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Gorse Ride Schools Calculation Policy
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
Children are given many opportunities to practise using given resources and strategies and will not be moved on to new methods until they are fluent in current ones.
They also revisit previous strategies as and when appropriate.
It is important that children experience a range of concrete materials such as Numicon, pictures, toys, to help them understand a concept before moving onto a more
abstract format, such as number lines and 100 squares.
OBJECTIVES
 Children count reliably with numbers
from one to 20, place them in order and
say which number is one more than a
given number.
 Using quantities and objects, they add
two single-digit numbers and count on to
find the answer.
STRATEGIES/RESOURCES

OBJECTIVES
 Children count reliably with numbers
from one to 20,place them in order
and say which number is one less than
a given number.
 Using quantities and objects, subtract
two single-digit numbers and count
STRATEGIES/RESOURCES
 Take away a number from a group and
count what is left.
Counting two groups by counting ALL.
Foundation
Stage

Counting two groups by counting ON
from the larger number.

Numicon

Counting objects

Counting objects

Subtraction facts up to and including
10

Singing number rhymes & songs
OBJECTIVES
 They solve problems, including doubling,
halving and sharing.
STRATEGIES/RESOURCES

Singing number rhymes & songs

Doubling and sharing in games and role
play
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Gorse Ride Schools Calculation Policy

Year 1

Number bonds up to and including 10

Singing number rhymes & songs

Addition in games and role play
OBJECTIVES
 given a number, identify one more
 identify and represent numbers using
objects and pictorial representations
including the number line, and use the
language of: equal to, more than, most,
 read, write and interpret mathematical
statements involving addition (+) and
equals (=) signs
 add one-digit and two-digit numbers to
20, including zero
 represent and use number bonds and
Subtraction in games and role play
OBJECTIVES
 given a number, identify one less
 identify and represent numbers using
objects and pictorial representations
including the number line, and use the
language of: equal to, less than (fewer),
least
 read, write and interpret mathematical
statements involving subtraction (–) and
equals (=) signs
 subtract one-digit and two-digit numbers
to 20, including zero
OBJECTIVES
 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.
STRATEGIES/RESOURCES

Counting on in 2s, 5s, 10s.
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Gorse Ride Schools Calculation Policy
related subtraction facts within 20
solve one-step problems that involve
addition using concrete objects and
pictorial representations, and missing
number problems such as 7 = – 9.

STRATEGIES/RESOURCES
 Start with larger number and count on


Find biggest number on number line
and move on the correct number of
jumps.


represent and use number bonds and
related subtraction facts within 20
solve one-step problems that involve
subtraction, using concrete objects and
pictorial representations, and missing
number problems such as 7 = – 9.
STRATEGIES/RESOURCES
 Start with larger number
and count back (moving on to bridging
10)

Jumping on in 2s, 5s, 10s on number track/
100 square

Model multiplication with a range of practical,
real life resources

Number stories

Recall of doubles and halves to 10.
Using prepared number lines


Use resources to ‘take away’ from the
larger number
Beadstrings

Mental recall of number bonds up to
and including 20.

Number stories (problems)

Numicon to represent calculations
 Counting ON to find the difference
12 – 9 =

Numicon to represent calculations
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Gorse Ride Schools Calculation Policy
ADDITION
Year 2
OBJECTIVES
 applying their increasing
knowledge of mental and
written methods
 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)
 recognise and use the inverse
relationship between addition
and subtraction and use this
SUBTRACTION

Division as sharing in real life contexts

Division as grouping in real life contexts
MULTIPLICATION
DIVISION
OBJECTIVES
 recall and use multiplication
facts for the 2, 5 and 10
multiplication tables, including
recognising odd and even
numbers
 calculate mathematical
statements for multiplication
within the multiplication
tables and write them using
the multiplication (×) and
equals (=) signs
 show that multiplication of
two numbers can be done in
any order (commutative)
 solve problems involving
multiplication, using materials,
arrays, repeated addition,
mental methods, and
multiplication and division
facts, including problems in
contexts.
OBJECTIVES
 recall and use division facts for
the 2, 5 and 10 multiplication
tables, including recognising
odd and even numbers
 calculate mathematical
statements for division within
the multiplication tables and
write them using the division
(÷) and equals (=) signs
 show that division of one
number by another cannot be
done in any order
 solve problems involving
multiplication and division,
using materials, arrays,
repeated addition, mental
methods, and multiplication
and division facts, including
problems in contexts.
STRATEGIES/ RESOURCES
 Sharing equally
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Gorse Ride Schools Calculation Policy
to check calculations and solve
missing number problems.
STRATEGIES/ RESOURCES
 Using prepared number lines

