BALFOUR INFANT SCHOOL
CALCULATION POLICY
PROGRESSION IN ADDITION – BALFOUR INFANT SCHOOL
EYFS - Early Learning Goal
Year 1 Objectives
Year 2 Objectives
Numbers: children count reliably with numbers from
1 to 20, place them in order and say which number
is one more or one less than a given number. Using
quantities and objects, they add and subtract two
single-digit numbers and count on or back to find
the answer.
Pupils should be taught to:
• read, write and interpret mathematical
statements involving addition (+), subtraction (–)
and equals (=) signs
• represent and use number bonds and related
subtraction facts within 20
• add and subtract one-digit and two-digit
numbers to 20, including zero
• solve one-step problems that involve addition
and subtraction, using concrete objects and
pictorial representations, and missing number
problems such as 7 = – 9.
Development matters
Non-statutory guidance
Pupils memorise and reason with number bonds
to 10 and 20 in several forms (for example, 9 + 7 =
16; 16 – 7 = 9; 7 = 16 – 9). They should realise the
effect of adding or subtracting zero. This
establishes addition and subtraction as related
operations.
Pupils combine and increase numbers, counting
forwards and backwards.
They discuss and solve problems in familiar
practical contexts, including using quantities.
Problems should include the terms: put together,
add, altogether, total, take away, distance
between, difference between, more than and less
than, so that pupils develop the concept of
addition and subtraction and are enabled to use
these operations flexibly.
Pupils should be taught to:
• 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 and
learning
• 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
• recognise and use the inverse relationship between addition and
subtraction and use this to check calculations and solve missing
number problems.
Non-statutory guidance
• Pupils extend their understanding of the language of addition and
subtraction to include sum and difference.
• Pupils practise addition and subtraction to 20 to become increasingly
fluent in deriving facts such as using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 –
3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30. They
check their calculations, including by adding to check subtraction and
adding numbers in a different order to check addition (for example, 5 +
2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and
associativity of addition.
• Recording addition and subtraction in columns supports place value
and prepares for formal written and learning with larger numbers.
30-50 months
• Shows an interest in number problems.
• Separates a group of three or four objects in different
ways, beginning to recognise that the total is still the same.
40 – 60+ months
• Uses the language of ‘more’ and ‘fewer’ to compare two
sets of objects.
• Finds the total number of items in two groups by counting
all of them.
• Says the number that is one more than a given number.
• Finds one more from a group of up to five objects,
then ten objects.
• In practical activities and discussion, beginning to use the
vocabulary involved in adding
• Records, using marks that they can interpret and explain.
• Begins to identify own mathematical problems based on
own interests and fascinations.
FS Teaching and learning
(taken from Development Matters – Positive relationships) 30-50 months
• Use number language, e.g. ‘one’, ‘two’, ‘three’, ‘lots’,‘ ‘how many?’ and
‘count’ in a variety of situations.
• As you read number stories or rhymes, ask e.g. ‘When one more frog
jumps in, how many will there be in the pool altogether?’
• Use pictures and objects to illustrate counting songs, rhymes and number
stories.
• Encourage children to use mark-making to support their thinking about
numbers and simple problems.
• Talk with children about the strategies they are using, e.g. to work out a
solution to a simple problem by using fingers or counting aloud.
40-60+ months
• Use rhymes, songs and stories involving counting on in ones, twos, fives
and tens.
• Show interest in how children solve problems and value their different
solutions.
• Make sure children are secure about the order of numbers before asking
what comes after each number.
• Discuss with children how problems relate to others they have met, and
their different solutions.
• Talk about the methods children use to answer a problem they have
posed, e.g. ‘Get one more, and then we will both have two.’
• Encourage children to make up their own story problems for other
children to solve.
• Use mathematical vocabulary and demonstrate methods of recording,
using standard notation where appropriate.
• Give children learning English as additional language opportunities to
work in their home language to ensure accurate understanding of
concepts.
