Oak Tree Primary School- Progression in Calculations document
This document provides guidance to all teachers and teaching assistants involved in children’s mathematical learning. It
focuses on the stages (not linked to Year groups or NC levels) of development in the ability to calculate – using addition,
subtraction, multiplication and division. It gives examples and suggestions for key activities.
Knowledge of number facts is key to developing confidence in calculation so there will be a focus of discrete teaching of
number facts.
If at any stage a child is having difficulties understanding the process then refer to the previous stage. Children should not
be rushed, but moved on when they are ready.
Children will work through the school’s agreed progression, with the number line being the school’s preferred method in the
early stages, leading to the knowledge and understanding of a compact standard method for each numerical operation by the
end of year 6. Potential level 6 children must show they can perform compact methods with confidence,speed and
accuracy.
Monitoring of Written Calculations.
It is important that procedures are in place to ensure that all staff are aware of the progression through calculations, and
that children are taught appropriate methods for their ability. The monitoring of this will include work sampling, monitoring
of plans, pupil interviews, test analysis and monitoring of target books.
M. Gash. Update 2013
Addition
Stage P (Pre school)
Stage 1
Stage 2
Stage 3
Objectives;
Begin to use the vocabulary involved in
addition.
Finding one more than a number from 1
to 10
Strategy; combining two groups and
counting to establish total.
Recording; teacher demonstration of
pictorial recording where appropriate.
Photographs.
Vocab; more, and , make, sum, total,
altogether
Equipment; every day objects, counters,
fingers etc.
Objectives;
Relating addition to combining 2 groups of
objects.
Relate addition to counting on.
Begin to use + and = to record calculations.
Strategy; combining two or more groups and
counting to establish total, counting on from
one number.
Recording; Teacher demonstrate transferring
objects onto a standard number line. Teacher
demonstration of calculation to match pictorial
recording using number lines and use of
standard notation when appropriate.
Vocab; add, more, and, make, sum, total,
altogether
Equipment; number lines, counters, fingers
Objectives;
Begin to recognise that
addition can be done in any
order.
Begin to introduce a
number line into whole
class teaching with the
adult modelling.
Pencil and paper informal
approaches – jottings
Strategy; Re-ordering to
begin with the largest
number and counting on.
Recording; Children to
continue to develop
pictorial recording, use
standard notation, using a
tally. Record addition on a
standard number line.
Begin to record on their
own number line, in jumps
of one, starting with the
largest number.
Vocab; add, more, and,
make, sum, total,
altogether, plus, equals.
Equipment; number lines,
counters, fingers, addition
& subtraction facts ITP.
Objectives;
Use knowledge that
addition can be done in any
order.
Partition additions into
tens and units and
recombine.
Use a number line to teach
children to mentally count
on.
To begin to introduce the
number line for the whole
class teaching of addition
TU+U.
Strategy; Reordering to
begin with largest number.
Partitioning other numbers
eg into tens and units.
Counting on in tens and
ones.
Recording; Children to
continue to develop
recording especially using
their own number lines and
standard notation to show
partitioning and
recombining.
Equipment; number lines,
hundred squares, base 10,
addition and subtraction
facts ITP.
Stage 4
Stage 5
Stage 6
Stage 7
Objective; Use informal pencil and paper methods
to support recording of addition TU+U then TU+TU
developing use of the number line.
Extend to HTU+HTU.
Objective; Begin to use column
addition for HTU+TU where the
calculation can not easily be done
mentally.
Adding least significant digit first
– units then tens
Strategy; reordering to begin with
largest number.
Recording; Children to make
decisions about appropriate
recording especially expanded
vertical method. Also use of own
number lines.
Vocab; add, more, and ,make, sum,
total, plus, addition, increase
Equipment; number lines, base 10.
Objective; Developing and using
with confidence column addition.
(Confident level 3+ ability children)
Strategy; Compact vertical method
beginning with least significant digit.
Recording; Children to make
decisions about appropriate recording
especially compact vertical standard
written method. Also use of own
number lines.
Vocab; add, more, and make, sum,
total, altogether, plus, addition,
increase
Equipment; number lines, base 10
Objective; To use a compact written
method for calculations involving
decimals (money, measures etc)
Strategy; Compact vertical method
beginning with least significant digits.
Recording; Children to make decisions
about appropriate recording especially
compact vertical standard written
method. Also use of own number line.
