LANDSCORE PRIMARY SCHOOL
DEVELOPING CALCULATION SKILLS
Years Five and Six
This booklet is designed to explain the approaches used at Landscore to develop your child’s
calculation skills. They may look different to those you may be familiar with but they are how
your child will be learning to work at school.
The booklet will set out some of the most common strategies that we use to teach calculation
work. You will find that regular practice of counting, including times tables will be invaluable
to your child, as will learning key number bonds and number facts. If you are unsure about any
of the strategies as set out in this booklet then please do not hesitate to speak to your child’s
teacher who will be more than happy to help you.
BAG OF TRICKS
As the children move into Key Stage 2 the emphasis falls on carefully studying a question and
choosing the best approach. We encourage them to expand their ‘bag of tricks’ to include a
range of mental, informal and written methods of calculation. As the children move from
Team 1 to Team 2 and then onto Team 3, we focus on different skills, with the work in Team 3
focussing much more on the written methods of calculation.
We encourage them to look at the numbers carefully and to generate a plan, for example if
looking at the sum 78 + 49, we would want the children to think about the methods in their
bag of tracks and choose the best one for that particular question. In this instance we would
hope the children would round to an easier sum and then adjust; (78+50) – 1.
As you will see, this booklet covers addition, subtraction, multiplication and division breaks
these down into three parts:
 Mental methods
 Informal jottings
 Written methods
LANDSCORE WEBSITE
A recent addition to the Landscore Website has been tutorial videos which can guide you on
how to use some of the methods of calculation described in this book, as well as helping with
other areas of learning. These can be very useful to support homework tasks and your child’s
general mathematical development.
The following How to ... videos are available on the Landscore website on the Parents menu
www.landscore-primary.devon.sch.uk
4 Quadrants and Co-ordinates
Bonds to 100
Bus Shelter with a remainder
Divide by 10 Part 1
Equivalent Fractions 2
Finding Simple Percentages
Mental Subtraction
Number Line Division
Perimeters of Shape
Times by 10 and 100
Area of Compound Shapes
Bus Shelter
Chinese Method
Divide by 10 Part 2
Finding Percentages
Fraction of a Shape
Missing Co-ordinates
Number Line Subtraction
Rounding to an easier sum
Using a Protractor
Area of a Shape
Bus Shelter with money
Co-ordinates
Equivalent Fractions 1
Finding Simple Percentages
Grid Method
Missing Numbers
Partitioning with +
Subtraction with decimals
ADDITION
MENTAL METHODS
Partitioning
A method of adding is to partition the numbers into parts, add the parts and then recombine
to find the total.
145 + 23 = ..............................
e.g.
100
+
40
+
5
20
+
3
100
60
8
You can partition both numbers as shown above, but we recommend to the children that one
number should be partitioned rather than both as it requires only to add on hundreds, tens or
units in small steps.
145 + 20 = ....................... (add the tens of the smallest number first)
..... + 3 = ............................ (add the units of the smaller number second)
Rounding to an easier sum
This is particularly effective as long as you think carefully about whether you need to add an
amount back on or take something away.
If you add on too many … you need to give it back (subtracting)
If you don’t add on enough … you need to add on some more (+)
24 + 19 = (24 + 20) – 1 = 43
458 + 71 = (458 + 70) + 1 = 529
166 + 47 = (166 + 50) – 3 = 213
This is great for decimals as well ;
£3.88 + £4.20 = £4.20 + £4.00 – 12p = £8.08
It can be useful to show this method alongside the number line to enable the children to see
exactly what is happening. The aim is for the children to look for easier sums that can be
calculated mentally and then adjust.
49 + 73 = 122
+50
-1
73
122 123
WRITTEN METHODS
From this, children will begin to carry below the line. These are the methods that we are most
likely to remember from school.
625
+ 48
673
783
+ 42
825
1
1
367
+ 85
452
11
The method is broken down into the following stages;
625
+ 48
3
add the ones (or units),
five add eight is thirteen
one carried ten under the tens column and 3 in the units column.
