YEAR 1 Addition
Addition
Written Methods (informal jottings
moving to formal strategies)
Progression
Add with numbers up to 20
Read, write and interpret
mathematical statements involving
addition (+), subtraction (–) and equals
(=) signs
Count on, ‘jump along’ the number
track/line, in 1s
1
2
3
4
5
Developing
conceptual
Key skills – NC programmes of
Study
Vocabulary
Just know it
Badges
Children use stories, songs and
games within real life contexts,
using real life objects.. They recount
the objects at the end.
They understand that addition can
be done in any order. Children are
taught to start with the larger /
greater number. Children create
stories of numbers eg. the stories
of 6 are 1 + 5, 2 + 4 etc.
* Pupils combine and increase
numbers, counting forward and
backwards.
Add, plus, more
than, most, make,
sum, put
together,
altogether, total,
equal to, is the
same as, equals,
greater, larger,
number line.
-1 more
-Number bonds: 5,
6,8,8,9 and 10
- Largest number
first.
- Add 10.
- Ten plus ones.
- Doubles up to 10
- Use number bonds
of 10 to derive bonds
of 11
White and White
star
Addition Numbers to
5, Addition and
Subtraction Numbers
to 5,
Number bonds
Use bonds of 10 to calculate bonds
of 20
Count
all
Count on
2
Looking for number bonds.
Year 1
* Identify one more and one less
*Recall number bonds to 10 and
20 and addition facts of one and
two digit numbers within 20
including adding zero.
*Read, write and interpret
mathematical statements
involving addition (+), and equals
(=) signs
(Ten frame) Numicon
Initially children should begin at the
first number in the number sentence.
When more confident (see year 2)
they can begin to use commutativity.
They should recognise that the
number they end on is the answer.
Children should begin with adding 2
numbers together, but should
progress to adding more numbers
when ready.
Children should look for number bonds
within these such as:
2 + 3 + 1 = 5 +1 = 6
7 + 5 = 7 + 3 + 2 = 12
7 + 3 + 2 = 10 + 2 = 12
*Count to and across 100
*Solve simple one-step problems
involving addition using objects,
number lines and pictorial
representations.
*Empty box problems and the
inverse
7
+
=9
*Introduce part, part whole
model – see progression in the
bar model.
12
4
Westbury On Trym C of E Academy Calculation Policy 2016
8
Blue and blue star
Addition and
subtraction numbers
to 10
Turquoise and
Turquoise star
Addition and
subtraction facts to
20 not bridging 10
Yellow and yellow
star
Addition Numbers to
20
YEAR 2 Addition
Addi
tion
Written Methods (informal
jottings moving to formal
strategies) Progression
Add with 2 digit numbers.
When using number lines, they will
start by counting on in ones, then
tens and ones and then tens and
ones in one jump as below.
Initially children will use marked
number lines until they are able to
move to empty number lines.
48 + 36 = 84
Developing
conceptual
Key skills - NC programmes of Study
Vocabulary
Just Know it
Children will use: numicon, dienes, marked
number lines, bead strings, place value cards,
They will move to an empty number line when
ready.
When adding they will start with the larger
number and count on. They are beginning to
understand the commutative nature of
addition.
They use number tracks / Number lines –
jumps of 1
then efficient jumps using number bonds
18 + 5 = 23
*recognise the place value of each digit in a
two-digit number (tens, ones)
Add, plus,
more, make,
sum,
altogether,
total, equal
to, is the
same as,
equals,
greater,
larger,
number line,
tens, ones,
partition,
addition,
column, tens
boundary
-10 more
-Number bonds: 12, 13,
14, 15, 16 17,18, 19, 20
- Add 1 digit to 2 digit
by bridging
-Partition second
number, add tens then
ones
- Add 10 and multiples.
- Doubles up to 20 and
multiples of 5
- Add near multiples of
10.
- Partition and
recombine numbers.
Year2
Then can round and adjust when adding.
25 + 9 ( + 10 then -1)
They can add near doubles eg. 6 + 7
Bridging through ten can help
children become more efficient.
Children can partition numbers in different
ways to support addition.
*recall and use addition and subtraction
facts to 20 fluently, and derive and use
related facts up to 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
* show that addition of two numbers can be
done in any order (commutative) and
subtraction of one number from another
cannot. Children can check their additions
by adding in a different order.
*Recognise and use the inverse relationship
between addition and subtraction and use
this to check calculations and solve missing
number problems. (continue to use the 2
part whole model to support this)
*solve problems with addition and
subtraction: using concrete objects and
pictorial representations, including those
involving numbers, quantities and measures
applying their increasing knowledge of
mental and written methods
Westbury On Trym C of E Academy Calculation Policy 2016
Badges
Blue and blue star
Addition and
subtraction numbers to
10
Turquoise and Turquoise
star
Addition and subtraction
facts not bridging 10
Yellow and Yellow Star
Addition and
subtraction facts.
Pink and pink star
Addition Numbers bonds
to 100
Addition and
Subtraction Number
bonds to 100
YEAR 3 Addition
Addition
Written Methods (informal
jottings moving to formal
strategies) Progression
Add with up to 3-digit
numbers.
Developing
conceptual
Key skills – NC programmes of Study
Vocabulary
Just know it
Badges
Number line: 25 + 36 using efficient jumps
* Recognise place value in 3 digit numbers.
Add, plus, more,
make, sum,
altogether,
total, equal to,
is the same as,
equals, greater,
larger, number
line, tens, units
/ ones,
partition,
addition,
column, tens
boundary,
hundreds
boundary,
increase,
vertical, carry,
expanded,
compact.
-Add multiples
of 10, 100
-Add single
digit bridging
through
boundaries
-Partition
second number
to add
-Pairs of 100
-Use near
doubles to add
-Add near
multiples of 10
and 100 by
rounding and
adjusting
-Partition and
recombine
numbers.