Vocab; add, more, and, make, sum,
total, altogether, plus, addition, increase
Equipment; number lines, base 10
Key skill; Always add tens first.
Strategy; reordering to begin with largest number,
partitioning other numbers eg. Into hundreds, tens
and units, counting on in hundreds, tens and ones.
Recording; Children to make decisions about
appropriate recording especially using their own
number lines. Begin to introduce expanded vertical
standard written method if secure with other
recording.
Vocab; add, more, and, make, sum, total, altogether,
plus.
Equipment; number lines, hundred squares, base 10.
Grading of difficulty
No carrying
+23
315
+ 42
+ 624
extra digit in answer
+94
561
+73
+ 718
47
 76
13
110
123
carrying ones to tens
+47
237
+25
+ 516
carrying tens to hundreds
+371
293
+485
+ 541
carrying ones to tens and tens to
hundreds
376
295
+485
+ 547
Subtraction.
Stage P (Pre school)
Stage 1
Stage 2
Stage 3
Objectives; Begin to use the
vocabulary involved in subtraction.
Finding one less than a number from 1
to 10.
Strategy; Begin to recognise
subtraction as taking away and
counting back. Also compare two
numbers to find difference.
Recording; teacher demonstration of
appropriate pictorial recording where
appropriate.
Vocab; take away, leaves.
Equipment; every day objects,
counters, fingers.
Objectives; Begin to relate subtraction
to taking away, difference between and
how many more to make.
Begin to use the – and = signs to record
mental calculations.
Strategy; Recognise subtraction as
taking away and counting back,
comparing two numbers to find the
difference.
Recording; teacher demonstration of
calculation to match pictorial recording
using standard notation of – and =.
Vocab; take away, leaves, how many
are left, how many fewer than,
difference between
Equipment; every day equipment,
counters, fingers
Objectives; Understand the operation of
subtraction as take away, difference and how
many more to make. Use the – and + signs.
Adult modelling using a number line to
support counting on.
Strategy; Recognise subtraction as taking away
and counting back as the most efficient way of
finding difference.
Recording; Children to continue to develop
pictorial recording, use standard notation,
begin to record on a standard number line.
Teacher to demonstrate drawing own number
line.
Vocab; take away, leaves, how many are left,
how many fewer than, difference between,
how much more is, subtract, minus, equals,
less
Equipment; number lines, counters, fingers,
addition and subtraction facts ITP, difference
ITP
To understand subtraction as the
inverse of addition. Use a number line
to support counting on, TU-U then
TU-TU.
Strategy; recognise subtraction as
taking away and counting back as the
most efficient way of finding the
difference.
Recording; Children to continue to
develop recording especially using
their own number lines and standard
notation. Counting back in tens and
then ones.
Vocab; take away, leave, how many
are left, how many fewer than,
difference between, how much more,
subtract, minus, subtraction, less
Equipment; number linees, hundred
squares, base 10, addition and
subtraction ITP, difference ITP
I have 2 in my hand how many
more do I need to make 6? …3
,4, 5, 6, (COUNTING ON)

12 – 7 (counting back) - marked line
3 4 5
6
7
8
9
10 11 12
Stage 4
Stage 5
Stage 6
Stage 7
Objectives; Use jottings, draw own
number line to support informal
recording of subtraction by counting
on.
 TU – TU. Count back in ones to
next multiple of ten, count back in
tens to last multiple of ten, count
back in ones to the target number.
 HTU – TU. Count back in ones to
next multiple of ten. Count back in
tens to the next hundred. Count
back in hundreds to the last
hundred. Count back in tens to the
last ten. Count back in ones to the
target number.
 Or count back in tens from the
number to the last possible
multiple, then count back ones.
Develop informal recording for two
whole numbers less than 1000. HTU –
TU
Strategy; recognise subtraction as
taking away and counting back
Recording; Children to make decisions
about appropriate recording especially
using their own number lines.
Vocab; take away, leave, how are
many are left, how many fewer than,
difference between, how much more is,
subtract, minus, subtraction
Equipment; number lines, hundred
squares, base 10.
Objectives; Introduce expanded
decomposition with no exchange.
Working with the least significant digit
first.
Use expanded method with money and
measures, with no exchange.
Strategy; Recognise subtraction as
taking away and counting back as the
most efficient way. Teacher to model
decomposition with no exchange.
Recording; Children to make decisions
about appropriate recording especially
expanded vertical standard written
method. Also use own number lines
and standard notation to show
partitioning and recombining.