Using a partially prepared or
empty number line, e.g. 9 + 5
-to count on in 1s, 10s, multiples of
10, bridging 10

Partition 2 digit numbers to
add. (only crossing the tens
when ready)
34 + 15 =
30 + 10 = 40
4+5=9
40 + 9 = 49

Use 100 square to
OBJECTIVES
 applying their increasing
knowledge of mental and
written methods
 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
 show that subtraction of one
number from another cannot
(be done in any order)
 recognise and use the inverse
relationship between addition
and subtraction and use this
to check calculations and
solve missing number
problems.
STRATEGIES/ RESOURCES
 Using prepared, partially
prepared and empty number
lines
-to count back in 10s and ones
-to count 10s and ones in one jump
STRATEGIES/ RESOURCES
 Repeated addition (on
number line, 100 square,
bead string etc)

Arrays

Grouping

Repeated subtraction
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Gorse Ride Schools Calculation Policy
consolidate

Concrete resources
(Numicon, counters, etc)
available.
-to bridge through 10
-to count on/ up
23 – 18 =
Children continue to learn using resources and models and images in Lower and Upper KS2 to help develop conceptual
understanding
Year 3
Consolidation of mental methods
Consolidation of mental methods
Expanded column addition for TU +
TU, HTU + TU and HTU + HTU
where necessary .
Expanded column subtraction with
decomposition for HTU – TU and
HTU – HTU where necessary
458
+ 373
700
120
11
831
457 – 226 = 231
400 + 50 + 7 200 + 20 + 6
200 + 30 + 1
=231
Using objects and other models and
images including arrays and
number lines to multiply and its
relation to scaling.
Consolidation of mental methods
including using knowledge of
number facts to derive related facts
of TU x U : If 2 x 3 = 6 then 2 x 30 =
60
Consolidation of mental methods
including using knowledge of
number facts to derive related facts
of TU ÷ U: For example, using 3 × 2
= 6 and 6 ÷ 3 = 2 to derive related
facts (for example, 30 × 2 = 60 and
60 ÷ 3 = 20)
Use number lines to calculate TU ÷
U where appropriate (including
remainders) by asking “How many
groups of U are in TU?” and
chunking on in groups of U (inverse
– repeated addition)
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Gorse Ride Schools Calculation Policy
Consolidation of mental methods
Consolidation of mental methods
Column addition up to 4 digits
Expanded column subtraction with
decomposition up to 4 digits
1458
+ 3473
2931
Year 4
2457 – 1229 =
11
40
Consolidation of mental methods
Grid multiplication (using arrays as
starting point) for HTU x U and TU x
U and TU x TU
Grid method - 72 x 38 is
approximately 70 x 40 = 2800
1
2000 + 400 + 50 + 7 1000 + 200 + 20 + 9
1000 + 200 + 20 + 8
x
30
8
Use number lines to calculate
TU÷U or HTU ÷U using chunks of 10
30 ÷ 6 can be modelled as:
grouping – groups of 6 taken away and the
number of groups counted e.g.
70 2
2100 60
560 16
= 1228
Year 5
Consolidation of mental methods
sharing – sharing among 6, the number
given to each person
Consolidation of mental methods
Consolidation of mental methods
Consolidation of mental methods
Consolidate grid method
Compact column addition
including:
Numbers up to 5 digits
Same number of decimal places
Different number of decimal places
Column subtraction with
decomposition for subtracting
whole numbers and numbers with
the same decimal places
Consolidate using number lines to
Short multiplication for multiplying chunk groups on a number line for
numbers up to 4 digits with U
TU÷U
2457.6 – 1229.8 =
14584
+34734
293 18
1 1
3 4 6. 6 7
+ 4 2 3. 4
7 7 0. 0 7
1
1
40
16 1
2000 + 400 + 50 + 7 . 6 1000 + 200 + 20 + 9 . 8
1000 + 200 + 20 + 7 . 8
= 1227.8
Grid method - 372 x 24 is
approximately 400 x 20 = 8000
x
20
4
300
70 2
6000 1400 40
1200 280 8
1223
×
5
6115
1 1 1
Consolidation of mental methods
Short division for TU ÷ U
Calculations with no “carrying”
(e.g. 96 ÷ 3)
Calculations with “carrying” (e.g.
72 ÷ 3)
Calculations with “carrying” and
remainders (e.g. 5309 ÷ 8)
2 42
3 712 6
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Gorse Ride Schools Calculation Policy
Consolidation of mental methods
Compact column addition to add
several numbers of increasing
