Progression and Methods in the Four Operations.
Addition
Reception Using quantities and
objects, they add two
single-digit numbers
and count on or back
to find the answer.
Year1
Read, interpret and
practise writing
mathematical
statements involving
addition (+) and equals
(=) signs.
Add and subtract 1digit numbers and 2digit numbers to 20
(9+9=), including
zero using a 100
square.
Add three 1-digit
numbers using a
using a 100 square.
Solve one step
problems that involve
addition, using
concrete objects, and
pictorial
representations, and
missing number
problems.
Subtraction
Using quantities
and objects, they
subtract two
single-digit
numbers and
count on or back
to find the
answer.
Read, interpret
and practise
writing
mathematical
statements
involving
subtraction (+)
and equals (=)
signs accurately.
Subtract 1-digit
number and 2digit numbers to
20 (18-9),
including zero
using a100
square.
Solve one step
problems that
involve addition,
using concrete
objects, and
pictorial
representations,
and missing
number problems.
Solve simple word
problems that
involve
subtraction.
Multiplication
Division
They solve
problems, including
sharing, using
objects.
Solve one-step problems
involving multiplication,
by calculating the
answer using concrete
objects (e.g. pin
boards), pictorial
representations and
arrays with the support
of the teacher.
Solve one-step
problems involving
division, by
calculating the
answer using
concrete objects
and pictorial
representations.
Year 2
Add numbers using a
100 square,
including:
-a two-digit number
and ones
-a two-digit number
and tens
-two two-digit
numbers
-adding three onedigit numbers
Begin to use column
addition without
carrying.
Solve problems with
addition.
Show that addition of
two numbers can be
done in any order
(commutative) .
Recognise and use the
inverse relationship
between addition and
subtraction and use
this to check
calculations and
missing number
problems.
Calculate the value of
unknown numbers in a
number sentence.
Year 3
Add numbers with up
to three digits, using
column addition.
Estimate the answer to
a calculation and use
inverse operations to
check answers.
Solve problems,
including missing number
problems, using number
facts, place value, and
more complex addition
and subtraction.
Subtract
numbers using a
100 square,
including:
-a two-digit
number and ones
-a two-digit
number and tens
-two two-digit
numbers
-adding three
one-digit
numbers
Calculate mathematical
statements for
multiplication within
the multiplication
tables and write them
using the multiplication
(×),and equals (=)
signs.
Solve problems
with subtraction.
Show subtraction
cannot be done in
any order
Solve problems involving
multiplication using
arraysand multiplication
and division facts,
including problems in
contexts.
Solve problems
involving division,
using the sharing
of practical
resourcesand
division facts,
including problems
in contexts.
Multiply 1-digit and 2-digit
numbers by 10 or 100;
understanding the effect.
(To be taught first)
Write and calculate
mathematical
statements for
division using the
multiplication tables
that they know.
Recognise and use
the inverse
relationship
between addition
and subtraction
and use this to
check calculations
and missing
number problems.
Calculate the
value of unknown
numbers in a
number sentence.
Subtract numbers
with up to three
digits, using
column
subtraction.
Estimate the
answer to a
calculation and use
inverse operations
to check answers.
Solve problems,
including missing
number problems,
Show that multiplication
of two numbers can be
done in any order
(commutative) .
Write and calculate
mathematical statements
for multiplication, using
the multiplication tables
that they know.
Multiply a two-digit
number by a one-digit
numbers, using the grid
method.
Calculate
mathematical
statements for
division within the
multiplication
tables and write
them using the
division (÷) and
equals (=) signs.
Show that division
cannot be done in
any order.
Divide a two-digit
number by a onedigit number, using
the bus stop
method.
Solve problems,
including missing
using number facts,
place value, and
more complex
addition and
subtraction.
Year 4
Add numbers with up
to 4 digits using
column addition.
Estimate and use
inverse operations to
check answers to a
calculation.
Solve addition and
subtraction two-step
problems in contexts,
deciding which
operations and
methods to use and
why.
Year 5
Add whole numbers
with more than 4
digits, using column
addition.
Solve addition and
subtraction multistep problems in
contexts, deciding
which operations and
methods to use and
why.
Subtract numbers
with up to 4 digits
using column
subtraction.
Estimate and use
inverse operations
to check answers
to a calculation.
Solve addition and
subtraction twostep problems in
contexts, deciding
which operations
and methods to use
and why.
Subtract whole
numbers with
more than 4
digits, using
column
subtraction.
Solve addition and
subtraction multistep problems in
contexts, deciding
which operations
Solve problems, including
missing number problems,
involving multiplication,
including integer scaling
problems and
correspondence problems
in which n objects are
connected to m objects.
Multiply two-digit and
three-digit numbers
by a one-digit
number, using the
grid method.
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.
Multiply whole numbers
and those involving
decimals by 10, 100 and
1000 (To be taught
first).
Multiply numbers up
to 4 digits by a oneor two-digit number
using the grid
method.
number problems,
involving
multiplication and
division, including
integer scaling
problems and
correspondence
problems in which n
objects are
connected to m
objects.
Divide two-digit
and three-digit
numbers by a
one-digit number
using the bus stop
method.
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.
Divide whole
numbers and those
involving decimals
by 10, 100 and
1000 (To be taught
first).
Divide numbers up
to 4 digits by a
one-digit number
using the bus stop
method and
and methods to use
and why.
Year 6
Add negative
integers (using a
number line if
required).
Use estimation to
check answers to
calculations and
determine in the
context of a
problem.
Carry out combined
calculations
involving the four
operations and
state the order of
operations.
Subtract
negative integers
(using a number
line if required).
interpret
remainders
appropriately for
the context.
Multiply numbers
with at least 4digits by a 2-digit
whole number using
the grid method.
Divide numbers
up to 4-digits by
a 2-digit number
using chunking,
and interpret
Use estimation to
remainders as
check answers to Multiply numbers
whole number
calculations and
with up to 2 decimal remainders,
determine in the places by 1-digit
fractions,
context of a
and 2-digit whole
decimals or by
problem.
numbers using the
rounding.
grid method.
Carry out
Divide numbers
combined
Use estimation to
with up to two
calculations
check answers to
decimal places
involving the four calculations and
by 1-digit (bus
operations and
determine in the
stop) and 2-digit
state the order
context of a
(chunking) whole
of operations.
problem.
numbers.
Use estimation to
check answers to
calculations and
determine in the
context of a
problem whether
an answer should
be rounded or
written as a
fraction or a
decimal.