Vocab; take away, leave, how many
are left, how many fewer than,
difference between, how much more is,
subtract, minus.
Equipment; number lines, arrow cards
Objectives; Continue to develop the expanded
method of decomposition with exchange.
Introduce compact method for subtraction,
using a lot of recap of expanded method to
support the children’s learning of this stage.
Strategy; Teacher to model decomposition
with exchange. If the children are secure with
this, introduce the standard compact method
with no exchange first, then with exchange.
Recording; Children to make decisions about
appropriate recording especially expanded or
compact vertical standard written method. Also
use of own number line.
Vocab; take away, leave, how many are left,
how many fewer than, difference between,
how much more is, subtract, minus,
subtraction, decrease
Objectives; To use compact written
method for calculations involving
decimals (money, measures)
Strategy; Compact vertical method
beginning with least significant digit,
– horizontal or expanded vertical
method recording.
Recording; Children to make decisions
about appropriate recording especially
expanded or compact vertical standard
written method. Also use own number
line.
Vocab; take away, leave, how many
are left, how many fewer than,
difference between, how much more is,
subtract, minus, subtraction, decrease.
+0.09
+0.1
(Confident Level 3+ children)
0.31
Example: 74 − 27
Expanded
70  4
 20  7
60
Compact
14
70  4
 20  7
40  7
6 14
7 4
27
4 7
Stages of exchange
Exchanging tens to units (expanded
method )
Double exchange (expanded method )
Compact decomposition
0.4
0.5
Multiplication.
Stage P (Pre school)
Stage 1
Stage 2
Stage 3
Objectives; To begin to use the
vocabulary involved in multiplication.
To begin to group objects into groups of
the same size.
Strategy; combining two groups and
counting to establish total.
Recording; teacher demonstration of
pictorial recording where appropriate.
Photographs.
Vocab; more, and, make, sum, total,
altogether, lots of
Equipment; every day objects, counters,
fingers etc
Objectives; To understand multiplication
as repeated addition. To begin counting
in 2s, 5s and 10s.
Strategy; begin to recognise repetitive
addition of groups of the same size.
Counting in steps of 2, 5 or 10.
Recording; teacher demonstration of
calculation to match pictorial recording
using standard notation of + and = for
repeated addition. Demonstration on a
number line.
Vocab; double, group, sets, lots of
Equipment; every day objects, counters,
fingers
Objectives; To develop the use of a
number line for multiplication.
Strategy; to recognise repetitive addition
of groups of the same size. Counting in
steps of 2, 5 and 10.
Recording; teacher demonstration of
calculation to match pictorial recording
using standard notation of + and = for
repeated addition. Also use of a tally.
Demonstrate on a standard number line.
Vocab; double, group. Lots of
Equipment; every day objects, counters,
fingers, multiplication facts ITP.
Objectives; Recognise that multiplication
can be done in any order. To describe
multiplication as an array.
Strategy; To recognise repetitive addition
of groups of the same size. Counting in
steps of 2, 5 and 10.
To recognise repeated addition as an
array.
Recording; teacher demonstration of
calculation to match pictorial recording
(array) using standard notation x and =.
Demonstrate on a number line. Children
to develop recording especially using
their own number lines.
Vocab; double, groups of, times,
multiply, multiple, lots of
Equipment; number lines, counters,
array, Multiplication facts ITP
Stage 4
Stage 5
Stage 6
Stage 7
Objectives; To understand that
multiplication can be done in any order.
To recognise scaling as repeated
addition.
Strategy; To recognise multiplication as
repetitive addition of groups of the same
size; as an array; as scaling.
Recording; Use standard notation of x
and =. Number lines. Introduce use of
facts box
Vocab; double, groups of, times,
multiply, multiple, lots of
Equipment; counters, number lines,
multiplication grids. Multiplication facts
ITP
Objectives; Begin to use partitioning to
multiply TU xU. Using a facts box.
Observe the effects of multiplying by 10
and then 100.
Strategy; to recognise addition as
repeated addition of groups of the same
size; as an array; as scaling.
Recording; Use of standard notation of x
and =. Number lines using a facts box.
Vocab; double, groups of, times,
multiply, multiple, lots of, product,
inverse
Objectives; Extend grid method to bigger
numbers and including decimals.
Strategy; To recognise multiplication as
repetitive addition of groups of the same
size; as an array; as scaling. Counting in
steps of any size to 10 and beyond.