complexity
Year 6
Consolidation of mental methods
Compact column subtraction with
decomposition to subtract numbers
of increasing complexity including
numbers with different number of
decimal places
4 1 2 4. 9
2 3 1 6. 8 9
+ 2 2 1. 2 5
6 6 6 5. 0 4
1
2
Consolidation of mental methods
Short multiplication to multiply
numbers with up to 2 d.p by U
1223.65
×
5
6118.25
1 1 1 3
19457.6 – 5229.8 =
16
15 1
59457.60
- 25229. 85
3 4 2 3 7 .7 5
Consolidation of mental methods
Consolidate short division
Long division for the higher
achievers with TU as divisors
2
Long multiplication for multiplying
numbers up to 4 digits and numbers
up to 2 decimal places by TU
×
= 34237.75
1223.65
25
6118.25
1 1 1 3
2
244 73.00
1 1
=
30591 .25
Appendix 1 – Mental Strategies
Foundation
Stage
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
Children are encouraged to develop a
mental picture of the number system
through activities such as:
1. Counting – forwards from zero and/or
on from a given number
2. Comparing two numbers to find one
more
3. Ordering numbers from smallest to
largest
4. Combining two groups of objects (or
two single digit numbers) to find how
many altogether; counting all, counting
Children are encouraged to develop a
mental picture of the number system
through activities such as:
1. Counting – backwards to zero and/or
back from a given number
2. Comparing two numbers to find one
less
3. Ordering numbers from largest to
smallest
4. Taking a group of objects from a given
set to find how many are left; counting
out
Children are encouraged to
develop a mental picture of the
number system through activities
such as:
1. Counting – in ones, twos,
fives and tens
2. Sharing objects into equal
groups and then counting
how many in each group
3. Using and discussing the
vocabulary involved in
multiplication
Children are encouraged to
develop a mental picture of the
number system through
activities such as:
1. Counting – in ones, twos,
fives and tens
2. Sharing objects into equal
groups and then counting
how many in each group
3. Using and discussing the
vocabulary involved in
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Gorse Ride Schools Calculation Policy
5.
Year 1
on from the first number, counting on
from the biggest number
Observing number relationships and
patterns in the environment to help
derive facts
Children should be able to use the
following strategies, as appropriate, for
mental calculations:
1. Counting forwards:
4 + 8 count on in ones from 4 or 8
13 + 4 count on from 13
2. Reorder numbers in a calculation:
2+7=7+2
1+6=6+1
3. Begin to bridge through 10, when adding
a single digit number:
9+5=
8+4=
4. Use known number facts and place value
to add pairs of single digit numbers:
3+2=6+4=
5. Add 9 to a single digit number by adding
10,then subtracting 1(compensating):
4 + 9 = 4 + 10 – 1 =
6. Identify near doubles, using doubles
already known:
4 + 3 = (3 + 3) + 1
5 + 6 = (5 + 5) + 1
Children need to know that doubling is
adding the same number to itself
7. Use patterns of similar calculations:
4+2=
14 + 2 =
24 + 2 =
5.
Observing number relationships and
patterns in the environment to help
derive facts
Children should be able to use the
following strategies, as appropriate, for
mental calculations:
1. Counting backwards:
7 - 3 count back in ones from 7 (a given
number)
15 - 3 count back in ones to 3 (a given
number)
18 – 6 count back in twos
2. Reorder numbers in a calculation:
It is important for children to know when
numbers can be reordered (e.g. 2 + 5 + 8
= 8 + 2 + 5 and when they cannot (e.g. 8 – 5
≠ 5 – 8).
3. Find a small difference by counting up
(on) from the smaller to the larger
number:
25 – 19 = 17 – 14 =
4. Use known number facts and place value
to subtract pairs of single digit
numbers:
6-4=
9–3=
5. Add 9 to a single digit number by adding
10, then subtracting 1:
6 + 9 = 6 + 10 – 1 =
6. Identify near doubles, using doubles
already known:
12 + 11 = 11 + 11 + 1 or 12 + 12 - 1
7. Use patterns of similar calculations:
10 – 0 = 10
10 – 1 = 9
10 – 2 = 8
4.
Observing number
relationships and patterns in
the environment to help
derive facts
Children should be able to use
the following strategies, as
