The success and progression of these methods is dependent upon accurate mental calculation which should be practised daily.
ADDITION
Use of objects and pictorial representation (up to 2 digit + 1 digit)
+
SUBTRACTION
Use of objects and pictorial representation (up to 2 digit – 1 digit)
=6
Practical representation and number sentences
-
=2
Practical representation and number sentences
7–3=4
Number lines and 100 squares for addition of 2 digit and 2 digit numbers
Number lines and 100 squares for subtraction of 2 digit and 2 digit numbers
Place value must be taught and understood before moving onto this method
Place value must be taught and understood before moving onto this method
Partitioning
Extend to adding HTO ALWAYS COUNT ABOVE THE LINE Extend to using HTO ALWAYS COUNT BACKWARDS, BELOW THE LINE
Partitioning
Column method – carry must be used
Column method – exchange must be used
Extend to using with larger numbers and decimals. Use diennes apparatus to
model
Use diennes apparatus to model the exchange process.
The success and progression of these methods is dependent upon accurate mental calculation which should be practised daily.
MULTIPLICATION
Use of objects and pictorial representation
DIVISION
Use of objects and pictorial representation
12 ÷2=6
3 x 2= 6
6 x 3 = 18
Practical representation and number sentences
Make links to repeated addition.
6x3=
Number lines and 100 squares
Grid method
18÷3 = 6
Practical representation and number sentences
Make links to repeated addition.
Chn have placed Numicon 3s over
6÷3=2
a 6 then counted how many groups
of 3 there are.
Number lines and 100 squares
Column multiplication
45
45.3
21 x
21.2x
5
0.06
40
1.0
100
8.0
800+
0.3
945
5.0
40.0
6.0
100.0
800.0 +
960.36
Bus stop method
Extend using larger numbers
The success and progression of these methods is dependent upon accurate mental
calculation which should be practised daily.
ADDITION AND SUBTRACTION
From the outset teach children that the largest number must go first in a calculation.
Use of objects and pictorial representation (up to 2 digit + 1 digit) Use photographs to evidence learning at this stage.
Use objects such as cubes, counters and compare bears alongside pictorial representations of the calculation.
Examples of suitable calculations at this stage include 4 + 5 or 14 + 6.
Practical representation and number sentences using practical resources (up to 2 digit + 1 digit) Number tracks and
printed number lines can also be used to support calculation. Use Numicon at this stage of development which
makes links to multiplication knowledge. The children’s work can continue to be recorded through photography and
through independently written number sentences in numeracy books. Examples of suitable calculations at this stage
include 4 + 5 or 14 + 6. Counting on is a useful mental strategy to teach at this stage.
Number lines and 100 squares for addition and subtraction of 2 digit and 2 digit numbers Teach place value
before calculating with 2, 2 digit numbers. Use Diennes and Numicon to demonstrate the value of digits. Children
should be able to identify the tens in numbers 10 – 99 and show the tens using apparatus.
After introducing place value, teach the children how to add and subtract tens using Diennes and Numicon along
with number lines and 100 squares. Examples of suitable calculations at this stage include 14 + 20 or 52 – 30. Chn
should be able to complete these calculations by using apparatus, jumping up or down on 100 squares and finally
being able to make a jump of ten on a number line to show their mental calculation.
Once chn are secure in addition and subtraction of tens begin to introduce calculations which include ones.
Examples of suitable calculations at this stage include 25 + 14 or 59 – 32. Always display calculation as a column so
chn begin to make links. When first introducing these calculations do not bridge ten, develop this as chn become
more confident. Teach the chn to calculate ones first then tens. These calculations should be recorded on number
lines in children’s numeracy books. Children should still continue to use apparatus such as Diennes, Numicon as the
children find helpful.
Extend by teaching children how to group ones and tens teaching them to make larger jumps eg 84 + 37 would be a
jump of 30 and a jump of 6 to the next 10 then a jump of 1. Do not force children to use number lines if they can
calculate mentally. Once children are at this stage, introduce partitioning. Encourage chn to move away from using
a number line by developing mental methods.
