Calculation Policy
Policy No.
The Bramble Academy
Last Reviewed: March 2016
1
Equality Statement
At The Bramble Academy, we are committed to ensuring equality of education
and opportunity for all pupils, staff, parents and carers receiving services from
the school, irrespective of race, gender, disability, faith or religion or socioeconomic background. We aim to develop a culture of inclusion and diversity in
which all those connected to the school feel proud of their identity and able to
participate fully in school life.
The achievement of pupils will be monitored by race, gender and disability and
we will use this data to support pupils, raise standards and ensure inclusive
teaching. We will tackle discrimination by the positive promotion of equality,
challenging bullying and stereotypes and creating an environment which
champions respect for all. At The Bramble Academy, we believe that diversity is
a strength, which should be respected and celebrated by all those who learn,
teach and visit here.
This booklet is designed to show the progression in calculation strategies for
each of the four operations: addition, subtraction, multiplication and division.
For each operation there are stages that children need to work through and
build upon their basic skills. This should be used to bridge gaps within calculation
processes and move through the stages when children are ready.
Last Reviewed: March 2016
2
Addition
Stage 1
Counting using fingers and objects.
Stage 2
Counters or pictures used to show
amounts.
+
=
=
=
Stage 3
Counting on a number track (single
numbers).
Stage 4
Using a number line (single jumps)
7+5=
5+3=
Stage 5
Counting on using a hundred square (tens).
24 + 10
Last Reviewed: March 2016
Stage 6
Counting on using a hundred square (tens
and units). 24 + 13
3
Stage 7
Using a number line with jumps in 10s (T)
and 1s (U).
Stage 8
Using a number line with partitioning
Stage 9
Move towards partitioned column method.
Stage 10
Column addition by partitioning.
23 + 43
135 + 143
20 + 3
40 + 3
60 + 6 = 66
Stage 11
Column addition by partitioning with the
brackets
Stage 12
Compact column addition involving
carrying.
135 + 143
165 + 143
Stage 13
Column addition involving decimals. When
adding decimals, it is vital that place value
is used and place holders are put in empty
columns.
Last Reviewed: March 2016
4
Expectations by the end of each year group.
Foundation Stage – up to stage 4 using 2 single digit numbers.
Year 1 – Up to Stage 5 - add with numbers up to 20.
Year 2 – Up to Stage 9 - add with 2-digit numbers (developing mental fluency
with addition and place value involving 2-digit numbers, then establish more
formal methods).
Year 3 – Up to Stage 11 but add numbers with up to 3 digits.
Year 4 – Stage 11 but add numbers with up to 4 digits.
Year 5 – Stage 13 but add numbers with more than 4 digits (Summer Term add
in decimals).
Year 6 – Stage 13 but add several numbers of increasing complexity (including
decimals).
Last Reviewed: March 2016
5
Addition Vocabulary
Year 1
add
more
plus
and
make
altogether
total
equal
to
equals
double
most
count on
number line
number
bonds
Year 4
(See Y2/3)
count on
number line
sum
tens
units
partition
addition
column
tens
boundary
hundreds
boundary
increase
vertical
carry
expanded
compact
thousands
hundreds
digits
inverse
Last Reviewed: March 2016
Year 3
Year 2
add
more
plus
and
make
altogether
total
equal to
equals
double
most
count on
number line
sum
tens
units
partition
addition
column
tens
boundary
inverse
Year 5
(See Y2/3/4)
addition
column
tens
boundary
hundreds
boundary
increase
vertical
carry
expanded
compact
thousands
hundreds
digits
inverse
decimal
places
decimal
point
tenths
hundredths
thousandths
(See Y2)
count on
number line
sum
tens
units
partition
addition
column
tens
boundary
hundreds
boundary
increase
vertical
carry
expanded
compact
inverse
Year 6
(See Y3/4/5)
addition
column
tens
boundary
hundreds
boundary
increase
vertical
carry
expanded
compact
thousands
hundreds
digits
inverse
decimal
places
decimal
point
tenths
hundredths
thousandths
6
Subtraction
Stage 1
Using fingers to show taking away.
Stage 2
Using objects/counters to show taking
away.
6–2=4
Stage 3
Using a number track to count back.
6–2=4
Stage 5
Using a hundred square to take away 1s.
72 - 5
Last Reviewed: March 2016
Stage 4
Using a number line to count back.
8–5=3
Stage 6
Using a hundred square to take away 10s.