Pink and pink
star
Addition
Numbers bonds
to 100
Addition and
Subtraction
Number bonds
to 100
*find 10 or 100 more or less than a given
number
When ready, children will begin
to use the partitioning written
method - adding the ones then
the tens.
*Add 2-digit numbers mentally, including
those exceeding 100.
Year 3
Using known facts:
40 + 80 = 120 using 4 + 8 = 12
So 400 + 800 = 1200
Children can move on to the
formal written method
(described in year 4) if ready.
This must be done using
manipulatives to develop
conceptual understanding.
(Round and adjust)
243 + 198
by +200 then -2
Pairs that make 100
23 + 77
Partitioning written method with diennes, or
place value counters and arrow cards.
Eg. 24 + 15=
Add together the ones first then add the
tens. Use the Base 10 blocks first before
moving onto place value counters
*Add a 3 – digit number and ones mentally
(175 + 8)
*Add a 3-digit number and tens mentally (249
+50)
* Add a three digit number and hundreds
mentally (246 +300)
*add and subtract numbers with up to three
digits, using formal written methods of
columnar addition and subtraction
*Estimate answers to calculations using the
inverse to check
*Solve problems including empty box
problems, using number facts, place value and
more complex addition.
*Continue to practise and increase fluency in
mental addition including number bonds, add
the nearest multiple of 10, 100, 1000 and
adjusting, using near doubles, partitioning and
recombining.
Westbury On Trym C of E Academy Calculation Policy 2016
Purple and
purple star
Addition
multiples of
100
Addition and
Subtraction
multiples of
100
YEAR 4 Addition
Addition
Written Methods (informal
jottings moving to formal
strategies) Progression
Add numbers with up to 4
digits using written methods.
When ready children can use
formal written methods
(compact method) with up to 4
digits. Children always add the
ones first.
Year 4
423
+88
511
11
Using similar methods, children
will be able to add several
numbers with different numbers
of digits and be able to add
money, knowing that the decimal
points should line up under each
other.
Developing
conceptual
Key skills – NC programmes of Study
Vocabulary
Just Know it
Continue to model using the resources as show
in year 2 and 3.
*Select the most appropriate method to
carry out a calculation: mental, jottings or
written and explain why.
Add, plus, more,
make, sum,
altogether,
total, equal to,
is the same as,
equals, greater,
larger, number
line, tens, units
/ ones,
partition,
addition,
column, tens
boundary,
hundreds
boundary,
increase,
vertical, carry,
expanded,
compact,
thousands,
inverse.
Add multiples
of 10s , 100s,
1000s
Children can continue to use diennes, place
value counters and arrow cards if needed.
Make both numbers on a place value grid.
* Find 1000 more than a given number.
*Estimate and use the inverse operations to
check answers.
*Solve 2-step problems in context, deciding
which operation to use and why.
Add up the ones and exchange 10 ones for one
10.
Add up the rest of the columns, exchanging
the 10 counters from one column for the next
place value column until every column has been
added.
This can also be done with Base 10 to help
children clearly see that 10 ones equal 1 ten
and 10 tens equal 100.
As children move on to decimals, money and
decimal place value counters can be used to
support learning.
http://mathsframe.co.uk/en/resources/resou
rce/241/Expanded_Addition_using_Place_Val
ue_Counters
Westbury On Trym C of E Academy Calculation Policy 2016
* Continue to practise and increase fluency in
mental addition including number bonds,
adding the nearest multiple of 10, 100, 1000
and adjusting, using near doubles, using known
number facts to calculate others, partitioning
and recombining.
*Add numbers up to 4- digits using the formal
written method for column addition
(depending on whether it is the appropriate
strategy and if children are ready.)
Fluency of 2
digit + 2 digit
addition
Partition
second number
to add
Decimal pairs
of 10 and 1
Use near
doubles to add
Adjust both
numbers before
adding
Add near
multiples
Partition and
recombine
Badges
YEAR 5 Addition
Addition
Written Methods (informal
jottings moving to formal
strategies) Progression
Add numbers with more than
4 digits using formal
methods. Use the context
of money, measures and
include numbers with
different numbers of
decimals places.
(Compact method) Always add
the ones first.
Developing
conceptual
Key skills – NC programmes of
Study
Vocabulary
Just know it
Continue to model using the
resources as shown in years 3
and 4.
Children can continue to use
diennes or place value counters
to support understanding.
* Continue to practise and
increase fluency in mental
addition including number bonds,
adding the nearest multiple of
10, 100, 1000 and adjusting,
using near doubles, using known
number facts to calculate
others, partitioning and
recombining.
Add, plus, more, make,
sum, altogether, total,
equal to, is the same as,
equals, greater, larger,
number line, tens, units /
ones, partition, addition,
column, tens boundary,
hundreds boundary,
increase, vertical carry,
expanded, compact,
thousands, inverse,
decimal places, decimal
point, tenths,
hundredths,
thousandths.
Add multiples of 10s ,
100s,
1000s, tenths
Fluency of 2 digit + 2 digit
including with decimals
Partition second number to
add
Use number facts, bridging
and place value
Adjust numbers to add
Partition and recombine
2634 + 4517 =
* Add increasingly large numbers
mentally using these strategies
Year 5
2458
+596
3054
1 11
£ 73.42
+ £ 84.73
£158.15
1 1
The decimal point should be
aligned in the correct place.
*Use rounding to estimate and
check answers.
http://mathsframe.co.uk/en/r
esources/resource/241/Expan
ded_Addition_using_Place_Val
ue_Counters
Always use the language:
Adding ones, then adding
tens eg. 5 tens add 9 tens
equal 14 tens.
Westbury On Trym C of E Academy Calculation Policy 2016
*Use formal column addition to
add numbers with more than 4
digits.
Badges
YEAR 6 Addition
Additio
n
Written Methods (informal
jottings moving to formal
strategies) Progression
Add several numbers with
increasing complexity
(compact method)
Always add the ones first.