(taken from Development matters – Enabling Environments) 30-50 months
• Include counting money in role-play games
• Create opportunities for children to separate objects into unequal groups
as well as equal groups.
40-60+ months
• Use a 100 square to show number patterns.
• Make number games readily available and teach children how to use
them.
• Encourage children to record what they have done, e.g. by drawing or
tallying.
• Use number staircases to show a starting point and how you arrive at
another point when something is added
• Provide a wide range of number resources and encourage children to be
creative in identifying and devising problems and solutions in all areas of
learning.
• Make number lines available for reference and encourage children to use
them in their own play.
• Big number lines may be more appropriate than counters for children
with physical impairments.
• Help children to understand that five fingers on each hand make a total
of ten fingers altogether, or that two rows of three eggs in the box make
six eggs altogether.
Year 1 Teaching and learning
Year 2 Teaching and learning
Children will draw their own numberlines to add by counting on
in tens and ones
Children use concrete resources (counters,
compare bears, jewels etc) and move onto
using use number lines to support calculation.
Then children will be helped to become more efficient by
adding the units in one jump (by using the known fact 4 + 3 = 7).
Followed by adding the tens in one jump and the units in one
jump.
• Children are encouraged to physically draw
on laminated number lines and count the
“froggy jumps”
• Addition is taught alongside subtraction,
encouraging children to see and understand
the inverse relationship.
• Children are taught the meaning of = as is
the same as and become familiar with the sign
in different positions e.g. 6 = 3 + 3
• Children use concrete objects or number
lines to solve one-step problems and missing
number problems.
Bridging through ten can help children become more efficient.
Children will be taught to partition numbers to add them
24 and 35 20 +30=50 4+5=9 50+9 = 59
Column addition will also be taught
EYFS – useful resources
Year 1 – useful resources
Year 2 – useful resources
Compare bears
ITP Number facts support teaching of addition
Interactive 100 square
(adding 10/9/11)
Bead strings
Bead strings and ict games brilliant beadstring
Large number track
ict games abacas topmarks
Large number line
Pegs on a coathanger/ruler
Ten frames/Numicon
Number tiles
expanded addition
Multibase/Dienes to support addition of 2 digit numbers
(http://www.harcourtschool.com/activity/elab2004/gr3/3.html)
PROGRESSION IN SUBTRACTION – BALFOUR INFANT SCHOOL
EYFS - Early Learning Goal
Year 1 Objectives
Numbers: children count reliably with numbers from 1
to 20, place them in order and say which number is
one more or one less than a given number. Using
quantities and objects, they add and subtract two
single-digit numbers and count on or back to find the
answer.
Pupils should be taught to:
• read, write and interpret mathematical statements involving
addition (+), subtraction (–) and equals (=) signs
• represent and use number bonds and related subtraction facts
within 20
• add and subtract one-digit and two-digit numbers to 20,
including zero
• solve one-step problems that involve addition and subtraction,
using concrete objects and pictorial representations, and missing
number problems such as 7 = – 9.
Development matters
Non-statutory guidance
Pupils memorise and reason with number bonds to 10 and 20 in
several forms (for example, 9 + 7 = 16; 16 – 7 = 9; 7 = 16 – 9).
They should realise the effect of adding or subtracting zero. This
establishes addition and subtraction as related operations.
Pupils combine and increase numbers, counting forwards and
backwards.
They discuss and solve problems in familiar practical contexts,
including using quantities. Problems should include the terms:
put together, add, altogether, total, take away, distance
between, difference between, more than and less than, so that
pupils develop the concept of addition and subtraction and are
enabled to use these operations flexibly.
(taken from Development Matters – Positive relationships) 30-50 months
• Shows an interest in number problems.
40-60+ months
• Uses the language of ‘fewer’ to compare two sets of objects.
• Finds one less from a group of up to five objects, then ten objects.
• In practical activities and discussion, beginning to use the vocabulary
involved in subtracting.
• Records, using marks that they can interpret and explain.