72 – 20
7
Stage 7
Using a hundred square to take away 10s
and 1s starting with 1s.
Stage 8
Using a number line to find the difference
between numbers
64 – 38
72 – 25
Stage 9
Using a number line to find the difference
between numbers.
Stage 10
Expanded vertical method without
exchanging.
67 – 45 = 22
Stage 11
Vertical method without exchanging.
89 – 35 = 54
89
- 35
54
89 – 35 = 54
80 + 9
- 30 + 5
50 + 4
Stage 12
Introduce exchanging through practical
subtraction. Make the large number with
Base 10, then subtract 47 from it.
72 – 47
Before subtracting 7 from 72 blocks, they
will need to exchange a row of 10 for ten
units. Then subtract 7 and subtract 4 tens.
Last Reviewed: March 2016
8
Stage 13
Using the column partitioned method for
exchanging.
327 – 136 = 191
Stage 14
Introduce the compact method, comparing
to the pervious one discussing what is the
same and different.
327 – 136 = 191
Stage 15
Use vertical column subtraction with whole
and decimal numbers.
Last Reviewed: March 2016
9
Expectations by the end of each year group.
Foundation Stage – up to Stage 4 – Using single digit numbers.
Year 1 – Up to and including Stage 4 - Subtract from numbers up to 20.
Year 2 – Up to and including Stage 9 – Subtract with 2-digit numbers.
Year 3 – Up to and including Stage 13 – subtracting with 2 and 3 digit numbers.
Year 4 – Up to and including Stage 14 but subtract with up to 4 digits.
Year 5 – Up to and including Stage 15 but subtract with at least 4-digit numbers
(including decimals)
Year 6 – Up to Stage and including Stage 15 but subtracting with increasingly
large and more complex numbers and decimal values.
Last Reviewed: March 2016
10
Subtraction Vocabulary
Year 1
equal to
take away
less
minus
subtract
distance
between
difference
number line
how many
more
how many
fewer
less than
most
least
count back
how many
left
how much
less is
Year 4
(See Y3)
exchange
how much
less is
decrease
value
difference
strategy
minus
inverse
Year 3
Year 2
equal to
take away
less
minus
subtract
distance
between
how many
more
how many
fewer
less than
most least
count back
how many
left
how much
less is
difference
count on
Year 5
(See Y3/4)
exchange
how much
less is
decrease
value
difference
strategy
minus
inverse
equal to
take away
less
minus
subtract
distance
between
how many
more
less than
most
least
count back
how many
left
how much
less is
difference
count on
strategy
Year 6
(See Y3/4/5)
decimal
point
decimal
tenths
hundredths
Multiplication
Last Reviewed: March 2016
11
Stage 1
Stage 2
Repeated addition using concrete objects
Songs and counting in 2s, 5s and 10s.
6 x 5 = 30
5 + 5 + 5 + 5 + 5 + 5 = 30
Stage 3
Use repeated addition on a number line.
Stage 4
Use arrays to show the commutative law of
multiplication.
5 x 4 = 20
Stage 5
Introduce the grid method linking the
layout to arrays (use as a visual only).
14 x 6 = 84
Stage 6
Use the grid method.
24 x 8 = 192
160 + 32 = 192
Stage 7
Use the grid method to multiply HTU x U
357 x 7
Stage 8
When confident with grid method,
introduce long multiplication (with
partitioning).
57 x 7
Last Reviewed: March 2016
2100 + 350 + 49 = 2499
12
Stage 9
Introduce long multiplication (compact).
57 x 7
Stage 10
Introduce Expanded Multiplication for TU x
TU e.g. 23 x 18
Stage 11
Use long multiplication (compact) for TU x
TU . 57 x 24
Last Reviewed: March 2016
13
Expectations by the end of each year group.
Foundation Stage – Stage 1 – doubling using fingers and objects.
Year 1 – Up to and including Stage 2 – Multiply with concrete objects, arrays and
pictorial representation.
Year 2 – Up to and including Stage 4 – Multiply using arrays and repeated
addition (using at least 2s, 5s and 10s).
Year 3 – Up to and including Stage 6 – Multiply 2-digits by a single digit number.
Year 4 – Up to and including Stage 7 – Multiply 2 and 3-digits by a single digit,
using all multiplication tables up 12 x 12.
Year 5 – Up to and including Stage 10 – Multiply up to 4-digits by 1 or 2 digits.