23454
+596
24050
Developing
conceptual
Key skills - NC programmes of
Study
Vocabulary
Just know it
Continue to model using the
resources as shown in stage 2
and 3.
*Continue to practise and increase
fluency in mental addition including
number bonds, adding the nearest
multiple of 10,100,1000 and
adjusting, using near doubles, using
known number facts to calculate
others, partitioning and
recombining.
Add, plus, more, make,
sum, altogether, total,
equal to, is the same
as, equals, greater,
larger, number line,
tens, units / ones,
partition, addition,
column, tens boundary,
hundreds boundary,
increase, vertical
carry, expanded,
compact, thousands,
inverse, decimal places,
decimal point, tenths,
hundredths,
thousandths.
Add multiples of 10s ,
100s, 1000s, tenths,
hundredths
Children can continue to use
diennes or place value counters
to support understanding.
2634 + 4517 =
1 1 1
*Perform mental calculations,
including with mixed operations
and larger numbers, using and
practising mental strategies such
as these.
Year 6
*Use rounding to estimate and
check answers.
*Use formal column addition to
add numbers with more than 4
digits.
Always use the language:
Adding ones, then adding
tens eg. 5 tens add 9 tens
equal 14 tens.
http://mathsframe.co.uk/en/r
esources/resource/241/Expan
ded_Addition_using_Place_Val
ue_Counters
Westbury On Trym C of E Academy Calculation Policy 2016
* Use negative numbers in context
and calculate increases in
temperature across zero.
Fluency of 2 digit + 2 digit
including with decimals
Partition second number to
add
Use number facts, bridging
and place value
Adjust numbers to add
Partition and recombine
Badges
YEAR 1 Subtraction
Subtracti
on
Written Methods (informal
jottings moving to formal
strategies) Progression
Subtract from
numbers up to 20
Read, write and
interpret
mathematical
statements involving
addition (+),
subtraction (–) and
equals (=) signs
Year 1
Children begin to use
numbered lines to
support their own
calculations - using a
numbered line to count
back in ones.
Developing
conceptual
Key skills - NC
programmes of Study
Vocabulary
Just know it
Subtraction is taught with stories and
children learn it is the inverse of addition.
Fingers, objects, bead strings etc should be
used. They compare quantities using greater
or less than. They continue taking away by
crossing out or removing objects from a
group.
*Given a number, say
one less.
Equal to, take, takeaway,
less, minus, subtract, leaves,
difference between,
distance between, how many
more, how many fewer/ less
than, most, least, count back,
how many left?
1 less
They begin to talk about subtraction as
finding the difference.
The difference in
the number of stripes
is?
Comparing quantities (less than)
10-1=9
The number line should
also be used to show
that 6 - 3 means the
‘difference between 6
and 3’ and how many
jumps they are apart.
U-U and TU- U as a
number sentence.
Children use simple number lines to count
backward/ down.
Number bonds
6 less than 10 is 4
Count out, then count how many are left. 7 –
4=3
Difference between
13 and 8
13 – 8 = _
8 + _ = 13
Westbury On Trym C of E Academy Calculation Policy 2016
*Count to and over 100,
forward and back.
* Represent and use
number bonds and
related subtraction
facts to 20 and within
20.
*Subtract numbers to
20 including zero.
*solve simple one-step
problems involving
addition using objects,
number lines and
pictorial
representations.
*Begin to understand
that subtraction is the
inverse of addition.
*Introduce part part
whole model – see
progression in the bar
model document.
12
4
8
Number bonds,
subtraction: 5, 6,7,8,9,10
Count back
Teens subtract 10.
Difference between 2
numbers
Badges
White and White star
Addition Numbers to 5,
Addition and Subtraction
Numbers to 5,
Blue and blue star
Addition and
Subtraction facts to
10
Turquoise and
Turquoise star
Addition and
subtraction facts to
20 - not bridging 10
Yellow and yellow star
Addition Numbers to 20
Addition and Subtraction
Numbers to 20
YEAR 2 Subtraction
Subtrac
tion
Written Methods (informal jottings
moving to formal strategies) Progression
Subtract with 2-digit numbers.
Year 2
When using the empty number lines children
will first count back in tens and ones, until
they eventually subtract the tens on one
jump and units / ones in one jump.
Developing
conceptual
Children will use a range of
resources to understand
counting on to find the
difference.
Children will use numicon,
dienes blocks, marked
number lines, bead strings,
place value cards. They
will move to using an empty
number line when ready.
Key skills - NC programmes
of Study
*Understand that
subtraction is the inverse
of addition
*Understand that
subtraction cannot be
reversed: 4-2 is not the
same as 2 – 4
* recall and use
subtraction facts to 20
fluently and derive and use
related facts to 100.
*Solve problems involving
subtraction, using objects,
pictorial representations,
using numbers, quantities
and measures. applying
their increasing knowledge
of mental and written
methods
The children will learn to count on when
finding the difference.
Children will begin to understand bridging
through ten by targeting the ten/ jumping
through ten.
*Understand both take –
away and find the
difference models of
subtraction through real
life examples.
Westbury On Trym C of E Academy Calculation Policy 2016
*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
Vocabulary
Just know it
Equal to, take, takeaway,
less, minus, subtract,
leaves, difference
between, how many more,
how many fewer/ less
than, most, least, count
back, how many left,
difference, count on,
strategy, partition,
tens, units / ones.
Ten less
Number bonds,
subtraction: 12, 13, 14, 15
16, 17, 18,19, 20,
Subtract 1 digit from 2
digit by bridging
Partition second number,
Count back in 10s then 1s
Badges
Blue and blue star
Addition and
Subtraction facts to
10
Turquoise and
Turquoise star
Addition and
subtraction facts not
bridging 10
Yellow and yellow star
Addition Numbers to 20
Addition and Subtraction
Numbers to 20
Subtract 10 and multiples
of 10
Subtract near multiples of
10
Difference between 2
numbers
Pink and pink star
Addition Numbers
bonds to 100
Addition and
Subtraction Number
bonds to 100
YEAR 3 Subtraction
Subtraction
Written Methods (informal
jottings moving to formal
strategies) Progression
Subtract with 2 and 3
digit numbers.
