Coffee and
Calculations
SUBTRACTION
_
Workshop 2
Aims of session
To help you:
 Develop your knowledge of the subtraction
methods that children use in school
 Understand the progression in methods used
as children move up through the school
 Support your child’s learning at home
Maths - The Revised curriculum (September 2013)
Year 1 – Be able to;
Read, write and interpret mathematical statements that involve addition (+),
subtraction (-) and equal (=) signs
Represent and use number bonds and related subtraction facts within 20,
e.g. 14+6= 20, 20-14=6
Add and subtract numbers to 20
Solve simple problems that involve addition and subtraction
(use concrete objects and pictures)
Year 2 – Be able to;
Solve problems involving addition and subtraction – apply increasing knowledge of
mental and written methods
Recall and use addition and subtraction facts to 20 fluently and derive and use
related facts up to 100, e.g. 3+7=10, 30+70=100, 10-7=3, 100-70=30
Add and subtract numbers to 100 using objects, pictures and mentally
Understand that addition can be done in any order, but subtraction cannot
Recognise and use the inverse (opposite) relationship between addition and
subtraction and use this to check calculations
Year 3 – Be able to;
Add and subtract numbers mentally
Add and subtract numbers up to 3-digits using formal written methods of column
addition and subtraction
Use inverse
Practise using column addition and subtraction with large 3-digit numbers- become
fluent
Year 4 – Be able to;
Use the formal written column method for addition and subtraction with up to 4
digit numbers
Year 5 – Be able to;
Add and subtract whole numbers with more than 4 digits using column method
Calculate mentally with larger numbers
Year 6 – Be able to;
Consolidate year 5 and be fluent and secure in both column addition and
subtraction with large numbers and those with decimals.
Key differences today
Interactive teaching
 Emphasis on mental calculation
Different approach to written
calculation
Maths through problem solving
 Maths is fun!
At Gillespie
We want children to be able to do
mathematics in their heads, and if the
numbers are too large, to use pencil and
paper.
also
We want children to learn quick and
efficient mental and written methods.
We want children to ask
themselves
 Do I need to use a
 Can I do this in my
head?
 Can I use drawings
or jottings to help
me?
written method?
(pencil and paper)
 Do I need a
calculator?
 Finally – Is my
answer sensible?
Head, written or calculator
2,254 - 1,306
46 - 37
1463 -102
(13 x 12) - ( 234 ÷ 9)
26.52 - 8.07
89 - 9
Mental strategies for
subtraction
Secure mental subtraction requires the ability to:
 recall key subtraction facts instantly (inverse of
number pairs to 10, 20 & 100, halves etc) and to apply
these to similar calculations
 mentally subtract combinations of one and two digit
numbers
 understand that subtraction is the inverse of addition
and recognise that subtraction unlike addition can’t be
done in any order (it has to start with the larger
number)
 understand the language of subtraction
Vocabulary of subtraction
Children are taught to understand
subtraction as taking away
(counting back) and finding the
difference (counting up)
Progression in written
methods for subtraction
5–2=
I had five balloons. Two burst. How many did I have left?
Take away
A teddy bear costs £5 and a doll costs £2.
How much more does the bear cost?
Find the
difference
7–3=
Mum baked 7 biscuits. I ate 3.
How many were left?
Take away
Lisa has 7 felt tip pens and Tim has 3.
How many more does Lisa have?
Find the difference
84 – 27 =
I cut 27cm off a ribbon measuring
84cm. How much is left?
57
57
-3
64
-7
60
84
-20
-4
64
84
-20
Counting back on an empty number line
54 - 38 =
There are 54 children in a school music show.
38 turn up late. How many are on time?
Children can partition (split) the smaller number into tens and units.
54 – 38
30 8
54 – 30 = 24
24 – 8 = 16
Exchange one long for 10
units. Then there will be 4
longs and 14 units. Then 38
can easily be subtracted.
834 – 378 =
The library has 834 books. 378 are out on loan.
How many books are left on the shelves?
+22
378
+400
400
+34
800
834
FINDING THE DIFFERENCE
22 (400)
+ 400 (800)
34 (834)
456
Counting up from the smallest number
to the biggest, using an empty number
line. It is easiest to count up to a
multiple of 10 or 100.
The steps can also be recorded vertically
– this works also for decimals!
8.23 – 4.55 =
+3
+0.23
+0.45
4.55
5.00
0.45
+ 3.00
0.23
3.68
8.00
8.23
Counting up from the smallest decimal
number to the biggest using the empty
number line.
AGAIN, FINDING THE DIFFERENCE!
Column subtraction
Expanded column subtraction (firstly without borrowing)
55 – 22
T U
50 5
- 20 2
30 3 = 33
Children should always ensure that the largest number
is at the top of the calculation and should start their
calculation with the units column
Then with borrowing!
(first using the expanded method)
71 -56 = 15
T U
60
1
- 70 1
50 6
10 5
If you read the units column as ‘1 take away
6’, this can’t be done (unless you want a
negative answer), so we have to take a ten
from the 70 and add it to the 1 so that the
calculation would read ’11 take away 6’
T U
6
1
7 1
5 6
1 5
Move towards the
standard column
method for subtraction
called ‘decomposition’
Development of subtraction...

Subtraction of decimal numbers
 Subtraction of 3, 4 and 5 digit
numbers and beyond
 Subtraction of mixed decimal e.g.
£1.34 – 75p
Over to
you!
Mistakes – Year 2
Mistakes seen where;
Learning Objectives

Understand that subtraction is
the inverse of addition and be
able to state the subtraction
corresponding to a given
addition
 Know by heart all subtraction
facts for each number to at least
10

Children believe that it is
possible to change any addition
and subtraction calculation
around, e.g. 9+3=12
9-12= 3
(instead of 12-9=3)
Mistakes – Year 4
Learning Objectives
 Use known number facts and
place value to subtract mentally,
including any pair of two digit
whole numbers.
 Carry out column subtraction of
two whole numbers less than
1000.
Mistakes seen where;
 Children sometimes begin
subtracting with the left hand
column first (hundreds or tens)
 In vertical subtraction
calculations, children sometimes
take the smaller unit number
from the larger, regardless of
whether it is part of the largest
or smallest number in the
calculation.
e.g. 45
- 37
Mistakes – Year 6
Learning Objectives
Mistakes seen where;
 Children have insufficient
 Carry out column subtraction of
numbers including involving
decimals.
understanding of place value &
exchanging
leading to –
Children believing that subtractions involving
zeros can’t be done,
e.g. 200
-146
Calculations like, 34 can’t be done
-27
Errors in column subtraction can easily be
dismissed as children just making careless
mistakes when in fact there is a
Fundamental weakness in understanding
- often highlighted when working with
decimals & a decimal point
Any questions?