Year 6 – Up to Stage and including Stage 11 – Short and long multiplication as in
Stage 10 and multiply decimals with up to 2d.p by a single digit.
Multiplication Vocabulary
Year 1
Last Reviewed: March 2016
groups of
lots of
times
multiply
count
array
altogether
Year 2
groups of
lots of times
array
altogether
column
row
sets of
commutative
Year 3
groups of
lots of
times
array
14
column
row
commutative
sets of
Year 4
(See Y3)
groups of
lots of
times
array
multiply
column
row
sets of
equal groups
times
grid method
multiple
product
inverse
commutative
Last Reviewed: March 2016
Year 5
(See Y3/4)
inverse
square
factor
integer
decimal
short/long
multiplication
carry
Year 6
(See
Y3/4/5)
Inverse
Square
Factor
hundredths
decimal
integer
decimal
short/long
multiplication
carry
tenths
15
Division
Stage 1
Halving shapes, numbers and quantity of
objects.
Stage 2
Sharing numbers using counters/objects (÷)
Stage 3
Grouping numbers using counters (÷)
Stage 4
Using arrays to work out division questions.
6÷2=3
12 ÷ 3
6÷2=3
Stage 6
Chunking on a number line.
Stage 5
Using known multiplication facts to work
out the inverse.
18 ÷ 3 = 6
4 x 10 = 40 therefore
40 ÷ 10 = 4 and
40 ÷ 4 = 10
Stage 7
Chunking TU ÷ U with no remainders.
Stage 8
Long division by chunking with U.
72 ÷ 4 = 18
Last Reviewed: March 2016
16
Stage 9
Introduce short division without
remainders.
Stage 10
Short division
205 ÷ 5
72 ÷ 4 = 18
How many 4s in 7? 1 remainder 3 and then
how many 4s in 32? 8
We always need to check the answer using
the inverse.
5 x 41 = 205
Stage 11
Use short division with remainders.
Stage 12
Long division by chunking with TU.
78 ÷ 5 = 15r3
180 ÷ 12 = 15
How many 5s in 7? 1 remainder 2 and then
how many 5s in 28? 5 with 3 left over.
10 + 5 = 15
Last Reviewed: March 2016
How many 5s in 7? 1 remainder 2 and then
how many 5s in 28? 5 with 3 left over.
17
Stage 13
For Level 5 and above, children are
expected to be able to convert the
remainder into a fraction or decimal. So, if
the remainder is 2 they would need to
know that it is 2/5 (two fifths) as they were
dividing by 5.
Last Reviewed: March 2016
18
Expectations by the end of each year group.
Foundation Stage – Up to Stage 2 – Halving quantities of objects and sharing
quantities of objects.
Year 1 – Up to and including Stage 3 – Group and share small quantities.
Year 2 – Up to and including Stage 6 – Group and share using the ÷ and = sign.
Year 3 – Up to and including Stage 7 – Divide 2-digit numbers by a single digit.
Year 4 – Up to and including Stage 8 – Divide up to 3-digit numbers by a single
digit.
Year 5 – Up to and including Stage 11 – Divide up to 4-digit numbers by a single
digit including those with remainders.
Year 6 – Up to Stage and including Stage 13 – Divide at least 4 digits by both
single and 2-digit numbers (including decimals and quantities).
Division Vocabulary
Last Reviewed: March 2016
19
Year 1
share
share
equally
one each
two each…
group
groups of
lots of
array
Year 4
(See Y2/3)
group
groups of
equal groups
of
lots of
array
divide
divided by
divided into
division
grouping
number line
left
left over
inverse
short
division
carry
remainder
multiple
divisible by
factor
Last Reviewed: March 2016
Year 2
share
share
equally
one each
two each…
group
groups of
equal groups
of
lots of
array
divide
divided by
divided into
division
grouping
number line
left
left over
Year 5
(See Y2/3/4)
divide
divided by
divided into
division
grouping
number line
left
left over
inverse
short
division
carry
remainder
multiple
divisible by
factor
quotient
prime
number
prime
factors
composite
number (non
prime)
Year 3
(See Y2)
one each
two each
group
groups of
equal groups
of
lots of
array
divide
divided by
divided into
division
grouping
number line
left
left over
inverse
short
division
carry
remainder
multiple
Year 6
(See Y3/4/5)
divided into
division
grouping
number line
left
left over
inverse
short
division
carry
remainder
multiple
divisible by
factor
quotient
prime
number
prime
factors
composite
number
common
factor
20