Calculation Policy 2020 2021 - Pre School to Year 3 - Hessle Mount School
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1 Calculation Policy 2020 – 2021 Pre School to Year 3
2
Maths Calculation Policy 2020-2021
This policy supports the Busy Ant maths scheme used throughout the school.
Progression within each area of calculation is in line with the programme of study
in the 2014 National Curriculum.
This calculation policy should be used to support children to develop a deep
understanding of number and calculation. This policy has been designed to teach
children through the use of concrete, pictorial and abstract representations.
Concrete representation — a pupil is first introduced to an idea or skill by acting
it out with real objects. This is a ‘hands on’ component using real objects and is
a foundation for conceptual understanding.
Pictorial representation – a pupil has sufficiently understood the ‘hands on’
experiences performed and can now relate them to representations, such as a
diagram or picture of the problem.
Abstract representation — a pupil is now capable of repreasenting problems by
using mathematical notation, for example 12 x 2 = 24.
It is important that conceptual understanding, supported by the use of
representation, is secure for all procedures. Reinforcement is achieved by going
back and forth between these representations.
3
EYFS
In the statutory framework for EYFS, an Early Learning Goal is the standard children are expected to achieve
by the end of their reception year. The ELG relevant to calculations is Number. Early Learning Goal - Number
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. They solve problems, including doubling, halving and sharing.
Calculations will be taught in a purposeful, practical way, starting in the preschool setting and children will use
play and exploration to acquire the relevant mathematical skills to solve them. A large majority of mathematical
work is practical, and learning will happen in many different contexts around the classroom and outside. Some
mathematical concepts relating to calculations will be teacher led and children can also freely explore these
concepts through a variety of different activities and resources set up each day. Learning is repeated using
different resources and representations to embed understanding. This calculation policy illustrates the
resources used in Preschool and Reception to support the development of mathematical concepts and an
understanding of number that lead to embedding the skills and increasing confidence to perform calculations.
Preschool
Addition (Pre school)
Explore part
part whole
relationship—
combining two
parts to make a
whole.
Discuss
language of
more / less
Children to count each group and use correct vocabulary to say how many in each group
and which group has more / less.
4
Solving
Sarah has 2 apples.
problems using John has 5 apples.
concrete, How many apples do they have
altogether?
pictorial images.
How many more apples does
John have than Sarah?
5
Preschool
Subtraction (Pre school)
Using
concrete
strategies for
counting.
Discuss
language of
more / less
Children to count each group and use correct vocabulary to say how many in each group
and which group has more / less.
Solving
Sarah has 2 apples.
problems John has 5 apples.
using How many more red apples than
green apples.
concrete, Who has the least apples?
pictorial images.
6
Multiplication and division (Preschool)
Make items Making equal groups and sharing equally. Children learn that sharing, doubling and
fair. halving must be fair and equal. Each group must be the same. Practical resources help
children to explore and manipulate numbers and learning is reinforced with our
mathematical resources.
7
Reception
Addition (Reception)
Explore part The pictures below show ways of recording
calculations.
part whole
relationship—
combining two
parts to make a
whole.
Using the ten
frame to
support
addition of
single digits—
counting all/
combining two
groups
Solving
Sarah has 2 apples.
problems using John has 5 apples.
concrete, How many apples do they have
altogether?
pictorial images. How many more apples does
John have than Sarah?
8
Reception
Subtraction (Reception)
Using Taking away after counting out practical equipment.
concrete Children would be encouraged to physically remove
strategies for these by touch counting
counting
By touch counting and dragging in this way, it allows
children to keep track of how many they are removing
so they don’t have to keep recounting. They will then
touch count the amount that are left to find to answer.
Those who are ready may record their own calculations
Using the ten
frames to
support
subtraction by
taking away
Solving
Peter has 5 pencils and 3 erasers. How many more pencils than erasers
problems does he have?
using
concrete,
pictorial images.
9
Reception
Multiplication (Reception)
Experiencing equal
groups of objects Children will experience equal groups of objects.