1
625
+ 48
73
add the tens, twenty add forty is
sixty, plus ten underneath (which we carried earlier), seventy.
Put the seventy in the tens column.
1
625
+ 48
673
add the hundreds, six hundreds.
Put the six hundreds in the hundreds
column.
1
Using similar methods, children will:
 add several numbers with different numbers of digits.
 begin to add two or more three-digit sums of money, with or without adjustment from
the pence to the pounds.
 know that the decimal points should line up under each other, particularly when adding
or subtracting mixed amounts, e.g. £3.59 + 78p.
Children should extend the carrying method to numbers with at least four digits.
587
+ 475
1062
1 1
3587
+ 675
4262
1 1 1
Using similar methods, children will, as above begin to:
 add several numbers with different numbers of digits.
 begin to add two or more decimal fractions with up to three digits and the same
number of decimal places;
 know that decimal points should line up under each other, particularly when adding or
subtracting mixed amounts, e.g. 3.2 m – 280 cm
Children should extend the carrying method to number with any number of digits.
7648
6584
42
+ 1486
+ 5848
6432
9134
12432
786
1 11
1 11
3
+ 4681
11944
121
and also to numbers which include decimals. When working with decimals it is vital that the
children line up the decimal point and if required, add a place holding zero to any spaces.
+
321.6
49.89
371.49
11
SUBTRACTION
MENTAL METHODS
Partitioning
Our advice when using partitioning, to help with subtraction, is to partition (break up) only the
smaller of the two numbers.
287 – 84
287 – 80 = ................... (take away the 80 from the smaller number first)
....... – 4 = ................... (take away the 4 from the answer second)
Find an easier sum and adjust
As with addition, looking at a sum carefully can help you to locate a much easier calculation.
385 – 79
Taking away 79 in one step is not an easy prospect, however if you change the 79 to 80 and try
taking 80 away, this is a much easier process. But remember, you’ve taken away too many so
what must you do?
Take away too many …. Give them back (+ them back on)
Don’t take away enough … Take away some more ( more -)
(385 – 80) + 1
Warning – Always be sure that you adjust very carefully. A common mistake is to either add or
subtract without thinking about what the question is asking of you.
INFORMAL JOTTINGS
Using the Number Line; Counting on (Finding the difference)
If the numbers involved in the calculation are close together or near to multiples of 10, 100
etc, it can be more efficient to count on.
We encourage the children to make the smallest amount of jumps possible. Quick recall of key
number facts would help. Children in year 5 and 6 would solve the following question
efficiently, like this;
82 – 47 =
+30
+3
Help children to b
3 + 30 + 2 = 35
47
50
+2
80
82
Children will continue to use empty number lines with increasingly large numbers. When the
children come into Year 5 and 6, we encourage them to visualise this as a mental method and
calculate the jumps in their heads. We like the children to study questions and choose the best
method. The number line is very useful with sums that are near to multiples of 10,100,1000.
e.g. 3002 – 1987 =
+3
Help children to b 1987
3 + 1000 + 2 = 1005
+ 1000
2000
+2
3000
3002
It can be an excellent method to use with decimals;
e.g. 18.7 – 8.9 =
+0.1
Help children to b
0.1 + 9 + 0.7 = 9.8
8.9
+9
9
+0.7
18
18.7
And also when working with £ and finding change.
e.g. £20 - £6.65
+£0.35
Help children to b £6.65
+ £3
£7
+ £10
£10
£20
£10 + £3 + £0.35 = £13.35
Children will begin to use informal pencil and paper methods (jottings) to support, record and
explain partial mental methods building on existing mental strategies.
Partitioning
This process should be demonstrated using arrow cards to show the partitioning and base 10
materials to show the decomposition (breaking up) of the number.
89
- 57
=
80 + 9
50 + 7
30 + 2 = 32
Initially, the children will be taught using examples that do not need them to borrow, where
the bottom number can be successfully taken away from the top number.
