Methods of Calculation: A Guide for Year 3
Addition:
Vocabulary
Addition, increase, plus, add, total, and, more than, sum, altogether
 Number lines:
Number lines help children articulate their mental processes and help record working out
informally. They also encourage the use of number bonds, partitioning and counting in “safe”
jumps.
 ‘Partition of the smaller number’
The addition is completed either mentally or on a number line by partitioning the
smaller number (into tens and units). Once the smaller number is partitioned the tens
are added first to the bigger number and then the units.
For example: find the total of 31 and 24
+10
Step 1: 31 + 20 = 51
+4
+10
Step 2: 51 + 4 = 55
31
41
51
5
 Column addition:
This method should be used when adding larger whole numbers and decimals. Once learned,
the method is quick and reliable and children should be able to use it without prompting.
*** Digits that need to be carried over are put “on the door stop”. ***
1) Recap understanding of place value by writing out H (hundreds), T (Tens) and U (units).
Carried digit
‘on the
doorstep’.
Skills drill
i) TU + U
ii) TU + TU
iii) HTU + TU
iv) HTU +HTU
v) ThHTU + HTU
vi) ThHTU + ThHTU
vii)Questions
involving money
and units of
measurement
Subtraction
Vocabulary
Take away, minus, difference between, reduce, decrease, subtract, more,
working out ‘change’, ‘er’ – i.e. fewer, further, higher, longer, etc.
 Number lines:
Number lines are arguably even more important with subtraction questions as many children
find it a lot harder to count backwards AND work through a process at the same time.
1) “Counting back”
When the numbers are FAR APART, it can be easier to count back in sensible jumps.
For example: what is 90 take away 27?
-7
63
-10
-10
70
80
90
2) “Counting on” [AKA. Finding the difference]
When the numbers are CLOSE TOGETHER, it can be easier to count on in sensible jumps.
For example: what is 90 take away 78?
(It would be silly to take away 78 when you only need to count up 12 until you get to 90 to find the difference)
+ ??
78
+??
88
90
Target number!
When you find the difference like above you need to look at the number and come up with a
sensible jump (often jumps of 5, 10 or 100) that will get you close to your target number…
 Column subtraction:
This method should be used when subtracting larger whole numbers and decimals,
especially when working out change given at the shop. Once learned, the method is quick
and reliable and children should be able to use it without prompting.
H T U
1)
a) Questions where you don’t need to take’
from the column to the left
Firstly, children are taught the standard compact
method for subtraction with questions that don’t
involve ‘taking’ from the column to the left
5 hundreds
become 4
hundreds
b) Questions involving ‘taking’ from the column
to the left
Begin with the units column.
Subtract the bottom digit from the
H T U
top digit.
If the digit at the top is smaller
than the bottom, it won’t work so
you must ‘take’ from the column
immediately to the left. In this
example 6 tens becomes 16 tens.
You can now do 16 tens – 7 tens.
*** The word ‘take’ should be used (not borrow) as digits taken are never ‘given back’. ***
Remind children that:
1. Unlike addition, the ordering of the numbers makes a
difference. Larger number at the top, smaller number at
the bottom.
2. We must take from the next column if the digit at the top
is ‘smaller in value than the digit at the top’.
Year 3 Skills drill
i)
ii)
iii)
iv)
v)
TU - TU
HTU - TU
HTU - HTU
HTU – TU
Questions involving money and units of measurement
Tip:
Can you spot how, even
though the number has
been ‘re-organised’, the
overall number still
adds up to the original
number?
i.e. 400+160+3 = 564
Multiplication
Vocabulary:
Product, groups of, multiply by, lots of, times, times tables, times, multiply,
total, and, altogether.
 Mental multiplication
Children in Year 3 should, as a minimum, know their 2, 3, 4, 5, and 10 times tables. By
the end of the year most children should be confident counting up in their 6 and 8 times
tables also.
1) Multiplication as repeated addition:
When a child doesn’t know a table off by heart, they need to know how to work it out.
For instance, being able to chant up in 4s is very important in Year 3, and using fingers
to keep track of how many you have counted is encouraged.
For example: What is 4 multiplied by 6?
+4
0
+4
+4
4
8
+4
12
+4
16
+4
20
24
2) Partitioning to multiply larger numbers
Partitioning is one of the most important strategies for mental maths.
When you need to multiply bigger numbers, first partition the number into tens and
units, then multiply them separately before adding together the two answers.
For example: What is 35 multiplied by 2?
Step 1: 30 x 2 = 60
Step 2: 5 x 2 = 10
Step 3: 60 + 10 = 70
Tip: If you know 3 x 2 = 6
then
30 x 2 = 60
 Expanded Column method:
Children should be able to use this method with prompting by the end of Year 3.
*** Children should describe what they do by referring to the actual values of the digits in the
columns. For example, the first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times
seven’, although the relationship 3 × 7 should be stressed. ***
H T U
Step 1: 8 x 7
Step 2: 30 x 7
Step 3: add together
Skills drill
i)
TU x U
ii)
HTU x U
iii)
Questions involving money and different measurement units
Division
Vocabulary:
Divided by, share equally, divide, group, divisible by, share, divided into,
‘each’, ‘how much is one’, quotient.
1) Division linked to repeated addition:
As division is the inverse of multiplication, you can use multiplication facts to help work
out division questions.
For example: What is 24 divided by 4?
If you don’t know your 4 times table by rote (and know what makes the product 24),
you can count up and see how many 4s FIT INTO 24.
Here it is clear looking at the jumps that the answer is 6.
+4
+4
+4
+4
+4
+4
1
2
3
4
5
6
0
4
8
12
16
20
24
Be careful!
4 has to fit in
exactly.
This method is also useful for finding remainders (what is left over):
For example: What is 26 divided by 4?
0
+4
+4
+4
+4
+4
+4
1
2
3
4
5
6
4
8
12
16
20
Here there are
2 remainders
[r]
r2
24
26
 Using partitioning
One way to work out TU ÷ U mentally is to partition TU into a multiple of the divisor plus the
remaining tens and units, then divide each part separately.
Informal recording in Year 3 for 84 ÷ 7 might be:
In this example, using knowledge of multiples, the 84 is partitioned into 70 (the highest
multiple of 7 that is also a multiple of 10 and less than 84) plus 14 and then each part is
divided separately.
Remainders after division can be recorded similarly. These questions should only
be attempted once children are secure with the method above.
86
70 + 16
10 + 2 r 2 = 12 r 2
Skills Drill
i)
ii)
iii)
iv)
U÷U
TU ÷ U
HTU ÷ U
Questions involving remainders. – once children are secure with the method.