Once children are secure
with an empty number line
they will then move on to
expanded subtraction
(using partitioning)
First without exchanging:
Developing
conceptual
Key skills- NC programmes of
Study
Vocabulary
Just know it
Badges
Children will continue to be shown a number line alongside
new strategies being taught.
*Subtract numbers mentally
including;
> a three-digit number and
ones
> a three-digit number and
tens
>a three-digit number and
hundreds
Equal to, take,
takeaway, less,
minus, subtract,
leaves,
difference
between, how
many more, how
many fewer/
less than, most,
least, count
back, how many
left,
difference,
count on,
strategy,
partition, tens,
units / ones,
exchange,
decrease,
hundreds,
value, digit.
Subtract
multiples of 10
and 100
Pink and pink star
Addition Numbers
bonds to 100
Addition and
Subtraction
Number bonds to
100
To build up to more formal methods, partitioning will be
demonstrated using arrow cards and base ten materials.
Children will be able to partition in different ways. Children
will understand that they can exchange a ten for ten units
/ones.
Year 3
Then begin to exchange:
Children will use diennes or place value counters to
subtract. Children will begin with numbers that do not
require exchanging. They can then use numbers that
require one exchange.
Expanded subtraction links
http://mathsframe.co.uk/e
n/resources/resource/48/
column_subtraction
http://www.topmarks.co.uk
/Flash.aspx?f=DecompExpa
ndv2
*Number lines or
partitioning are still used
for informal jottings.
Use base 10 to make the bigger number, then take the
smaller number away.
Then move on to place value counters.
Show how you partition numbers to
subtract. Again make the larger
number first.
Westbury On Trym C of E Academy Calculation Policy 2016
* Understand that subtraction
is the inverse of addition.
* Find 10 or 100 more or less
than any given number up to
1000
*Know and practise mental
calculating strategies such as
subtracting near multiples of
10 and adjusting.
*Solve problems, including
missing number problems, using
number facts, place value, and
more complex subtraction.
Subtract single
digit by
bridging
through
Boundaries
Partition
second number
to subtract
Difference
between
Subtract near
multiples of 10
and 100 by
rounding and
adjusting
Purple and purple
star
Addition multiples
of 100
Addition and
Subtraction
multiples of 100
YEAR 4 Subtraction
Subtraction
Written Methods (informal
jottings moving to formal
strategies) Progression
Subtract with up to 4 digit
numbers.
Continue to build on
subtraction using the
expanded method with
exchanging.
Developing
conceptual
Key skills - NC programmes of
Study
Vocabulary
Just know it
Badges
Children continue to use
diennes or place value
counters.
They continue to use
partitioning for taking away
and exchanging, They start
with one exchange before
moving onto subtractions with
2 exchanges.
*Select the best method for
subtraction calculations.
Equal to, take, takeaway,
less, minus, subtract,
leaves, difference
between, how many more,
how many fewer/ less
than, most, least, count
back, how many left,
difference, count on,
strategy, partition, tens,
units / ones, exchange,
decrease, hundreds,
value, digit, inverse
Subtract multiples of 10s ,
100s,
1000s
Pink and pink star
Addition Numbers
bonds to 100
Addition and
Subtraction
Number bonds to 100
*Understand both take – away
and find the difference models
of subtraction.
*Understand that subtraction is
the inverse of addition.
*Find 1000 less than a given
number.
Year 4
*Know and practise mental
calculating strategies such as
subtracting near multiples of 10
and adjusting.
Once secure – move on to
compact method of
subtraction for up to 4 digit
numbers.
*Number lines or partitioning
are still used for informal
jottings.
http://mathsframe.co.uk/en/r
esources/resource/242/Colum
n_Subtraction_using_Place_Va
lue_Counters
*Use inverse operation and
estimation to check answers.
*Add and subtract numbers with
up to 4 digits using the formal
written methods of columnar
addition and subtraction where
appropriate and if ready.
Draw the counters onto a place
value grid and show what you
have taken away by crossing
the counters out as well as
clearly showing the exchanges
you make.
Westbury On Trym C of E Academy Calculation Policy 2016
Fluency of 2 digit subtract
2 digit
Partition second number to
Subtract
Decimal subtraction from
10 or 1
Difference between
Subtract near multiples by
rounding and adjusting
Purple and purple
star
Addition multiples of
100
Addition and
Subtraction multiples
of 100
YEAR 5 Subtraction
Subtraction
Written Methods (informal
jottings moving to formal
strategies) Progression
Subtract whole numbers with
at least 4 digits, including
money, measures and numbers
with decimal fractions.
Year 5
Children will continue to use
compact subtraction.
Developing
conceptual
Key skills - NC programmes of Study
Vocabulary
Just know it
Continue to model using the
resources as show in years 3
and 4.
*Select the best method for
subtraction calculations.
Equal to, take,
takeaway, less, minus,
subtract, leaves,
difference between,
how many more, how
many fewer/ less
than, most, least,
count back, how many
left, difference,
count on, strategy,
partition, tens, units
/ ones, exchange,
decrease, hundreds,
value, digit, inverse,
tenth, hundredth,
decimal, decimal
point
Subtract multiples of
10s , 100s, 1000s,
tenths,
Children can continue to use
diennes and place value
counters.
*understand that subtraction is the
inverse of addition.
* know and practise mental calculating
strategies such as subtracting near
multiples of 10. 100 and adjusting.
Subtract using larger numbers.
They will also be able to
subtract decimals by lining up
the decimal point.
*Use inverse operation and estimation
to check answers.