• Begins to identify own mathematical problems based on own interests and
fascinations.
(taken from Development matters – Enabling Environments) 30-50 months
• Include counting change in role-play games
40-60+ months
• Use a 100 square to show number patterns.
• Make number games readily available and teach children how to use them.
• Encourage children to record what they have done, e.g. by drawing or
tallying.
• Provide a wide range of number resources and encourage children to be
creative in identifying and devising problems and solutions in all areas of
learning.
• Make number lines available for reference and encourage children to use
them in their own play.
• Big number lines may be more appropriate than counters for children with
physical impairments.
Year 2 Objectives
Pupils should be taught to:
• 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
and learning
• 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
• recognise and use the inverse relationship between
addition and subtraction and use this to check calculations
and solve missing number problems.
Non-statutory guidance
• Pupils extend their understanding of the language of
addition and subtraction to include sum and
difference.
• Pupils practise addition and subtraction to 20 to
become increasingly fluent in deriving facts such as
using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 – 3 to calculate
30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30. They
check their calculations, including by adding to check
subtraction and adding numbers in a different order to
check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2
+ 5). This establishes commutativity and associativity of
addition.
• Recording addition and subtraction in columns
supports place value and prepares for formal written
and learning with larger numbers.
FS Teaching and learning
Year 1 Teaching and learning
(taken from Development Matters – Positive
relationships)
Children use concrete resources (counters,
compare bears, jewels etc) Bead strings can be used to
30-50 months
• Use number language, e.g. ‘one’, ‘two’, ‘three’,
‘fewer’, ‘hundreds’, and ‘count’ in a variety
of situations.
• Use pictures and objects to illustrate counting
songs,rhymes and number stories.
• Encourage children to use mark-making to
support their thinking about numbers and
simple problems.
• Talk with children about the strategies they
are using, e.g. to work out a solution to a simple
problem by using fingers or counting aloud.
40-60+months
• Use rhymes, songs and stories involving
counting back in ones, twos, fives and tens.
• Show interest in how children solve problems
and value their different solutions.
• Make sure children are secure about the order
of numbers before asking what comes before
each number.
• Discuss with children how problems relate to
others they have met, and their different
solutions.
• Talk about the methods children use to answer
a problem they have posed.
• Encourage children to make up their own story
problems for other children to solve.
• Use mathematical vocabulary and
demonstrate methods of recording, using
standard notation where appropriate.
• Give children learning English as additional
language opportunities to work in their home
language to ensure accurate understanding of
concepts.
Year 2 Teaching and learning
Finding the difference between numbers in taught by counting on from the smallest to
the largest number.
illustrate subtraction including bridging through ten by counting back 3
then counting back 2.
13-5=8
Children use pictorial
representations and cross out to
show taking away
Children begin to use empty number lines to support counting back
First counting back in tens and ones then by subtracting the units in one jump (by
using the known fact 7 – 3 = 4).
Number lines are used to support calculation with
children counting jumps back.
Then helping children to become more efficient by subtracting the tens in one jump
and the units in one jump. Bridging through ten can help children become more
efficient.
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.
Children will be taught to partition numbers to subtract them
68 - 35 60 -30=30 8-5=3 30+3 = 33
Column subtraction will also be taught
• Children use concrete objects or number lines to
solve one-step problems and missing number
problems.
EYFS – useful resources
Year 1 – useful resources
Year 2 – useful resources
ITP Number facts support teaching of subtraction
Interactive 100 square (taking 10/9/11)
Compare bears
Bead strings
ITP difference supports finding the difference
Large number track
ict games abacas
topmarks decomposition
Large number line
Bead strings. Pegs on a coat hanger/ruler. Ten frames/Numicon
Multibase/Dienes to support subtraction of 2 digit numbers
PROGRESSION IN MULTIPLICATION – BALFOUR INFANT SCHOOL
EYFS - Early Learning Goal
They solve problems, including doubling,
halving and sharing.