They will think
They will work in practical problem solving activities.
about doubling
when solving
There are 6
practical pairs of
problems. socks. How
many socks
are there
altogether?
2 children leave their
wellies by the door.
How many wellies are there
altogether?
Division (Reception)
Sharing practical
objects.
Hearing and
being exposed to
language to
describe half and
seeing visual
representations.
10
Year 1
Addition (Year 1)
Combining two parts
to make a whole: part
whole model. Joining
two groups and then
recounting all objects
(lots of practice
making 10 and
numbers to 10 e.g.
6 + 4 = 10 or
3 + 5 = 8)
Number Bonds Learn
number bonds to 20
and demonstrate
related facts.
Addition and
subtraction
8 + 4 = 12
taught alongside 4 + 8 = 12
each other as pupils
need to see the
relationship
12 - 4 = 8
between the facts. 12 - 8 = 4
Add and subtract one
digit numbers and two
digit numbers to 20,
including zero
Bridging 10;
6 + 6 = 12
Make 9 in one and 3
in the other.
Take one from the 3
to make the 9 into a
ten….10+2 = 12 use
ten frames, and
number lines to
practice. Children
should start with the
larger number and
add the smaller
number.11
Year 1
Subtraction (Year 1)
Taking away
should begin with
physical objects:
counters, cubes,
Dienes etc
Subtraction by Count back 3 steps from 15 Count back 3
steps from 15
counting back Subtract 3 from 15
15 – 3 = 12
There are 12 flowers left
Subtracting a single
digit number from a Subtract by crossing out
single digit number
and a single digit
from a two digit by
7–2=5
crossing out There are 5 ladybirds
pictures. left
Subtracting using the
part part whole model
(include problem
solving with missing
digits).
7–5=2
?- 5=2 There are 2 boats that are not
red
When subtracting
using Dienes children
should be taught to
regroup (rename) a
ten rod for 10 ones
and then subatract
from those.
Transfer 10 into 10 ones 20 – 4 = 16
20
Subtracting
Multiples of 10.
Using the vocabulary
of 1 ten, two tens,
etc, alongside 10,
20, 30 is important.12
Year 1
Multiplication (Year 1)
Counting in
Multiples of 2, 5
and 10 from zero.
Children should
count the number of
groups on their
fingers as they are
skip counting.
When moving to
pictorial/written
calculations the
language is
important
Solving
Multiplication
Problems using
repeated
addition13
Year 1
Division (Year 1)
Pupils should be
taught to divide
by working
practically and
the sharing
should be shown
below the whole
to familiarise
children with the
concept of the
whole.14
Year 2
Addition (Year 2)
Using concrete
and pictorial
representations
to add a 2 digit
number to a 1
digit number
and a 2 digit
number to a tens
number.
Using concrete
and pictorial
representations
to add two 2
digit numbers.15
Year 2
Addition (Year 2)
Using concrete
and pictorial
representations
to add 3 single
digit numbers.
Using the bar
model to find
missing digits:
It is important for the
children to use the
bar model in this
way to encourage
the use of it to aid
problem solving.16
Year 2
Subtraction (Year 2)
Using concret
and pictorial
representations
to subtract a
1 digit number
from a 2 digit
number
Using concrete
and pictorial
representations
to subtract a
2 digit number
from a tens
number.
Using concrete
and pictorial
representations
to subtract a
2 digit number
from a 2 digit
number.
Recognise and
use the inverse
relationship
between addition
and subtraction.17
Year 2
Multiplication (Year 2)
Skip counting in
multiples of 2,
3, 5 and 10 from
zero.
Recall and reuse
multiplication
facts for the 2,
3, 5 and 10 times
tables.
Use multiplication
sign (X) and
equals sign (=)
when writing out
multiplication
tables.
Understand that
multiplication is
commutative.
Pupils should
understand that an
array can represent
different equations
and that as
multiplication is
commutative the
order doesn’t affect
2 x 5 = 10 5 x 2 = 10
the answer.