From this the children will begin to borrow.
71
- 46
=
Step 1
=
70 + 1
- 40 + 6
The calculation should be
60 + 11
read as e.g. take 6 from 1.
- 40 + 6
20 + 5 = 25
In step 2, the children have borrowed a ten from the tens column and carried it across.
Step 2
This would be recorded by the children as
60
70 + 11
- 40 + 6
20 + 5 = 25
Children should know that units line up under units, tens under tens, and so on.
WRITTEN METHODS
Partitioning and decomposition HTU - TU
754
- 86
Step 1
=
-
700 + 50 + 4
80 + 6
-
700 + 40 + 14
80 + 6
Step 2
Step 3
-
(adjust from T to U)
600 + 140 + 14
(adjust from H to T)
80 + 6
600 + 60 + 8 = 668
This would be recorded by the children as
600
700
600
140
+ 50 + 14
80 + 6
+ 60 + 8 = 668
Decomposition (the compact method)
A method that we were taught at school is the more compact method. This is a great method,
as long as the children are aware of what they are borrowing and why they are borrowing it.
We teach the children the compact method alongside the method above, allowing them to
see what they are borrowing and why. This method is quick and easy but needs a good level of
understanding to be carried out correctly. Encourage your child to talk through their
understanding while calculating.
614 1
//
754
- 86
668
It can also be an excellent method for decimals, although the children need to line up the
numbers very carefully using the decimal point as the clue and if necessary add in place
holding zeros.
324.6 – 179.85
2 11
13 15 1
324.60
1 79.85
1 44.75
200
110
13
1.5
0.10
300 + 20 + 4 + 0.6 + 0.00
100 + 70 + 9 + 0.8 + 0.05
100 + 40 + 4 + 0.7 + 0.05
MULTIPLICATION
MENTAL METHODS
Multiplying by 10 or 100
Knowing that the effect of multiplying by 10 is a shift in the digits one place to the left.
Knowing that the effect of multiplying by 100 is a shift in the digits two places to the left.
Using and applying multiplication and division facts
Children should be able to utilise their tables knowledge to derive other facts, for example, by
using knowledge of place value, equivalent facts and near facts.
e.g. If I know 3 x 7 = 21, what else do I know?
30 x 7 = 210, 300 x 7 = 2100, 3000 x 7 = 21 000, 0.3 x 7 = 2.1, 1.5 x 14 = 21, 6 x 3.5 = 21, 4 x 7 =
28 etc.
INFORMAL JOTTINGS
Rounding to an Easier Sum:
Look for a calculation that is much easier to solve and then adjust. The children need to think
very carefully about whether they need to add more lots of on, or take these away.
e.g. for this sum we have selected a sum that is easier, but have to remember that we need to
add on one more lot of 13. It is important your child thinks carefully about the lots of when
them on.
13 x 11 = (13 x 10) + (13 x 1)
=
130 + 13
=
143
e.g. for this sum we have selected a sum that is easier, but have to remember that we need to
add on one more lot of 13. It is important your child thinks carefully about the lots of when
them on.
23 x 19 = (23 x 20) – (23 x 1)
=
460 - 23
=
437
Partitioning
Children use partitioning when multiplying larger numbers. This method is quick and draws on
the children’s awareness of times tables and the effect of multiplying by 10/100.
(30 x 9)
32 x 9 =
+
(2 x 9)
(1) multiply the tens
(2) multiply the units
(3) add the totals together
This Method works brilliantly with decimals as well;
42.6 x 7
(40 x 7) + (2 x 7) + (0.6 x 7)
Using FACTORS
Children will need to factorise some of the more tricky multiplication facts down into much
easier sums.
e.g. rather than x 8 in one go, you could x2, x the answer by 2 and then x that answer by 2,
which is equal to x the original number by 8.
Other examples include;
e.g. x 8 = x2, x2, x2
x20 = x2, x10
x5 = x10, ÷ 2
x32 = x2, x2, x2, x2, x2 etc.
