Addition
Count objects to 20, moving
objects whilst counting
• Say one more than a number to
10 e.g. one more than 7
• Compare two numbers under
10– which is more?
• Adding by combining groups–
use pictures and drawings
Foundation stage
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Subtraction
Count objects to 20, moving
objects whilst counting
• Say one less than a number to
10 e.g. one less than 7
• Compare two numbers under
10– which is less?
• Subtraction as taking away
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Begin to count in 2s to 20
Begin to count in 10s to 100
They will work on putting
objects in equal groups and
counting them
Division
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Begin to count in 2s to 20
Begin to count in 10s to 100
Halving
Division as sharing
Share the pears equally between
three people
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Count objects to 20, moving
objects whilst counting
Read, write and order numbers
to 20
Say one more than a number to
30 e.g. one more than 27
Adding by combining groups–
use pictures and drawings
Use of + and = signs to write
number sentences
How many cherries are there?
2, 4, 6
There are four bananas and I eat
two. How many are left?
Count one group, then start
counting from that total when
adding on e.g. 1,2 then 3,4,5
Level One
Multiplication
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Count objects to 20, moving
objects whilst counting
Read, write and order numbers
to 20
Say one less than a number to
30 e.g. one less than 27
Subtraction as taking away
Subtraction as finding the
difference
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Count in 2s to 20
Count in 5s to 50
Count in 10s to 100
They will work on putting
objects in equal groups and
counting them
9-4 = 5
This can also be used to illustrate
that the difference between 9 and 5
is 4 (4 hops back)
Use a number line to count in hops
of 2, 5s and 10s
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Begin to count in 2s to 20
Begin to count in 10s to 100
Halving
Division as sharing
Division as grouping
Use a number line to count the
number of hops taken e.g. how
many 2s are in 10? (how many
hops have you taken)
Addition
Read, write and order numbers
to 100
• Be able to say one more to 100
e.g. one more than 58
• Addition by partitioning and
recombining (TU)
Level Two
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Children will use tens and units
equipment– make both numbers
then add the tens together, then the
units. The children will move onto
drawing the equipment.
Children will move onto
an expanded written
method– layout is
crucial.
Subtraction
Read, write and order numbers
to 100
• Be able to say one less to 100
e.g. one more than 58
• Subtraction by partitioning
and recombining (TU)
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32 - 11
Children will use tens
and units equipment
to subtract. Make the
first number then
take away the second.
Read, write and order numbers • Read, write and order numbers
to 1000
to 1000, be able to say one less
• Be able to say one more to
to 1000 e.g. one less than 348
1000 e.g. one more than 348
• Subtraction by partitioning
• Addition by partitioning and
and recombining (HTU,
recombining (HTU, decimals)
decimals) Introduction of
decomposition
Level Three
Decomposition. In this
example breaking down
50 into 40+10 and
moving the ten into the
units because 3-8 does
not work
3.9
Subtraction can be
done by finding the
difference–
counting on from the
smaller number to the
bigger one
Division
• Know 2, 5 and 10 times tables
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Children will move onto
an expanded written
method– layout is
crucial.
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The layout is crucial–
hundreds, tens and
units needs to be
carefully lined up
Multiplication
• Know 2, 5 and 10 times tables
off by heart. Begin to learn 3
off by heart. Begin to learn 3
times table
times table
Count in 2s to 20, 5s to 50 and • Know halves of even numbers
10s to 100
to 20 off by heart e.g. half of 14
Know doubles of numbers to 10 • Division as sharing
off by heart e.g. double of 4
• Division as grouping
Multiplication as repeated
addition
Use of x and = signs to write
15 ÷ 3
number sentences
Division by grouping becomes the
main way to divide. Use equipment
to do this. Children will learn what
a remainder is.
In this example there are 5 groups
of 3 in 15.
Children use their own pictures too as
well as equipment to multiply using
repeated addition. They do not count in
1s, but count in 2s, 5s, 10s as
appropriate.
Know 2, 3, 5, 6 and 10 times
tables off by heart
• Multiply numbers by 10 or 100
• Multiply two digit numbers
using the grid method
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16 x 4
X 10
6
4
24
40
Know 2, 3, 5, 6 and 10 times
tables off by heart
• Find a quarter of a number by
halving and halving again
• Dividing by 10
• Introducing written methods
of division (chunking on a
numberline)
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40 + 24 = 64
Partition the two digit number into
tens and units. Multiply each part
by the single digit. Then add each
part to work out the answer
(mentally is possible). At this level
only numbers with one ten will be
used. It is important to keep the
numbers lined up.
This example shows children counting
how many groups of 5 there are in 55.
Start at 0 and think of counting in more
than one group at a time. Here they
have counted on 10 groups of 5 and
then another 5. the answer is how many
groups there are, in this case 11.
Addition
Subtraction
Multiplication
Read, write and order numbers • Read, write and order numbers • Know times tables off by heart
to 10 000 and know the value of to 10 000 and know the value of to 10x10
• Multiply whole and decimal
each digit
each digit
numbers by 10 and 100
• Add mentally two digit
• Subtract mentally two digit
• Use efficient written methods
numbers
numbers
• Use efficient written methods • Use efficient written methods
Level Four
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Contracted method of
addition. Layout is
crucial. The number
of digits in a number
may not be the same.
2?8
+3?
251
Missing number
problems extend
children’s thinking
Add numbers to 10 000
Read, write an order numbers to
two decimal places, say which
is more e.g. which is more 2.36
or 2.64? How do you know?
• Use simple algebra
• Use written methods to add
numbers where the number of
digits is not the same
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Level Five
Decomposition–
contracted method
Layout is crucial. The
number of digits in a
number may not be
the same.
Children will be able to chunk on
a number line confidently, with
remainders
Children will use the grid method
to multiply numbers with different
numbers of digits, including
decimals
Use written
method of
chunking
Subtract numbers to 10 000
• Know times tables off by heart
Read, write an order numbers to to 12x12
two decimal places, say which • Multiply whole and decimal
is less e.g. which is less 2.36 or
numbers by 10, 100 and 1000
2.64? How do you know?
• Use efficient written methods
• Use simple algebra
36.21 x 8
• Use written methods to subtract numbers where the number
of digits is not the same
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Decomposition
more than once!
Partition the number into tens,
units, tenths and hundredths.
Multiply each part and then
recombine.
Calculate 1.2 x (1.3 + 1.4) x 1.5
Children will
learn how to use
simple algebra
Know times tables off by heart
to 10x10
• Divide whole and decimal
numbers by 10 and 100
• Use efficient written methods
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Children will subtract
decimals using a
written method
The number of
digits may not be
the same!
2n + 2n = 4n
Division
2n - 1n = n
Children will
learn how to use
simple algebra
Children will use brackets
Know times tables off by heart
to 12x12
• Divide whole and decimal
numbers by 10, 100 and 1000
• Use efficient written methods
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Continue to
use written
method of
chunking
Begin to use the
bus stop method