Where the numbers involved in
the calculation are close together
or near to multiples of 10, 100 etc
counting on using a number line
should be used.
*Add and subtract whole numbers with
more than 4 digits, including using
formal written methods (columnar
subtraction if appropriate and able to
use.)
Children should be able to choose
the most efficient method / type
of strategy for calculating
depending on the numbers.
*Number lines or partitioning
are still used for informal
jottings.
*Understand both take – away and find
the difference models of subtraction.
http://mathsframe.co.uk/en
/resources/resource/242/Col
umn_Subtraction_using_Place
_Value_Counters
Westbury On Trym C of E Academy Calculation Policy 2016
*Solve addition and subtraction multistep problems in contexts, deciding
which operations and methods to use
and why
Fluency of 2 digit - 2
digit including with
Decimals
Partition second
number to subtract
Difference between
Adjust numbers to
subtract
Badges
YEAR 6 Subtraction
Subtraction
Written Methods (informal
jottings moving to formal
strategies) Progression
Children can subtract with
increasingly large and more
complex numbers including
money, measures and
numbers with different
decimal places.
Developing
conceptual
Key skills - NC programmes of
Study
Vocabulary
Just know it
Continue to model using the
resources as show in years 3
and 4.
Children can continue to use
diennes and place value
counters.
* Use negative numbers in
context and calculate
differences across zero.
Equal to, take, takeaway,
less, minus, subtract,
leaves, difference
between, how many more,
how many fewer/ less
than, most, least, count
back, how many left,
difference, count on,
strategy, partition, tens,
units / ones, exchange,
decrease, hundreds,
value, digit, inverse,
tenth, hundredth,
decimal, decimal point
Subtract multiples of 10s ,
100s, 1000s,
tenths, hundredths
Year 6
E.g. 105.419 – 36.08
* know and practise mental
calculating strategies such as
subtracting near multiples of 10.
100 and adjusting, partitioning.
*Use inverse operation and
estimation to check answers.
*Number lines and portioning
can still be used for informal
jottings.
*Solve subtraction multi-step
problems in contexts, deciding
which operations and methods to
use and why
http://mathsframe.co.uk/en/r
esources/resource/242/Colum
n_Subtraction_using_Place_Va
lue_Counters
Westbury On Trym C of E Academy Calculation Policy 2016
Fluency of 2 digit - 2 digit
including with
Decimals
Partition second number to
subtract
Use number facts, bridging
and place value
Adjust numbers to
subtract
Difference between
Badges
YEAR 1 Multiplication
Multiplication
Written Methods
(informal jottings moving to
formal strategies)
Progression
Multiply with concrete
objects and pictorial
representation.
Multiplication is
represented as repeated
addition (sets, groups, lots
of)
Developing
conceptual
Key skills - NC programmes
of Study
Vocabulary
Just know it
Badges
Children will experience equal groups of
objects.
They will count in 2s, 10s and 5s and use
money to count.
*Understand multiplication
and division problems as
being the reverse.
Groups of, lots of,
times, altogether,
count, pairs, double.
Count in 2s
They will work on practical problem solving
activities involving equal sets or groups.
* Solve one step problems
involving multiplication using
concrete objects, pictorial
representations and arrays
Red and red star
Multiplication facts
2.5 and 10
Multiplication and
division facts; 2,5
and 10
*Make connections between
these objects and pictures
and counting in 2s, 10s and
5s.
Year 1
* Begin to understand
doubling.
They will use a hundred square to explore
visual patterns and patterns in numbers
when counting in 2s, 5s and 10s
The will be able to jump along a number
line in groups.
Westbury On Trym C of E Academy Calculation Policy 2016
Count in 10s
Doubles up to 10
Count in 5s
Double multiples of
10
YEAR 2 Multiplication
Multi
plicat
ion
Written Methods (informal jottings moving to formal
strategies) Progression
Multiply using arrays and repeated addition
ltiplcaionMultiplication
Developing conceptual
Key skills - NC
programmes of Study
Vocabulary
Just know it
Badges
They will see multiplication as
repeated addition
*Calculate mathematical
Groups of, lots
of, times,
altogether,
count, pairs,
double,
multiplied by,
column, row,
sets of, equal
groups…..times
as, big as.
2 x table
Red and red star
Multiplication
facts 2.5 and 10
Multiplication and
division facts; 2,5
and 10
Multiplication
Repeated addition on a number line. Make equal jumps along the
line number line to work out multiplication facts.
Write number sentences using the x and ÷ sign.
5 x 3 is 5 + 5 + 5 = 15
lots of 5 or
or 3
statements for
multiplication within the
multiplication tables and
write them using the
multiplication (×) and
equals (=) signs
Repeated addition can be shown
on a number line:
Year 2
Children should know that 5 x 3
has the same answer as
3 x 5 (commutativity)
Children should be able to model
a multiplication calculation using
an array. This knowledge will
support development of the grid
method.
Children should count in jumps,
multiples using a counting stick.
Bead strings can be used to show
groups of.
Westbury On Trym C of E Academy Calculation Policy 2016
*Recall and use
multiplication facts for
the 2, 5 and 10
multiplication tables
*Use commutativity
and inverse relations to
develop multiplicative
reasoning (for example,
4 × 5 = 20 and 20 ÷ 5 =
4).
*Connect the 10
multiplication table to
place value, and the 5
multiplication table to
the divisions on the
clock face.
*Solve problems
involving multiplication
using materials, arrays,
repeated addition,
mental methods, and
multiplication facts,
including problems in
contexts
5 x table
10 x table
Count in 3s
Doubles up to
20 and
multiples of 5
Recognise odd
and even
numbers.
YEAR 3 Multiplication
Multi
plicat
ion
Written Methods (informal jottings moving to formal strategies)
Progression
Multiply two digits by a single digit number.
ltiplcaionMultiplication
Key skills - NC
programmes of Study
Vocabulary
Just know it
Badges
Use their understanding of place
value to solve unknown
multiplication facts.