appropriate, for mental
calculations:
1. Counting forwards:
Count in twos – 2, 4, 6, 8, …to 20
Count in fives – 5, 10, 15, 20, … to
20 or more
Count in tens – 10, 20, 30, … to 50
or more
2. Doubling:
7 + 7 is double 7
Double 7 = 14
division
4. Observing number
relationships and patterns
in the environment to help
derive facts
Children should be able to use
the following strategies, as
appropriate, for mental
calculations:
1. Counting backwards:
In twos – 10, 8, 6, … 0
In tens – 50, 40, 30, … 0
2. Halving:
10 shared by 2 is 5
Half 10 = 5
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Gorse Ride Schools Calculation Policy
Year 2
Children should be able to use the
following strategies, as appropriate, for
mental calculations:
1. Count on in ones or tens:
15 + 4 =
5 + 30 =
2. Reorder numbers in a calculation:
2 + 15 = 15 + 2
4 + 13 = 13 + 4
3. Add three small numbers by putting the
larger number first and/or finding a
pair totalling 10:
4+8+2=8+2+4
7+6+3=7+3+6
4. Partition additions into 10’s and ones
then recombine:
23 + 14 = 20 + 10 = 30, 3 + 4 = 7, 30 + 7 = 37
5. Bridge through 10 or 20:
6+5=
16 + 7 =
6. Use known number facts and place value
to add pairs of numbers:
42 + 3 =
? + 4 = 34
7. Partition into ‘5 and a bit’ when adding
6, 7, 8, 9, then recombine:
25 + 8 = 25 + 5 + 3 = 33
8. Add 9, 19, 11, 21, by rounding up and
compensating:
23 + 9 = 23 + 10 – 1
34 + 11 = 34 + 10 + 1 6
9. Identify near doubles:
8 + 9 = (8 + 8) + 1 11 + 12 = (11 + 11) + 1
10. Use patterns of similar calculations:
4+3=7
40 + 30 = 70
400 + 300 = 700
11. Use the relationship between addition
and subtraction (Inverse):
15 + 4 = 19
Children should be able to use the
following strategies, as appropriate, for
mental calculations:
1. Counting on / backwards:
27 – 4 count on or back in ones from any
two digit number
18 – 4 count back in twos from 18
46 – 30 count back in tens from 46
2. Find a small difference by counting up
(on) from the smaller to the larger
number:
33 - 28 = 74 – 68 =
3. Reorder numbers in a calculation:
It is important for children to know when
numbers can be reordered (e.g. 2 + 36
= 36 + 2 and when they cannot (e.g. 36 – 2 ≠
2 – 36).
4. Partition subtractions into 10’s and ones
and then recombine:
78 – 40 = 70 - 40 + 8
5. Bridge through 10 or 20:
14 - 6 =
28 - 9 =
6. Use known number facts and place value
to subtract pairs of numbers:
20 - 16 =
20 - ? = 16
7. Subtract 9, 19, 11, 21, by rounding up
and compensating:
42 - 19 = 42 - 20 + 1
64 - 21 = 64 - 20 – 1
8. Identify near doubles:
13 + 14 = Double 14 and subtract 1 or
double 13 and add 1
40 + 39 = Double 40 and subtract 1
9. Use patterns of similar calculations:
4 - 3 =1 14 - 3 =11 24 - 3 =23 7
10. Use the relationship between addition
and subtraction (Inverse):
27 - 13 = 14
Children should be able to use
the following strategies, as
appropriate, for mental
calculations:
1. Counting on forwards:
Count in fives – 5, 10, 15, 20…
The 2 times table up to 2 x 10
The 10 times table up to 10 x 10
2. Use knowledge of number facts
and place value to multiply by 2,
5 or 10:
3x2=
4x5=
5 x 10 =
3. Doubling:
7 + 7 = 7 x 2 Children need to
understand that doubling is
multiplying by 2
Children should be able to use
the following strategies, as
appropriate, for mental
calculations:
1. Counting backwards:
In fives – 30, 25, 20, … 0
Division facts for the 2, 5 and
10 times tables
2. Use knowledge of number
facts and place value to
multiply and divide by 2, 5
or 10:
9 x 2 = 4 x 5 = 7 x 10 =
18 ÷ 2 = 20 ÷ 5 = 70 ÷ 10 =
3. Use doubles and halves and
halving as the inverse of
doubling:
7 + 7 = 7 x 2 half of 14 is 7 14 ÷
2
Children need to understand
that halving is dividing by 2
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Gorse Ride Schools Calculation Policy
19 – 4 = 15
12. Use doubles and halves, and halving as
the inverse of doubling:
Double 12 (12 + 12) = 24, therefore what is
half of 24?
13. Bridging through 60 to calculate a time
interval:
What will be the time 20 minutes after
8.50? (not 8.70)
8.50 + 10 minutes = 9.00
9.00 + 10 minutes = 9.10
14 + 13 = 27
11. Use doubles and halves, and halving as
the inverse of doubling:
Double 16 (16 + 16) = 32, therefore what is
half of 32?