Emmbrook Junior School
Calculation Policy
This calculation policy has been created to meet the expectations of the new
national curriculum but most importantly the learning needs of our children at
Emmbrook Junior School. The methods chosen to match the expectations of the
national curriculum but also to build on previous knowledge.
The policy has been organised by year group, considering the national curriculum
2014 expectations. The new curriculum focuses on skills and mastery and is not
about moving children on to the next method as soon as they can do the one
before. Working with more complex and richer problems rather than new methods
will support this ‘mastering’ of maths. However, some children will be working at
levels above their age and will require the introduction of new methods.
Multiplication (x)
Year 1
Children experience counting equal group of objects in 2s, 5s and 10s.
Year 2
Use repeated addition on a number line
Present practical problem solving activities involving counting equal sets or
groups, as above.
Starting from zero, make equal jumps up on a number line to work out
multiplication facts and write multiplication statements using x and = signs.
Use arrays
How many frogs on the lily pads
5x2=2x5
5 x 3 = 3 + 3 + 3 + 3 + 3 = 15
3 x 5 = 5 + 5 + 5 = 15
Use arrays to help teach children to understand the commutative law of
multiplication, and give examples such as 3 x __ = 6.
Multiplication (x)
Year 3
Introduce the Grid Method
Introduce the Grid Method with children physically making/ drawing an array to
represent the calculation e.g. make 10 lots of 4 with counters and dots, then
translate this to grid method format.
Year 4
Continue to show the Grid Method using the arrays model.
13 x 4
500 + 150 + 30 = 680
Children can use column addition method if needed at this point.
Progressing to expanded column multiplication
13 x 4 = (4 x 10) + (4 x 3)
Progress to
Discuss how the grid method is shown in the column method.
Compare the methods. What is the same and what is different?
Multiplication (x)
Year 5
Introduce Short Column Multiplication linked to the expanded method.
Year 6
Use Short Multiplication (see Y5) to multiply numbers with more
than 4-digits by a single digit; to multiply money and measures,
and to multiply decimals with up to 2d.p. by a single digit.
Compare the Expanded and Compact methods highlighting similarities and
differences
Introduce long column multiplication
18 x 13
243 x 36
Children must ensure the 8 is in the ones column
Use the grid before long column multiplication as the relationship can be seen
in the answers in each row.
18 x 3 first row
18 x 10 second row
243 x 6 first row
243 x 30 second row
Use long multiplication (see Y5) to multiply numbers with at least
4 digits by a 2-digit number.
Division (÷)
Year 1
Discuss division as both grouping and sharing
Grouping
How many groups of 4 can be made with 12 stars? = 3
Year 2
Group and share using the ÷ and = symbols
Use objects, arrays, diagrams and pictorial representations, and grouping on a
number line.
This represents 12 ÷ 3, posed as how many groups of 3 are in 12? Pupils
should also show that the same array can represent 12 ÷ 4 = 3 if grouped
horizontally.
Sharing
15 shared between 3 ( 15 ÷ 3 = 5)
15 grouped in to 5s (15 ÷ 5 = 3)
Using a number line.
Group from zero in equal jumps of the divisor to find out ‟how many groups of _
in _ ?‟. Pupils could and using a bead string or practical apparatus to work out
problems like „A CD costs £3. How many CDs can I buy with £12? ‟ This is an
important method to develop understanding of division as grouping.
12 ÷ 3 = 4
Division (÷)
Year 3
Children to work out unknown division facts by grouping on a number line
from zero.
How many 3s in 18 (18 ÷ 3)?
Year 4
Short division
Start with calculations with no remainders. 96 ÷ 3
Remind children of correct place value, that 96 is equal to 90 and 6.
How many 3s in 9? = 3, and record it above the 9 tens.
How many 3s in 6? = 2, and record it above the 6 units.
They are also now taught the concept of remainders, as in the example. This is
introduced practically as well as being shown on a number line. Children should
work towards calculating some basic division facts with remainders mentally for
the 2s, 3s, 4s, 5s, 8s and 10s,
Next step will be the use of remainders in the calculation
72 ÷ 4
How many 3s are in 20 (20 ÷ 3)?