12 = 3 x 4 12 = 4 x 318
Year 2
Multiplication (Year 2)
Solve
multiplication
problems using 3x5=
arrays and
repeated 5x3=
addition.19
Year 2
Division (Year 2)
Recall and use
the division facts
for 2, 3, 5 and
10 multiplication
tables.
Solve division There are 18 sausages.
problems in
context by using
concrete objects
Put 18 sausages
by sharing.
Equally on 2 plates
There are 9 sausages on each plate.
18 ÷ 2 = 9
Solve division
problems in
context using
arrays.
Solve division Put 10 buns in groups of 2.
using grouping. How many plates are there?
Put into groups of 5.
There are _____ groups?20
Year 2
Division (Year 2)
Use the inverse
This should be
Make a family of multiplication and division facts.
taught alongside
both
multiplication and
division.
2 x 10 = 20 20 ÷ 10 = ______
10 x 2 = 20 20 ÷ 2 = ______21
Year 3
Addition (Year 3)
Add two three Step 2 Add the tens.
3 tens + 2 tens = 5 tens
Step 1 Add the ones.
digit numbers. 2 ones + 1 one = 3 ones
Children need to
first use
equipment to
support Step 3 Add the hundreds.
4 hundreds + 5 hundreds = 9 hundreds
understanding of
place value.
Start without
renaming then
gradually move
onto renaming.
Step 1 Add the ones.
6 ones + 5 one = 11 ones
11 ones is 1 ten which we carry and 1 one
Step 2 Add the tens.
1 ten + 3 tens + 4 tens = 8 tens
Step 3 Add the hundreds.
2 hundreds + 3 hundreds = 5 hundreds
Bar Modelling.
It is important for the
children to use the
bar model in this way
to encourage the use
of it to aid problem
solving. Morning Afternoon22
Year 3
Subtraction (Year 3)
Subtract up to Subtract 723 from 975 Subtract 269 from 520
Step 1 Subtract the ones Step 1 Regroup 1 ten into 10 ones
3 digits from 3 5 ones – 3 ones = 2 ones Subtract the ones
10 ones – 9 ones = 1 one
digits.
Children need to
first use
equipment to
support
Step 2 Subtract the tens
11 tens – 6 tens = 5 tens
Step 2 Subtract the tens
7 tens – 2 tens = 5 tens
understanding of
place value.
Only when
children are
Step 3 Subtract the hundreds
secure with 4 hundreds – 2 hundreds = 2 hundreds
method should Step 3 Subtract the hundreds
9 hundreds – 7 hundreds = 2 hundreds
exchanging be
introduced.
520 – 269 = 251
975 – 723 = 252
Bar Modelling
It is important for
the children to
use the bar
model in this
way to
encourage the
use of it to aid
problem solving.23
Year 3
Multiplication (Year 3)
Children should be
There are 4 groups of 23 fish
able to recall the 2,
5, 10, 3, 4, 6 and 8
How do we multiply 23 by 4?
multiplication tables.
Multiply a 2 digit
number by a 1
Step 1 Multiply the ones by 4
digit number.
Step 2 Multiply the tens by 4
Step 3 Add the products
23 x 4 = 92
There are 92 fish in 4 tanks
Bar Modelling
It is important for
the children to use
the bar model in
this way to
encourage the use
of it to aid
problem solving.24
Year 3
Division (Year 3)
Dividing and
grouping
understanding
the concept of
remainders.
Dividing using
short division
Once the children
are secure with
division as
grouping and can
demonstrate this
on number lines,
arrays etc.
Short division
should be
introduced for
dividing larger 2
digit numbers.
Initially with
carefully chosen
calculations
requiring no Exchange 1 ten into 10 ones
remainders.
Compare the lay
out of short division
to that of an array.
Bar Modelling
It is important for
the children to
use the bar
model in this
way to
encourage the
use of it to aid
problem solving.25
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