*Write and calculate
mathematical
statements for
multiplication using the
multiplication tables
that they know,
including for two-digit
numbers times onedigit numbers, using
mental methods
Groups of, lots
of, times,
altogether,
count, pairs,
double,
multiplied by,
column, row,
sets of, equal
groups…..times
as, big as,
partition, grid
method,
multiple,
product, tens,
units / ones,
value, digit.
Review 2, 3,
4, 5, 8 and 10
times tables.
Orange and
orange star
Multiplication
facts; 3,4, 6
and 11
Multiplication
and division
facts 3,4 6 and
11.
Multiplication
Children will continue to use repeated addition. Children will use
number lines to support their understanding.
Eg. 6 times 4
18 x 5
Developing
conceptual
Children should be able to
model a multiplication
calculation using an array.
They will begin to partition a
two digit number to multiply.
EG. If I know 10 x 8 = 80 then I
know… 100 x 8 = 800
Use a grid to support
multiplication:
13 x 4 = 10 x 4 + 3 x 4
Year 3
10 + 8
10 x 5
8x5
Children will continue to use arrays where appropriate leading into
the grid method of multiplication.
4 rows of 10
4 rows of 3
Move on to using Base 10 to move towards a more compact method.
4 rows of 13
Link: multiplication arrays
http://mathsframe.co.uk/en/res
ources/resource/131/representi
ng_multiplication__arrays_and_
number_lines
Continue to build on
multiplication facts by linking to
equal jumps: A bar model can
also be used to show equal
groups.
Move on to place value counters to show how we are finding groups
of a number. We are multiplying by 4 so we need 4 rows
Trio cards can be used to
demonstrate inverse of
multiplication and division.
Westbury On Trym C of E Academy Calculation Policy 2016
*Solve problems,
involving multiplication,
including positive
integer scaling
problems and
correspondence
problems in which n
objects are connected
to m objects (for
example, 3 hats and 4
coats, how many
different outfits?)
*Missing number
problems, involving
multiplication
Double two
digit numbers
(Through
doubling, they
connect the 2, 4
and 8
multiplication
tables)
6 x table or
review
others
YEAR 4 Multiplication
Multiplication
Written Methods (informal jottings
moving to formal strategies)
Progression
Multiply 2 and 3 – digit numbers by
a single digit using all multiplication
tables.
Developing
conceptual
ltiplcaionMultiplication
Vocabulary
Just know it
Badges
Multiplication
Groups of, lots of,
times, altogether,
count, pairs, double,
multiplied by, column,
row, sets of, equal
groups…..times as, big
as, partition, grid
method, multiple,
product, tens, units /
ones, value, digit,
approximate,
estimate, inverse
Multiplication facts
up to 12 x 12
Green and green
star
Multiplication
facts; 7, 8, 9 and
12
Multiplication and
division facts; 7,8,9
and 12
Key skills - NC programmes
of Study
43 x 6 by partitioning
Children will use the grid method.
Multiply by one digit number and show
the clear addition alongside the grid.
If I know 4 x 6 = 24
Then 40 x 60 is ten times bigger
Year 4
Some will move on to a grid method
multiplying HTU x U or even THTU
Grid method links:
.
Children should be taught special
strategies, e,g multiplying by 4 as
x2 then x2 again.
http://mathsframe.co.uk/en/resour
ces/resource/11/multiplication_grid
_method
http://mathsframe.co.uk/en/resour
ces/resource/131/representing_mul
tiplication__arrays_and_number_lin
es
Or to multiply by 5, you can multiply
by 10 and then halve the answer.
To multiply by 6, you can multiply by 3
and then double.
Westbury On Trym C of E Academy Calculation Policy 2016
*Use place value, known and
derived facts to multiply and
divide mentally, including:
multiplying by 0 and 1;
multiplying together three
numbers
*Multiply two-digit and
three-digit numbers by a
one-digit number
*Solve problems involving
multiplying and adding,
including using the
distributive law to multiply
two digit numbers by one
digit, integer scaling
problems and harder
correspondence problems
such as n objects are
connected to m objects
Recognise and use factor
pairs and commutativity in
mental calculations
Double larger
numbers and
decimals
YEAR 5 Multiplication
Multplication
Written Methods (informal jottings
moving to formal strategies)
Progression
Developing
conceptual
Multiply numbers up to 4 digits by a
one- or two-digit number using
a
formal written method,
ltiplcaionMultiplication
Just know it
*Identify multiples and
factors, including finding
all factor pairs of a
number, and common
factors of two numbers
Groups of, lots of,
times, altogether,
count, pairs, double,
multiplied by, column,
row, sets of, equal
groups…..times as, big
as, partition, grid
method, multiple,
product, tens, units /
ones, value, digit,
approximate, estimate,
inverse, square,
factor, integer,
decimal, short/ long
multiplication, “carry”
Multiplication
facts up to 12 x
12
*Know and use the
vocabulary of prime
numbers, prime factors
and composite (non-prime)
numbers
http://mathsframe.co.uk/en/resource
s/resource/11/multiplication_grid_me
thod
Year 5
Vocabulary
Multiplication
Some children will keep using the grid
method and using this method they will
be able to multiply decimals with one
decimal place by a single digit number,
approximating first. They should know
that the decimal points line up under
each other. Money is a good context to
introduce decimal multiplication.
e.g. 4.9 x 3
They will learn about the importance of
zero as a place holder, and the way
numbers move if multiplied.
Key skills - NC programmes
of Study
http://mathsframe.co.uk/en/resource
s/resource/131/representing_multiplic
ation__arrays_and_number_lines
They will then move onto a more
compact method for TU x U or HTU x
U, carrying below the line.
*Establish whether a
number up to 100 is prime
and recall prime numbers
up to 19
*Multiply numbers up to 4
digits by a one- or twodigit number using a
written method, including
long multiplication for twodigit numbers when ready.