Encourage your child to explore other ways of making the sums easier.
WRITTEN METHODS OF CALCULATION
Grid Method
Numbers are partitioned when using the grid method to multiply. This method helps children
deal with calculation in easier steps and links well with their understanding of partitioning.
The size of the grid increases as the size of the numbers increase:
72 x 38 =
Both numbers are partitioned into tens and ones before multiplying.
Multiply by the 30 first:
x
70
30 2100
8
2
x
70
30 2100
8
2
60
Multiply by the 8 second (units):
x
70
30 2100
8
2
x
60
30 2100
6
8
16
560
70
560
2
Total the rows
x
70
2
30
2100 60
= 2160
8
560
= 576
2736 then total the columns to get the answer.
16
The grids can be used to multiply larger numbers, remembering to multiply across each row,
total each row and then add the totals of each row together.
4346 x 8
X 4000 300
8 32000 2400
40 6
320 48 = 34768
372 x 24
X
300
20 6000
4 1200
70
1400
280
2
40
8
7440
+ 1488
8928
and also decimals – the children have been taught about the close relationship that exists
between multiplying decimals and whole numbers;
32.4 x 8
X
8
30
2
0.4
Chinese Method
The Chinese method is an excellent calculation strategy which helps avoid errors with place
value and decimals. This method tends to be introduced to children in Year 5 and 6 as an
alternate way of calculating.
To begin with the children need to draw an array similar to the one below. The size of the
array depends on the number of digits you are multiplying by. 37 x 5 needs a 2 by 1 grid.
Then record the numbers you are multiplying by around the outside of the array.
3
7
5
Then begin carrying out the multiplication facts, which you record in the spaces. If the answer
is less than 10, you record as 05, for 5.
First we do 7 x 5
3
7
3
5
then we do 3 x 5
3
7
5
3
1
5
5
5
We then extend the array and add up the numbers in the array diagonally starting with the
right hand side.
37 x 5
In the event of there being a two digit answer when adding up diagonally, you record the unit
number and then carry the tens across into the next diagonal, ready to add on again.
By the end of year 6, children will have a range of calculation methods, mental and written.
Selection will depend upon the numbers involved.
DIVISION
MENTAL CALCULATIONS
If a child in key stage 2 was asked whether they are more confident using multiplication or
division, the answer will invariably be multiplication. So why not exploit this skill. We
encourage the children to use the number line, alongside their knowledge of multiplication, to
support mental division.
Using the Number Line with Division
The number line is an excellent way of allowing the children to use multiplication to support
their division work. The children are looking to use known times table facts to enable them to
move towards their target number. We always encourage children to make the biggest jump
possible. In the example below it may be possible to do a jump of 20 x 3 at the start.
e.g. 72 ÷ 3
10 x 3
0
10 x 3
4x3
30
60
72
10 lots + 10 lots + 4 lots = 24 lots .... so 72 ÷ 3 = 24
This is a very good method for larger calculations, although relies on the children having a very
good understanding of times tables facts.
Encourage your child to use their times tables knowledge to make the biggest first step
possible.
e.g. 496 ÷ 8
60 x 8
0
3x8
480
60 lots + 3 lots = 63 lots .... so 496 ÷ 8 = 63
496
WRITTEN DIVISION
Short Division (Bus Shelter)
This method is a compact method. We encourage the children to record their times tables
next to the calculation to assist with how much remainder we have each time.
0
36 972
We begin by trying to work out how many 36s go into 9, the answer being none, so we have to
carry the 9 across and record it next to the 7, making a value of 97.
02
36 9972
We next try to work out how many 36s go into 97. The answer being 2 with a remainder of
25, which needs to be carried across to the next number
0 2 7
36 997252
We complete the calculation by working out how many 36s go into 252, which equals 7, with
no remainder. Our final answer is 27.
By the end of year 6, children will have a range of calculation methods, mental and written.
Selection will depend upon the numbers involved.