Colebrook Infant Academy Calculation Policy
Addition
step
Mental Strategies
Practical Strategies
3
Use knowledge that + is inverse of
-, including for checking
calculations.
Begin to add 2 digit numbers
mentally e.g. add multiples of 10
to any 2 digit number by counting
on in tens. Add a single digit
number to any 2 digit number.
Use known facts to derive new
facts e.g. some number bonds to
100 e.g. 49 + 52, 95 + 5
Know by heart pairs of multiples of
10 that total 100.
Rapidly recall and use all number
bonds to 20
Count in multiples of 2,3,4,5,8,10
Apply the above to begin to
explore 3 digit numbers e.g. 150 +
2, 200 + 100 +10
base 10 to explore partitioning and
recombining, adding multiples of 10 etc.
To add
TU +TU
Begin to add
HTU
2
To add
U+U+U
Add
TU + U
TU +T
Numbers to
100.
1
To add
U+U
concept of
‘more’ and
‘add’
conservation
of number
Numbers to
20
Count on to add units to any
number to 100.
Count in 2s, 5s and 10s (not
always from 0) and recognise this
is repeated addition.
Count in 2s from any number
(including odd numbers)
Say 1 more or 10 more than any
number to 100.
Rapid recall of doubles up to
double 10.
Rapid recall number bonds which
total 20.
Quickly derive number bonds for
all numbers up to 20.
Understand that addition is
commutative. Use this to add
efficiently.
Count on to add a small number.
Say what one more than any
number up to 10.
Understand concept of double and
know by heart doubles up to
double 5.
Rapid recall of number bonds
which total 10.
Derive bonds of other numbers up
to 10.
Recorded Strategies
Add 2, or more, 2 digit
numbers. Partition and
recombine.
Once secure with using Base
10, represent tens and units
as symbols │││▪▪▪
Use number lines, (as step 2) e.g. to
explore adding 2 digit numbers, tens
first, then units or partitioning small
numbers to bridge tens.
HTU arrow cards
hundred squares
base 10 to explore numbers greater
than 10 e.g.
double 12 is │.. │..
34 + 10
│││▪▪▪▪ + │
Progress rapidly to expanded
written method of addition –
38 + 41 =
38 + 40 + 1
keep first number together
and partition second number
Draw own number lines
Draw/represent tens and
units
Read and write number
sentences using + and =
Number lines labelled in ones to at least
20 and in 10s to 100 (with and without
marks for ones). Begin to use these for
jumps of 1, 2, 5 or 10.
songs/action rhymes
role play
exploring real situations and
environment
use of counting apparatus – beads,
counters, cubes, objects.
Number lines marked and labelled in
ones.
Introduce base 10 to explore 10 + 1, 10
+2 etc.
Introduce + symbol and
number sentences.
Tally
Draw sets.
Colebrook Infant Academy Calculation Policy
step
Mental Strategies
3
Use knowledge that + is inverse
of -, including for checking
calculations and subtracting by
adding on.
Begin to subtract 2 digit numbers
mentally e.g. subtract multiples
of 10 from any 2 digit number by
counting back in tens.
subtract
TU – TU
TU – U
TU – T
Begin to
subtract HTU
Subtract a single digit number
from any 2 digit number by
counting back or using known
facts.
Rapidly recall some subtraction
facts to 100 e.g. 100 – 49, 100 –
5.
Rapidly recall, and use, pairs of
numbers of 10 that total 100 e.g.
100 – 30 = 70
Subtraction
Practical Strategies
Use base 10 to explore partitioning and
recombining, subtracting multiples of 10
etc.
Use number lines, (as Step 2) e.g. to
explore subtracting 2 digit numbers, tens
first, then units or partitioning small
numbers to bridge tens
HTU cards to explore the effect of
subtracting units, tens or hundreds.
Rapidly recall all subtraction facts
within 20.
Recorded Strategies
Subtract 2 digit numbers.
Partition first number and
then subtract tens and
then units.
Once secure with using
base 10, represent tens
and units as symbols
│││▪▪▪ cross out the
number to be subtracted.
Progress rapidly to
expanded written method
of subtraction – keep first
number whole and
partition second number
into tens and units
68 – 41 =
Use subtraction in ‘find the
difference’ problems
68 – 40 – 1=
hundred squares
2
subtract U-U
Subtract
TU – U
TU – T
Numbers to 100
Apply the above to begin to
explore 3 digit numbers
subtract by adding on, using number lines.
Count back to subtract units from
any number to 100.
base 10 to explore numbers greater than 10
e.g.
Count back in 2s, 5s, and 10s and
recognise that this is repeated
subtraction.
halve 12 │▪▪
Count back in 2s from any
number (including odd numbers).
34 – 10 │││▪▪▪▪
Say 1 less or 10 less than any
number to 100.
Draw/represent tens and
units once secure with
apparatus
│▪▪
Number lines labelled in ones to at least 20
and in 10s to 100 (with and without marks
for ones). Begin to use these for ‘jumps’ of
1, 2, 5 or 10
Rapidly recall halves to 20
e.g. 70 – 30
Know by heart number bonds
to 10 and use then in subtraction.