Partition
6
So 20 ÷ 3 = 6 r2
r2
group the tens
Exchange the remainder of tens for 1s then group the 1s.
Division (÷)
Year 5
Short division with remainders: Now that children are introduced to examples
that give rise to remainder answers, they must consider the meaning of the
remainder and how to express it, ie. as a fraction, a decimal, or as a rounded
number.
The answer to 5309 ÷ 8 could be expressed as 663 and five eighths, 663 r 5, as
a decimal, or rounded as appropriate to the problem involved.
See Y6 for how to continue the short division to give a decimal answer for
children who are confident.
Year 6
Calculating a decimal remainder: In this example, rather than expressing the
remainder as r 1, a decimal point is added after the units because there is still
a remainder, and the one remainder is carried onto zeros after the decimal
point (to show there was no decimal value in the original number). Keep dividing
to an appropriate degree of accuracy for the problem being solved.
Long division
Addition (+)
Year 1
Count all
Record as 8
Year 2
Add 10s then add units using a number line.
+ 5 = 13
Counting on
46 + 27 = 73 (bridging tens when 10s are added)
Record as 8 + 5 = 13
Progress to showing this on a number line
Step 1) Partition numbers then recombine
Start with numbers that do not cross 10s boundary
Step 2) Pupils then progress to numbers which cross the tens boundary. NOTE:
Children must be secure in their mental addition of numbers within 20 at this
step.
Record as 9 + 6 = 15
Bead strings can be used to illustrate addition including bridging 10
Confident and accurate children can also use this method for numbers with 3
digits.
Addition (+)
Year 3
Introduce the expanded method
Children continue to use physical representation of addition using place value
counters
Year 4
Introduce the compact method
Move from expanded addition to the compact method, adding ones first and
carrying over numbers underneath the calculation. Include money and measures.
Show children how carrying is needed when the ones and tens columns add to
more than 10.
Children then add the columns up starting with the ones column in preparation
for the expanded column method.
Add the ones column first.
Carried numbers go below the calculation
NOTE: reinforce correct place value terminology especially when carrying/
exchanging numbers.
Children should discuss how this method is linked to the previous method.
Children again discuss how this method is linked to the previous. Discuss if this
is easier/ quicker. Why?
Addition (+)
Year 5
Continue with the compact method of addition.
Numbers exceeding 4 digits
Decimal numbers including money and measures.
Year 6
Continue with compact method but now adding larger numbers and decimal
numbers
Subtraction (-)
Year 1
Take away
Year 2
Take away
47 – 23
Count back on a number track, then number line in ones with numbers up to 20.
15 – 6 = 9
Partition the 2nd number in to tens and units.
Subtract the tens then the units.
Finding the difference/ distance between.
Move on to more efficient methods
7 is 3 more than 4 (7 - __ = 4)
Children record this using (-) and (=) signs. E.g 7 – 3 = 4
Using a number line to count on showing the blocks alongside
Finding the difference
Difference between 73 and 58 (73 - __ = 58)
Develop understanding of inverse 58 + ___ = 73
16 - __ = 9 diffence between 9 and 16 = 7
Bridging 10s
Subtraction (-)
Year 3
Year 4
Introduce partitioned subtraction method.
Step 1) No Exchanging
Step 3) 3-4 digit partitioned method
As introduced in Y3, but moving towards more complex numbers and values.
Step 2) Exchanging
73 – 46
You can’t take 6
from 3.
Step 4) Introduce the compact method of subtraction
Children begin with completing the partitioned method and the compact
method and discussing how they have changed. How is it easier/ quicker?
exchange a ten for
units to make 60 + 13
Now subtract 46
Subtraction (-)
Year 5
Year 6
Continue with compact column method
Subtract with decimal values, including mixtures of integers and decimals,
aligning the decimal point.
Create lots of opportunities to use subtractions in different contexts including
money and measures
Using the compact column method to subtract larger numbers and decimals with
different numbers of decimal places
Empty decimal places can be filled with zero to show the place value in each
column.