*Multiply numbers mentally
drawing upon known facts
*multiply and divide whole
numbers and those
involving decimals by 10,
100 and 1000
Westbury On Trym C of E Academy Calculation Policy 2016
10, 100, 1000
times bigger
Double larger
numbers and
decimals
Partition to
multiply mentally
Badges
Bronze
All multiplication
facts
Silver
Fractions of an
amount
YEAR 6 Multiplication
multiplication
Written Methods (informal
jottings moving to formal
strategies) Progression
Many children will continue to
use the grid method.
Developing
conceptual
ltiplcaionMultiplication
Key skills- NC programmes of
Study
Vocabulary
Just know it
Badges
*Identify multiples and
factors, including finding all
factor pairs of a number, and
common factors of two
numbers
*Know and use the vocabulary
of prime numbers, prime
factors and composite (nonprime) numbers
Groups of, lots of,
times, altogether,
count, pairs, double,
multiplied by, column,
row, sets of, equal
groups…..times as, big
as, partition, grid
method, multiple,
product, tens, units /
ones, value, digit,
approximate, estimate,
inverse, square, factor,
integer, decimal,
short/ long
multiplication, “carry”
Multiplication
facts up to 12 x
12
Gold
X10 x 100 ÷10 ÷100
% of Numbers
Advanced
Multiplication
Short and long multiplication
using formal methods with a
range of complexity in numbers.
Year 6
*Establish whether a number
up to 100 is prime and recall
prime numbers up to 19
http://mathsframe.co.uk/en/resource
s/resource/11/multiplication_grid_me
thod
http://mathsframe.co.uk/en/resource
s/resource/131/representing_multipli
cation__arrays_and_number_lines
*Multiply numbers up to 4
digits by a one- or two-digit
number using a written
method, including long
multiplication for two-digit
numbers.
*Multiply numbers mentally
drawing upon known facts
*Multiply whole numbers and
those involving decimals by 10,
100 and 1000
*Use their knowledge of the
order of operations to carry
out calculations involving the
four operations
Westbury On Trym C of E Academy Calculation Policy 2016
Partition to
multiply mentally
Double larger
numbers and
decimals
Topaz badge
Converting
measures
Ruby Badge
Equivalent
Fractions
Emerald Badge
Converting volume
and weight
YEAR 1 Division
Subtraction
Written Methods
(informal jottings
moving to formal
strategies) Progression
Group and share small
quantities using
concrete objects and
pictorial
representations.
Developing
conceptual
Key skills - NC programmes
of Study
Vocabulary
Just know it
Badges
Children will understand equal groups and
share or group items out in play and problem
solving. Sharing and grouping will both be
used as models of division.
*Solve one-step problems
involving division, by
calculating the answer
using concrete objects,
pictorial representations
and arrays with the
support of the teacher
Share, share equally,
group, divide into groups
of, lots of
Count back in 2s
Red and red star
Multiplication
facts 2.5 and 10
Multiplication and
division facts; 2,5
and 10
Sharing model of division:
Year 1
I have 10 cubes, can you
share them equally in 2
groups?
Grouping model of division:
Divide quantities into equal
groups. Use cubes,
counters, objects or place
value counters to aid
understanding.
They will count in 2s and 10s and later in 5s.
Opportunities are given to discuss how many
groups- e.g counting money in 2s - how many
2s have we counted?
Children can match groups of numicon to a
given shape.
Westbury On Trym C of E Academy Calculation Policy 2016
*Begin to understand
halving.
Count back in 10s
Count back in 5s
How many 2s? 5s? 10s?
Halve multiples of 10
Halves up to 10
YEAR 2 Division
Subtraction
Written Methods (informal
jottings moving to formal
strategies) Progression
Group and share using the ÷
and = symbols.
Developing
conceptual
Key skills - NC programmes of
Study
Vocabulary
Just know it
Badges
15 = 3 x 5 in each group
(sharing)
*Show that although
multiplication of two numbers
can be done in any order
(commutative) division of one
number by another cannot.
Share, share equally,
group, divide into groups
of, lots of, divide,
divided by, division,
grouping, number line,
left over.
Division facts for 2, 5 and
10 times tables.
Red and red star
Multiplication facts
2.5 and 10
Multiplication and
division facts; 2,5
and 10
Children will learn about
division as Sharing equally
6 sweets shared between 2
people, how many do they each
get?
*Recall and use division facts for
the 2, 5 and 10 multiplication
tables, including recognising odd
and even numbers
Year 2
15 ÷ 3 = 5 groups of 3 (grouping)
They will also learn about it as
grouping or repeated
subtraction. There are 6
sweets, how many people can
have 2 sweets each?
Link division to multiplication by
creating an array and thinking
about the number sentences that
can be created
15 ÷ 5 =
15 ÷ 3 =
This can be modelled as
repeated subtraction using a
number line
6÷3=2
Draw an array and use lines to split
the array into groups to make
multiplication and division
sentences.
Use language of division linked to
multiplication facts and the inverse.
Westbury On Trym C of E Academy Calculation Policy 2016
*Calculate mathematical
statements for division within
the multiplication tables and
write them using the division (÷)
and equals (=) signs
*Solve problems involving
division, using materials, arrays,
repeated addition and
subtraction, mental methods,
and division facts, including
problems in contexts
Halves up to 20
Count back in 3s
YEAR 3 Division
Subtracti
on
Written Methods (informal
jottings moving to formal
strategies) Progression
Divide 2 – digit numbers by a
single digit (with no remainder in
the final answer)
Year 3, children will think about
division as sharing but the
emphasis for moving towards
written calculations will be on
grouping
Key skills- NC programmes of
Study
Vocabulary
Just know it
Badges
Children will use arrays to
understand grouping.
