Rec
Addition
Children are encouraged to develop
a mental picture of the number
system in their heads to use for
calculation.
Relate addition to combining two
groups of objects.
They develop ways of recording
calculations using pictures etc.
Bead strings or bead bars can be
used to illustrate addition.
e.g. 7 + 3 = 10
The children will use number lines
and practical resources to support
calculation and teachers
demonstrate the use of a number
line.
Subtraction
Children are encouraged to develop
a mental picture of the number
system in their heads to use for
calculation.
Relate subtraction to ‘taking away’.
The children develop ways of
recording calculations using pictures
etc.
Bead strings or bead bars can be
used to illustrate subtraction
including bridging through ten by
counting back.
e.g. 10 – 7 = 3
The children will use number lines
and practical resources to support
calculation and teachers
demonstrate the use of a number
line.
Multiplication
Children will experience equal
groups of objects.
Count repeated groups of the same
size.
Some children may begin to count in
5s and 10s.
Division
Children will understand equal
groups and share items out in play
and problem solving.
Share objects into equal groups.
The children will work on practical
problem solving activities involving
equal sets or groups.
Children will learn to count in 2s
through pairs of objects.
Children will solve problems using
halving and sharing.
Year 1
Addition
Using pictures.
Bead strings or bead bars can be used
to illustrate addition including
bridging through 10 by counting on.
Subtraction
Using pictures.
Bead strings or bead bars can be used
to illustrate subtraction including
bridging through 10 by counting back.
e.g. 6 + 4 = 10.
e.g. 10 – 6 = 4
The children use number lines and
practical resources to support
calculation and teachers demonstrate
the use of the number line.
Children will draw the Empty Number
Line.
Children begin to use number lines to
support their own calculations using a
numbered line to count on in ones.
Children need to understand addition
as combining groups and counting or
jumping on in steps of 1.
Add single digit numbers using a
beadframe 20.
Add and subtract one-digit and two
digit numbers to 20, including zero.
Read, write and interpret
mathematical statements involving
addition (+), subtraction (-) and
equals (=) signs.
The children use number lines and
practical resources to support
calculation and teachers demonstrate
the use of the number line.
Children will draw the Empty Number
Line.
Children begin to use number lines to
support their own calculations using a
numbered line to count back in ones.
The number line should also be used
to show that 6 – 3 means the
‘difference between 6 and 3’ or the
‘difference between 3 and 6’ and how
many jumps they are apart counting
back in ones.
Children need to understand
subtraction as taking away and
counting or jumping back.
Add and subtract one-digit and two
digit numbers to 20, including zero.
Multiplication
Children will experience equal groups
of objects.
The children will count in 2s, and 10s
and begin to count in 5s.
The children will work on practical
problem solving activities involving
equal sets or groups.
Division
Children will understand equal groups
and share items out in play and
problem solving.
They will count in 2s and 10s and later
in 5s.
Solve one-step problems involving
multiplication and division, by
calculating the answer using
concrete objects, pictorial
representations and arrays with the
support of the teacher.
Solve one-step problems involving
multiplication and division, by
calculating the answer using
concrete objects, pictorial
representations and arrays with the
support of the teacher.
Year 2
Addition
Children will begin to use Empty Number
Lines themselves starting with the larger
number and counting on.
First counting on in tens and ones/units.
e.g. 45 + 31 = 76
Then helping the children to become more
efficient by adding the ones/units in one
jump.
Followed by adding the tens in one jump
and the ones/units in one jump.
Children need to be familiar with counting
on in tens from any number, recognising
patterns with numbers.
Children to develop their mental skills of
‘overjumping’ to aid calculation.
Add and subtract numbers using concrete
operations, 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
Non Statutory – recording in columns
supports place value and prepares for
formal methods.
Subtraction
Children will begin to use Empty
Number lines to support calculations.
Counting back:
First counting back in tens and
ones/units.
e.g. 72 – 23 = 49
Multiplication
Count in steps of 2, 3, and 5 from 0,
and in tens from any number forward
or backward.
Recall and use multiplication and
division facts for the 2, 5 & 10 times
tables.
Children will develop their
understanding of multiplication and
use jottings to support calculation.
Repeated addition
3 times 5 is: 3 + 3 + 3 + 3 + 3 = 15
or 3 x 5
Then children become more efficient
by subtracting the ones/units in one
jump.
e.g.
Repeated addition can be shown easily
on a number line or bead frame.
As children become confident the tens
can be subtracted in larger steps until
they are completed in one jump.