Recording; use of standard notation of x
and =, number lines and facts box
Vocab; double, groups of, times,
multiply, multiple, lots of, product,
inverse.
Equipment; array/ square grid, number
lines, multiplication grids.
Objectives; Introduce expanded short
multiplication including decimals,
moving to a more compact method.
Strategy; to recognise multiplication as
repetitive addition of groups of the same
size; as an array; as scaling. Counting in
steps of any size.
Recording; use of standard notation of x
and =, number lines and arrays.
Standard method of short and long
multiplication.
Vocab; double, groups of, times,
multiply, multiple, lots of, product,
inverse.
Equipment; array/ square grid, number
lines, multiplication grids.
15 x 3 = 10 x 3 = 30
= 5 x 3 = 15
45
(Confident level 3+ children)
(Confident level 4/5 children)
38 x 7 = ?

38
7
210
56
266
Division.
Stage P (Pre school)
Stage 1
Stage 2
Stage 3
Objective; To share objects equally.
Strategy; begin to recognise sharing
equally, also repetitive addition or
subtraction of groups of the same size.
Recording; teacher demonstration of
appropriate pictorial recording.
Vocab; groups, share
Equipment; every day objects, counters,
fingers
Objective; To share objects into equal
groups.
Strategy; Begin to recognise sharing
equally, ie- grouping.
Recording; teacher demonstration of
calculation to match pictorial recording
using standard notation. Teacher to
demonstrate on a standard number line.
Vocab; groups, share, left over, half
Equipment; every day objects, counters,
fingers
Objective; Counting on in groups of. To
begin to use a standard number line to
support informal recordings of division.
To recognise that division is the inverse
of multiplication.
Strategy; Begin to recognise sharing
equally, also repetitive addition of
groups of the same size ie; grouping.
Recording; Teacher demonstration of
calculation to match pictorial recording
using standard notation .
Demonstration on a standard number
line. Begin to use a number line for their
informal jottings.
Vocab; groups, share, left over, divide,
divided by, equal groups of
Equipment; number lines, counters,
Grouping ITP
Objective; To develop use of children’s
own number line to support informal
recordings of division. To derive halves
and doubles of numbers.
Strategy; Begin to recognise sharing
equally, also repetitive addition of
groups of the same size ie; grouping.
Recording; Teacher demonstration of
calculation to match pictorial recording
using standard notation of . Drawing own
number line.
Vocab; groups, share, left over, divide,
divided by, equal groups of.
Equipment; number lines, counters,
Grouping ITP
There are twelve fish to share between 6
bowls. There will be two in each bowl.
Stage 4
Stage 5
Stage 6
Stage 7
Objective; Use a number line to support
informal recordings of division. Use
standard notation to record calculations.
Strategy; Begin to recognise sharing
equally, also repetitive addition of
groups of the same size ie; grouping.
Recording; Teacher demonstration to
record calculation using standard
notation. Use of a number line and facts
box. Expressing remainders as a whole
number.
Vocab; groups, share, left over, divide,
divided by, equal groups of, remainder.
Equipment; number lines, counters,
Grouping ITP
Objective; To begin to use formal
methods for subtraction based on
repeated subtraction.
Strategy; Begin to recognise sharing
equally, also repetitive addition of
groups of the same size ie; grouping.
Recording; Written calculation using
standard notation. Continuing to use a
number line and facts box . Use
multiples that children are comfortable
with. Expressing remainders as a whole
number.
Vocab; groups, share, left over, divide,
divided by, equal groups of, remainder,
divided into, divisible by, factor, quotient
Equipment; number lines, counters,
Grouping ITP
Objective; To develop and refine formal
methods for division calculations.
Strategy; Begin to recognise sharing
equally, also repetitive addition or
subtraction of groups of the same size ie;
grouping.
Recording; Children developing a more
compact method (Bus shelter) for
division expressing remainders as a
whole number
Vocab; groups, share, left over, divide,
divided by, equal groups of, remainder,
divided into, divisible by, factor, quotient
Equipment; number lines
Objective; To develop a more compact
method for recording division.
Strategy; Begin to recognise sharing
equally, also repetitive addition or
subtraction of groups of the same size ie;
grouping.
Recording; Teacher demonstration of
compact method. Expressing remainders
as a decimal
Vocab; ; groups, share, left over, divide,
divided by, equal groups of, remainder,
divided into, divisible by, factor, quotient
Equipment; number lines.
(Level 4/5 children)
(Confident level 4+ children)