Development Matters
40-60+ months (positive relationships)
• Use rhymes, songs and stories involving counting
on in ones, twos, fives and tens.
• Show interest in how children solve problems and
value their different solutions.
• Discuss with children how problems relate to
others they have met, and their different solutions.
• Talk about the methods children use to answer a
problem they have posed
• Encourage children to make up their own story
problems for other children to solve.
• Use mathematical vocabulary and demonstrate
methods of recording, using standard notation
where appropriate.
• Give children learning English as additional
language opportunities to work in their home
language to ensure accurate understanding of
concepts.
40-60+ months (enabling environments)
Help children to understand that two
rows of three eggs in the box make six eggs
altogether.
Year 1 Objectives
Pupils should be taught to:
• 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.
Non-statutory guidance
Through grouping and sharing small quantities,
pupils begin to understand: multiplication and
division; doubling numbers and quantities; and
finding simple fractions of objects, numbers and
quantities.
They make connections between arrays, number
patterns, and counting in twos, fives and tens.
Year 2 Objectives
Pupils should be taught to:
• recall and use multiplication and division facts for the 2, 5
and 10 multiplication tables, including recognising odd and
even numbers
• calculate mathematical statements for multiplication and
division within the multiplication tables and write them using
the multiplication (×), division (÷) and equals (=) signs
• show that multiplication of two numbers can be done in
any order (commutative) and division of one number by
another cannot
• solve problems involving multiplication and division, using
materials, arrays, repeated addition, mental and learning, and
multiplication and division facts, including problems in
contexts.
Non-statutory guidance
Pupils use a variety of language to describe multiplication
and division.
Pupils are introduced to the multiplication tables. They
practise to become fluent in the 2, 5 and 10 multiplication
tables and connect them to each other. They connect the 10
multiplication table to place value, and the 5 multiplication
table to the divisions on the clock face. They begin to use
other multiplication tables and recall multiplication facts,
including using related division facts to perform written and
mental calculations.
Pupils work with a range of materials and contexts in which
multiplication and division relate to grouping and sharing
discrete and continuous quantities, to arrays and to repeated
addition. They begin to relate these to fractions and
measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They
use commutativity and inverse relations to develop
multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 =
4).
Teaching and learning
Teaching and learning
Teaching and learning
EYFS
Year 1
Year 2
Children will experience equal groups of
objects.
Children will experience equal groups of objects and
arrays in real life.
Children will develop their understanding of multiplication and use
jottings to support calculation:
Repeated addition
3 times 5 is 5 + 5 + 5 = 15 or 3 lots of 5 or 5 x3
They will count in 2s and 10s and begin to
count in 5s.
Repeated addition can be shown easily on a number line:
They will work on practical problem solving
activities involving equal sets or groups.
e.g. laying the table for the 3 bears and
goldilocks
They will count in 2s, 5s and 10s.
Children should know that 3 x 5 has the same answer as 5 x 3. This
can also be shown on the number line.
They will work on practical problem solving activities
involving equal sets or groups.
Begin to introduce children to the visual images
of arrays – using real-life examples – egg
boxes, cake tins windows in a building, anything
with a repeating pattern in rows and columns!)
Arrays
Children should be able to model a multiplication calculation using an
array. This knowledge will support with the development of the grid
method.
Relate x2 to doubling
EYFS – useful resources
Year 1 – useful resources
Year 2 – useful resources
Itp multi array
Real life objects
Count in 2’s to find out how many socks are on the washing
line:
Compare bears
Real life arrays
2p 5p and 10p coins (providing children have a good understanding
of coin value)
Topmarks – hit the button
Noah’s Ark to explore groups of 2 and repeated
addition
Speedstacking cups
BBC Camel times tables
Pegboards for arrays
PROGRESSION IN DIVISION – BALFOUR INFANT SCHOOL
EYFS - Early Learning Goal
They solve problems, including doubling, halving and
sharing.