Again, the children need to apply their
knowledge of number patterns to
ensure accuracy.
Commutativity
Children should know that 3 x 5 has
the same answer as 5 x 3.
This can be shown on a number line by
counting in steps of 3 or 5 and
identifying the finishing point on both
lines.
Add and subtract numbers using
concrete operations, 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
Division
Children will develop their
understanding of division and
use jottings to support their
calculation.
Sharing equally
6 sweets are shared between
2 people, how many do they
get each?
Grouping or repeated
subtraction
There are 6 sweets, how many
people can have 2 sweets
each?
Arrays
Children should be able to model a
multiplication calculation using an
array. This knowledge will support the
development of the grid method.
6 x 3 = 18
3 x 6 = 18
Using symbols to stand for
unknown numbers to
complete equations using
inverse operations
e.g. ? ÷ 2 = 4
20 ÷ ? = 5
When appropriate, the
children will taught
remainders.
Year
3
Addition
Children will continue to use the Empty
Number Line with increasingly larger numbers.
Methods include jumping in hundreds, tens and
ones and bridging.
Mentally children will continue to be taught
over jumping.
The largest number will be placed at the start
of the number line, counting in tens and blocks
of ones.
e.g. 150 + 58 = 208
Subtraction
Children will continue to count back on
an Empty Number Line.
Once secure the children will be
introduced to column methods.
For numbers that are near multiples of ten the
children will be taught to compensate.
e.g. 49 + 73
Add the nearest multiple of ten (50)
So, 73 + 50 = 123 then subtract the 1 which was
added to 49,
Therefore 123 – 1 = 122.
Subtract numbers up to three digits,
using formal written methods of
columnar subtraction.
Subtract numbers mentally, including:
 three-digit number and ones
 a three-digit number and tens
 a three-digit number and
hundreds
Multiplication
Count from 0 in multiples of 4, 8, 50
and 100.
Recall and use multiplication and
division facts for the 3, 4 and 8 times
tables.
Children will continue to use
repeated addition as a strategy for
multiplication.
4 x 6 is:
4 + 4 + 4 + 4 + 4 + 4 = 24
Reinforced by commutativity
So,
6 x 4 is:
6 + 6 + 6 + 6 = 24
Arrays
Children should be able to model a
multiplication calculation using an
array. This knowledge will support
with the development of the grid
method.
6 x 3 =18
Add numbers up to three digits, using formal
written methods of columnar addition.
Children will be taught equivalence
? + ? = ? - ? e.g. 6 + 7 = 14 – 1
3 x 6 = 18
Partitioning
As children become confident in
tables facts to 10 x 10 multiplication
will be extended to TU x U
e.g 18 x 6 = 108
Add and subtract numbers mentally, including:
 three-digit number and ones
 a three-digit number and tens
 a three-digit number and hundreds
Progressing to formal methods
Division
Ensure that the emphasis in
Year 3 is on grouping rather
than sharing.
Children will continue to use
repeated addition.
12 ÷ 4 = 3
3 equal jumps of 4 can be
made to get to the target
number of 12.
Children will also move onto
calculations with remainders.
e.g. 13 ÷ 4 = 3 r 1
Using an Empty Number Line
to count in steps of 4. How
close can you get to the
target number without going
beyond?
The difference between the
nearest multiple and the
target number equals the
remainder.
Progressing to formal
methods
Addition
Year 4 Children will be taught the column
method, adding the least significant
digits first.
Initially this will be taught as:
e.g 67 + 24 =
67
+ 24
11 (7 + 4)
80 (60 + 20)
91
267 + 85 =
267
+85
12 (5 + 7)
140 ( 60 + 80)
200
352
Children will then move on to ‘carry
below the line’
625
+48
673
1
Using similar methods children will:
 add numbers with up to 4
digits using formal written
methods
 begin to add two or more
three digit sums of money,
with or without adjustment
from the pence to the
pounds
 know that the decimal points
must line up under each
other, particularly when
adding or subtracting
Subtraction
Children will continue to use Empty
Number Line with increasingly large
numbers.
Partitioning and decomposition
Partitioning – demonstrated using
arrow cards
Decomposition – base 10 materials
and counters.
89
-57
= 80 + 9
50 + 7
30 + 2 = 32
Begin to exchange
71
-46
- 70 + 1
40 + 6
Multiplication
Count in multiples of 6, 7, 9, 25 and
1000
Recall multiplication and division facts
for times tables to 12 x 12
Children will continue to use arrays
where appropriate leading into the grid
method for multiplication.
