5 starfish
on a rock, the tide
comes in and washes 2
away. How many are
left?’
Written calculations
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Represent and use
number bonds and
related subtraction
facts within 20.
Recall and use addition and
subtraction facts to 20
fluently, and derive and use
related facts up to 100.
Recall and use addition and
subtraction facts for 100.
Recall and use addition and
subtraction facts for 100.
Add and subtract
one-digit and twodigit numbers to 20,
including zero.
Add and subtract numbers
using concrete objects,
pictorial representations,
and mentally, including:

a two-digit number
and ones

a two-digit number
and tens

two two-digit numbers

adding three one-digit
numbers
Add and subtract numbers
mentally, including:

a three-digit number and
ones

a three-digit number and
tens

a three-digit number and
hundreds
Derive and use addition and
subtraction facts for 1 and 10
(with decimal numbers to one
place).
Recall and use
addition and
subtraction facts
for 1 and 10 (with
decimal numbers
to one place).
Recall and use
addition and
subtraction facts
for 1 and 10
(with decimal
numbers to two
places).
Use partitioning to reflect
mental methods.
Recall and use addition and
subtraction facts for
multiples of 100 totalling
1000.
Add and subtract numbers
mentally combinations of one,
two and three digit numbers
and decimals to one decimal
place numbers.
Derive and use
addition and
subtraction facts
for 1 and 10 (with
decimal numbers
to two places).
Perform mental
calculations,
including with
mixed operations
and large
numbers and
decimals.
Use their
knowledge of the
order of
operations to
carry out
calculations
involving the four
operations.
Read, write and
interpret
mathematical
statements involving
subtraction (-) and
equals (=) signs.
Use a given number line to
make jottings.
Draw a number line to make
informal jottings.
Use a number line to count
on and back for
subtraction.
Awareness of whether
counting on or back is the most
efficient method.
Use a number line to record
complementary addition.
Use vertical subtraction in
expanded form.
Expanded subtraction without
crossing 10/100’s boundaries.
84 – 56 = 28
Expanded subtraction
crossing boundaries.
Growing awareness of
whether counting on or
back is the most efficient
method.
74 – 27 = 47
Move towards contracted
subtraction using
decomposition.
15 – 7 = 8
or
15 – 7 =
15 – 5 = 10
10 – 2 = 8
or with larger numbers,
65 – 17 =
65 – 10 = 55
55 – 7 = 48
Example:
503-278=225
Partitioned numbers are then
written under one another:
Example: 74 − 27
70 + 4
60 + 14
- 20 + 7
- 20 + 7
40 + 7
(Use of manipulatives to move
on)
70  4
 20  7
60
14
70  4
 20  7
40  7
In this example 503 has to be
partitioned into 400+90+13 in
order to carry out the
subtraction calculation.
This leads into the formal
written method (there is
potential for error in this
example):
6 14
74
27
47
There are no tens in the first
number (503) so we have to
exchange a hundred for 10
tens before we can exchange
a ten for ten ones/units.
Subtract whole
numbers with
more than 4
digits, including
using formal
written methods
(columnar
subtraction).
Subtract
numbers with two
decimal places
using the formal
written methods
of columnar
subtraction
where
appropriate.
Subtract whole
numbers and
decimals using
formal written
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.