Derive subtraction facts to 20 e.g.
19 – 8 = 11
1
subtract
numbers to 20
concept of ‘less’
and ‘subtract’
conservation of
number
Count back to subtract a small
number.
songs/action rhymes
Introduce symbol and
number sentences
role play
Say what is one less than any
number up to 20
exploring real situations and environment
draw sets and cross out
Understand concept of half and
know by heart halves up to 10.
counting apparatus- beads, counters cubes,
objects.
Rapid recall of all subtraction
facts to 10 e.g. 9 – 2 = 7
number lines marked and labelled in ones
Colebrook Infant Academy Calculation Policy
Step
3
UxU
U x TU
Multiplication
Mental Strategies
Know that x is the inverse of ÷
Know by heart multiplication facts for
the 2, 5 and 10 times tables
Practical Strategies
Use number lines and hundred
squares to explore patterns of
repeated addition
Count in steps of 3 and derive x3 facts
times tables posters for quick
reference
Use known facts to derive further
multiplication facts e.g. 6 x 100 = 600.
base 10 to explore multiplying 2 digit
numbers.
Use the fact that multiplication is
commutative to multiply efficiently.
continue to make arrays where
support is needed
Recorded Strategies
Write number sentences using
x and = symbols
draw symbols to represent
groups, including as arrays
οοοοοο
Count in steps of ½ to 10
recognise the effect to multiplying by 1
or 0
2
solve x
questions
with teacher
support
numbers to
100
UxU
10 X U
count in 2s, 5s and 10s
οοοοοο
οοοοοο
draw own number lines with
steps of repeated addition
e.g. 4 x 5
0 5 10 15 20
recognise multiples of 2, 5 and 10
cubes, counters etc. to make equal
groups – explore 2s, 5s and 10s then
other multiples of small numbers
rapidly recall doubles up to totals of 20
and begin to relate this to 2x
make arrays with objects or peg
boards
read and write number
sentences using x and =
draw pictures and symbols in
sets
know by heart the multiplication facts
for the 2x table up to 2 x 10
know by heart doubles of multiples of
10 to 100
understand that multiplication is
commutative
introduce vocabulary ‘times’, ‘multiply’,
‘multiple’
draw arrays
Number lines labelled in ones to at
least 20 and in 10s to 100 (with or
without marks for ones). Begin to use
these for ‘jumps’ of 1,2,5 or 10
× × × ×
× × × ×
2x4
or 4 x 2
write number sentences to
describe arrays
1
concept of
equal
understand concept of double and
know by heart doubles up to 5
use vocab such as ‘equal groups’,
‘same amount’ and ‘sets’
role play
exploring real situations and
environment
numbers to
20
counting apparatus - beads, counters,
cubes, objects
number lines marked and labelled in
ones.
draw sets of objects of real
objects or symbols
Colebrook Infant Academy Calculation Policy
step
3
TU ÷ U
begin to
recognise
remainders
Division
Mental Strategies
Know that x is the inverse of ÷
Practical Strategies
groups and share using objects
Know by heart division facts for the
2, 5 and 10 times tables
count in steps of 3 and derive ÷3
facts
use known facts to derive further
division facts e.g. 9÷ 3 = 3 so 90 ÷3
= 30
Recorded Strategies
write number sentences using
÷ and =
draw symbols to represent
grouping and sharing
use number lines and hundred
squares to explore patterns of
repeated subtraction
draw own number lines with
steps of repeated subtraction
e.g. 20 ÷ 5 =
time tables posters for quick
reference
count in steps of ½ to 10
recognise the effect of dividing by 1
2
solve division
questions with
teacher support
numbers to 100
understand that
division is not
commutative
count on and back in 2s, 5s, and 10s
base 10 to model division with and
without exchanging (borrowing)
cubes, counters etc. to make equal
groups or share
read and write number
sentences using ÷ and =
make arrays with objects or peg
boards
draw pictures and symbols in
sets 6 ÷ 2 = 3
recognise multiples of 2, 5 and 10
know by heart the division facts for
the 2x table up to 10 x 2
rapidly recall halves of even numbers
up to 20
know by heart half of 20, 40, 60, 80,
100
introduce vocabulary ‘divide’ and
‘division’
draw arrays
Number lines labelled in ones to at
least 20 and in 10s to 100 (with or
without marks for ones). Begin to
use these for ‘jumps back’ of 1, 2, 5
or 10.
× × × ×
× × × ×
8÷2=4
8÷4=2
write number sentences to
describe arrays or groups
1
concept of
equal
numbers to 20
understand concept of half and find
half of even numbers up to 20 with
support
role play
drawn sets of pictures of real
objects or symbols
exploring real situations and
environment
use vocab such as ‘equal groups’,
‘same amount’ and ‘sets’
counting apparatus –
beads, counters, cubes, objects
Share and group ‘fairly’ ‘equally’
own drawings to show sharing
or grouping