Short division TU ÷ U
Chunking method
Grid method
TU x U
(short multiplication – multiplication by
a single digit
e.g. 14 x 2
This calculation
should be read as
‘take 6 from 1’.
72 ÷5
10 x 5 = 50
4 x 5 = 20
70
= 14 r 2
This method can be expanded for
larger numbers, with children looking
to see if they can multiply by 10
initially and then by 5. Children to
apply multiplication skills to aid
division.
- 60 + 11
40 + 6
20 + 5 = 25
Children should:
 be able to subtract numbers
with up to 4 digits using
columnar subtraction
 Using this method, children
should begin to find the
difference between two
three digit sums of money.
 Know that decimal points
must line up under each
other.
Division
Children will develop further their
use of repeated addition on an empty
number line to add multiples of the
divisor. Initially there should be
multiples of 10s, 5s and 2s – numbers
with which the children are more
familiar.
This method can be extended to any
two digit number, with the children
applying their understanding of single
multiplication to multiples of 10.
Multiply two-digit and three-digit
numbers by a one-digit number using
formal written layout
Remainders to be shown as integers
(whole numbers).
Continue to progress to formal
methods where appropriate.
Year 5
Addition
Children will extend the carrying method to
numbers with at least four digits.
Using similar methods children will:
 add several numbers with different
numbers of digits.
 begin to add two or more numbers
with decimal places and these
numbers to have up to 3 decimal
places.
 know that decimal points should
line up under each other,
particularly when adding or
subtracting mixed amounts e.g.
3.2m & 280cm
Add and subtract numbers mentally with
increasingly large numbers.
Add whole numbers with more than four
digits using the formal method of columnar
addition.
Subtraction
Partitioning and decomposition
Using counters where appropriate.
754
86
Step 1
-
700 + 50 + 4
80 + 6
Step 2 700 + 40 + 14
80 + 6
(adjust from T to U)
Multiplication
Count forwards or backwards in
steps of powers of 10 for any
number up to 1,000,000
Grid method
HTU x U
(short multiplication by a single digit)
e.g. 367 x 5
 Children to approximate first
Step 3 600 + 140 + 14 (adjust from H to T)
80 + 6
600 + 60 + 8 = 668
Once secure, subtract whole
numbers with more than 4 digits
using formal written methods.
Children should:
 be able to subtract numbers
with different numbers of
digits.
 begin to find the difference
between two decimal
fractions with up to three
digits and the same number
of decimal places.
 know that decimal points
must line up under each
other.
Progressing to …
Multiply numbers up to 4 digits by a
one or two digit number using a
formal written method, including
long multiplication for two – digit
numbers
Division
Children will continue to
use written methods to
solve short division
Divide numbers up to 4
digits by a one-digit
number using the formal
written of short division
and interpret remainders
appropriately for the
context
Long division using the
formal method
196 ÷1 6
12 r 4
196
160 (10 x1 6)
36
32 (2 x 16)
4
Answer = 12 r 4
16
Any remainders shown as
integers (whole numbers)
and where appropriate
decimal numbers.
Year 6
Addition
Children should extend the
carrying method to a number with
any number of digits including
decimals.
Subtraction
Continue with standard
decomposition method.
Children should:
 be able to subtract
Using this method children should
numbers with different
be able to:
numbers of digits.
 add several numbers with
 be able to subtract two or
different numbers of digits.
more decimal fractions
 begin to add two or more
with up to three digits and
decimal fractions with up to
either one or two decimal
four digits and either one
places.
or two decimal places.
 know that decimal points
 know that each decimal
must line up with each
point should line up under
other.
each other, particularly
when adding or subtracting
mixed amounts,
 e.g. 401.2 + 26.85 + 0.71
perform mental calculations,
including with mixed operations
and large numbers
Multiplication
Multiply multi digit numbers up to 4
digits by a two digit whole number
using a formal written method of long
multiplication
Division
Divide numbers up to 4-digits by a
two-digit whole number using the
formal written method of short
division where appropriate for the
context.
Divide numbers up to 4 digits by a
two-digit whole number using the
formal method of long division,
and interpret remainders as whole
number remainders, fractions, or
by rounding, as appropriate for the
context.
972 ÷ 36
36
27
972
720
252
180
72
72
0
( 20
x 36)
( 5
x 36)
(2
x 36)
Any remainders should be shown as
fractions, simplified where possible.
Remainders to be converted to
decimals where possible using the
formal method.
V2 – SEPTEMBER 2015