Development matters
30-50 months
Help children to understand that one thing can be shared by
number of pieces, e.g. a pizza.
40-60+ months (positive relationships)
• Show interest in how children solve problems and value
their different solutions.
• Discuss with children how problems relate to others they
have met, and their different solutions.
• Talk about the methods children use to answer a problem
they have posed
• Encourage children to make up their own story problems
for other children to solve.
• Encourage children to extend problems, e.g. “Suppose
there were three people to share the bricks between instead
of two”.
• Use mathematical vocabulary and demonstrate methods of
recording, using standard notation where appropriate.
• Give children learning English as additional language
opportunities to work in their home language to ensure
accurate understanding of concepts.
Year 1 Objectives
Pupils should be taught to:
• 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 Objectives
Pupils should be taught to:
• recall and use multiplication and division facts for the 2, 5
and 10 multiplication tables, including recognising odd and
even numbers
• calculate mathematical statements for multiplication and
division within the multiplication tables and write them using
the multiplication (×), division (÷) and equals (=) signs
• show that multiplication of two numbers can be done in
any order (commutative) and division of one number by
another cannot
• solve problems involving multiplication and division, using
materials, arrays, repeated addition, mental and learning,
and multiplication and division facts, including problems in
contexts.
Non-statutory guidance
Non-statutory guidance
Through grouping and sharing small
Pupils use a variety of language to describe multiplication
quantities, pupils begin to understand:
and division.
multiplication and division; doubling
Pupils are introduced to the multiplication tables. They
numbers and quantities; and finding simple
practise to become fluent in the 2, 5 and 10 multiplication
fractions of objects, numbers and quantities. tables and connect them to each other. They connect the 10
They make connections between arrays,
multiplication table to place value, and the 5 multiplication
number patterns, and counting in twos, fives table to the divisions on the clock face. They begin to use
and tens.
other multiplication tables and recall multiplication facts,
including using related division facts to perform written and
mental calculations.
Pupils work with a range of materials and contexts in which
multiplication and division relate to grouping and sharing
discrete and continuous quantities, to arrays and to repeated
addition. They begin to relate these to fractions and
measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They
use commutativity and inverse relations to develop
multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 =
4).
Teaching and learning
Teaching and learning
Teaching and learning
EYFS
Year 1
Year 2
Children will develop their understanding of division and use jottings to support
calculation by drawing circles or stick people to share equally
• Help children to understand that one thing can be
shared by number of pieces, e.g. an apple, a pizza.
Children will be taught to share a number of
objects equally in practical situations.
6 sweets shared between 2 people, how many do they each get? (1 for you one
for me)
Children will understand equal groups and share items
out in play and problem solving. (fruit/stationery)
Ensure sharing is not always just between 2
people otherwise children get the misconception
that dividing is sharing by 2 rather than sharing a
number equally.
Children will count in 2s, 10s and 5s.
OOO
OOO
The emphasis in Year 2 should be on grouping.
Grouping or repeated subtraction
There are 6 sweets, how many people can have 2 sweets each? (How many
groups of 2 in 6?)
Repeated subtraction using a number line or beads
12 ÷ 3 = 4
Using symbols to stand for unknown numbers to complete equations using
inverse operations. Number trios to see the link between multiplication and
division.
÷2=4
20 ÷  = 4
÷=4
Read 12 ÷ 3 = ? as ‘How many groups of 3 are in 12?
Relate ÷2 to halving and relate division to fractions
Introduce the idea of remainders to HA children using sharing method.
EYFS – useful resources
Year 1 – useful resources
Objects for sharing
Year 2 – useful resources
Itp fractions
Real-life objects
Sweets, counters, classroom equipment such
as pencils, glue sticks etc.
Fraction games e.g. pizza game
Objects for sharing
Itp grouping
Sweets, counters, classroom equipment such as pencils,
glue sticks etc.
(Try to make sure children see halves of
different shapes – not just circles)
Topmarks What fraction/egg fractions
Fraction sets and fraction games