Partition method
Chn need to add ones and then tens. Introduce carrying and exchanging once children are accurate with layout and
process of partition addition and subtraction. Use Diennes apparatus to show how ones can be added to make tens
and ones, or exchanged to increase the value of a one when necessary
Column method NOTE CARRYING and EXCHANGING are the chosen vocabulary for teaching these methods. They
must be used in all year groups and not replaced with alternatives.
Introduce carrying and exchanging once children are accurate with layout and process of column addition and
subtraction. Use Diennes apparatus to show how ones can be added to make tens and ones, or exchanged to
increase the value of a one when necessary.
The success and progression of these methods is dependent upon accurate mental
calculation which should be practised daily.
MULTIPLICATION AND DIVISION
Use of objects and pictorial representation When introducing multiplication and division first explore sharing and
develop that understanding before moving onto groups of. Use photographs to evidence learning at this stage. Use
objects such as cubes, counters and compare bears alongside pictorial representations of the calculation to make
arrays.
Practical representation and number sentences using practical resources Use Numicon at this stage of
development and make obvious and purposeful links to repeated addition and subtraction. Begin to use the
vocabulary of grouping and groups (eg there are 2 groups of 3 in 6.) The children’s work can continue to be recorded
through photography and through independently written number sentences in numeracy books. Support children to
count in patterns such as 2s, 5s or 10s by using coins (eg there are 4 5p pieces in 20p) or Numicon (eg 3 10s in 30)
as they count.
Number lines and 100 squares (multiplication) Continue to use Numicon but use it along side number lines and
100 squares. Multiplication is to be done on a number line or 100 square, starting from 0 then making jumps above
the line to represent the calculation. This should be linked to repeated addition. Eg 6 x 3 could be 3 jumps of 6 or 6
jumps of 3 arriving at the answer of 18. These calculations can be recorded in numeracy books. Do not force
children to use number lines if they can calculate mentally. Once children are at this stage, introduce grid method.
Number lines and 100 squares (division) Continue to use Numicon but use it along side number lines and 100
squares. Division is to be done on a number line or 100 square, starting from 0 then making jumps above the line to
represent the calculation. The children then count the number of jumps to find their answer. This should be linked
to repeated addition. Eg 18 ÷ 3 would be 6 jumps of 3. Once children are confident with this introduce remainders
and calculate them using the same method, finding the remainder by making jumps of 1 when no more jumps of the
dividend can be made.
Grid method Begin with 1 digit x 2 digit then move onto 2 digit x 2 digit. Complete the grid method alongside the
calculation laid out as a column so children can begin to make links. Continue to use apparatus such as Numicon
and Diennes to support children as they get used to a new layout and reinforce understanding of place value, but
their mental recall of x facts should be strong. Without that understanding the children are simply completing a
series of steps, not developing understanding. The final addition step must be explicitly taught as this is commonly
where children make errors. Once children are proficient they need to be introduced to column x.
Column method for multiplication Continue to use apparatus such as Numicon and Diennes to support chn as they
get used to a new layout and reinforce understanding of place value. Extend by introducing HTO x TO and HTO x
HTO and then decimals.
Bus stop method for division When first introducing this method make clear links with multiplication by getting chn
to write fact boxes alongside each calculation. Chn to then use these fact boxes to assist in finding answers, once
chn can see these links do not continue to insist on fact boxes. Ensure calculations do not lead to remainders until
chn are secure in completing the bus stop method where carrying will be necessary. Then move onto calculations
with remainders, continue to use apparatus such as Numicon and Diennes to explore and understand this
thoroughly. Once chn can find remainders, teach them how to calculate a decimal instead with a limit of 2 decimal
places, and then how to write a remainder as a fraction. (Remainder as numerator, dividend as denominator then
simplify.)
Long division For long division continue to use the bus stop method but encourage the children to write fact boxes
with the times table they will need, and then calculate as normal.