*Recall and use division facts
for the 3, 4 and 8 times tables
Share, share equally,
group, divide into
groups of, lots of,
divide, divided by,
division, grouping,
number line, left
over, inverse, short
division, carry,
remainder.
Review division facts for 2,
5 and 10 times tables.
Orange and orange
star
Multiplication
facts; 3,4, 6 and
11
Multiplication and
division facts 3,4
6 and 11.lication
facts; 3,4, 6 and
11
Multiplication and
division facts 3,4
6 and 11.
20 ÷ 4 =
20 ÷ 5 =
Children will understand grouping
through partitioning
43 ÷ 3 If I know 10 x 3 …
Year 3
Children will continue to use
repeated subtraction using a
number line
24÷4=6
Developing
conceptual
Children can then move onto
calculations involving remainders.
14 ÷ 3 =
Children will use the realtionship
between multiplication and division
to help them work out calculations.
Westbury On Trym C of E Academy Calculation Policy 2016
*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
*Solve problems, including
missing number problems,
involving multiplication and
division, including positive
integer scaling problems and
correspondence problems in
which n objects are connected
to m objects.
Division facts: 4, 3, 6 and 8
Halve two digit numbers
YEAR 4 Division
Division
Written Methods (informal jottings
moving to formal strategies)
Progression
Divide up to 3 – digit numbers by a
single digit
Year 4
Children will develop their use of
repeated subtraction to be able to
subtract multiples of the divisor.
Initially, these should be multiples of
10s, 5s, 2s and 1s – numbers with
which the children are more familiar.
72÷5=14 r 2
Developing
conceptual
Key skills - NC
programmes of Study
Vocabulary
Just know it
Badges
Grouping using partitioning
196 ÷ 6 If I know 3 x 6 … then 30 x 6…
*Use place value, known
and derived facts to
divide mentally,
including: dividing by 1.
Share, share
equally, group,
divide into
groups of,
lots of,
divide,
divided by,
division,
grouping,
number line,
left over,
inverse, short
division,
carry,
remainder,
divisible by,
factor.
All division
facts up to x 12
Green and green
star
Multiplication
facts; 7, 8, 9 and
12
Multiplication and
division facts; 7,8,9
and 12
‘
When children are secure using the
number line (including chunking on a
number line) they can then move to
vertical chunking.
Continue to use language of division linked to
multiplication facts. Children understand that division is
the inverse of multiplication.
Chunking down:
http://mathsframe.co.uk/en/resources/resource/102/div
ision_by_chunking_down
Westbury On Trym C of E Academy Calculation Policy 2016
*Recall multiplication
and division facts for
multiplication tables up
to 12 × 12
10 times
smaller
Halve larger
numbers and
simple decimals
YEAR 5 Division
Subtraction
Written Methods (informal jottings moving
to formal strategies) Progression
Divide up to 4 – digit numbers by a single
digit, including those with remainders.
Year 5
Children, if ready, can move on to the written
formal method of division when the divisor is
a single digit. Children will continue to use
chunking when the divisor is 2 digits.
Children should be taught how to Interpret
remainders as whole numbers and fractions by
rounding as appropriate for the context.
Developing
conceptual
Model using the short
method of division alongside
a number line.
Use diennes and place value
counters to support written
method
NCETM Professional
development – how to use
place value counters to
support short division
(various video material)
https://www.ncetm.org.uk/re
sources/43589
http://mathsframe.co.uk/en/resources/resou
rce/102/division_by_chunking_down
Westbury On Trym C of E Academy Calculation Policy 2016
Key skills - NC
programmes of Study
*Divide numbers mentally
drawing upon known facts
Divide whole numbers
and those involving
decimals by 10, 100 and
1000
*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
Vocabulary
Just know it
Badges
Share, share equally,
group, divide into groups
of, lots of, divide,
divided by, division,
grouping, number line,
left over, inverse, short
division, carry,
remainder, divisible by,
factor, quotient, prime
numbers, prime factors.
All division facts up
to 12 times table.
Bronze
All multiplication
facts
10, 100, 1000 times
smaller
Partition to divide
mentally
Halve larger numbers
and decimals
Silver
Fractions of an
amount
YEAR 6 Division
Subtraction
Written Methods (informal jottings moving to formal
strategies) Progression
Divide at least 4 – digits by both single – digits and 2 –
digit numbers.
Children, if ready, can move on to the written formal method
of division when the divisor is a single digit.
Developing
conceptual
Model using the short
method of division
alongside a number line.
Use diennes and place value
counters to support
written method
When ready children will learn how to use the formal written
method of division for 2 or more digit divisors
Year 6
NCETM Professional
development – how to use
place value counters to
support short division
(various video material)
https://www.ncetm.org.uk/
resources/43589
Key skills - NC
programmes of Study
*Perform mental
calculations, including
with mixed operations
and large numbers
*Divide numbers up to
4 digits by a two-digit
whole number using the
formal written method
of long division,
*Use their knowledge
of the order of
operations to carry out
calculations involving
the four operations
Vocabulary
Just know it
Badges
Share, share
equally, group,
divide into groups
of, lots of, divide,
divided by,
division, grouping,
number line, left
over, inverse,
short division,
carry, remainder,
divisible by,
factor, quotient,
prime numbers,
prime factors,
common factors.
Division facts up
to 12 times
tables.
Gold
X10 x 100 ÷10 ÷100 %
of Numbers
Advanced
Partition to
divide mentally
Halve larger
numbers and
decimals
Topaz badge
Converting measures
Ruby Badge
Equivalent Fractions
Emerald Badge
Converting volume
and weight
Amethyst
Percentages of an
amount
Rose Quartz
Improper fractions
to mixed numbers.
Amber
Rounding
Children should be taught how to Interpret remainders as
whole numbers and fractions by rounding as appropriate for
the context.
Sun stone
Calculating with
fractions.
Pearl
Order of operations.
Westbury On Trym C of E Academy Calculation Policy 2016