Numeracy
Teaching Numeracy at KS2
Core Principles
Calculations done horizontally first
Emphasis on mental calculation
Emphasis on place value
• Firstly
Standard written • .
calculations are
•
132+29
=
132
+20
+9
delayed until pupils
have firm working
ideas about place • before
value and have a
bank of mental
calculation strategies
Two key points
The children need to know their
multiplication (and division) tables OFF BY
HEART.
These should be taught in a fun way the
children are likely to enjoy. For example:
Place Value
Place value means the value of digits
depending on the column they are in
Money is the best vehicle for teaching
PLACE VALUE.
The children use money in real life and
need to be encouraged to know the
decimal value of it’s coins.
How many of these are there
in £20?
How many 5p make this?
If I split a pound up, how many
of these will I have?
How would you work out ….
23 + 24 =
45 + 46 =
68 – 34 =
101 – 59 =
Addition


At Key Stage 1 calculations are
usually written horizontally
Number lines are often used to
support informal methods and help
build up imagery
132 + 29 =
Addition continued…
Children are introduced
to ‘partitioning’
Early stage:
38 + 27 =
30 + 20 = 50
8 + 7 = 15
38 + 27 = 65
Then:
38
+ 87
110
15
125
Lastly:
38
+ 87
15
110
125
Subtraction at KS2
Children are taught to subtract by finding the
difference between the two numbers.
This method involves counting on from the smaller
to the larger number and is called ’complementary
addition’
85 – 57
_85
57
3 (60)
25 (85)
28
Subtraction with larger numbers
326 – 178
-
326
178
22 (200)
126 (326)
148
Subtraction at KS2
Finding the difference
continues to be an
important informal method
When children are ready,
they are introduced to
‘decomposition’, which
involves partitioning
Leading (eventually) to:
Multiplication
Early work on multiplication
involves images of groups and
arrays:
Next children use partitioning
for calculations:
26 x 7 =
20 x 7 = 140
6 x 7 = 42
26 x 7 = 182
Multiplication – children move on to the
‘grid method’
7 x 23 = 161
x
20
3
7
140
21
Multiplication - continued
The following method of recording is
taught to children when they are
ready
534
x 6
468
x 52
Division
Early work on division involves ‘sharing’
and ‘grouping’
6 pens shared between 2 children.
They get 3 each.
2 groups of 3 pens. 6 pens in total.
It helps if the children are taught this
using practical apparatus (counters are
best as they can be placed in ‘arrays’
– see previous)
Division – the ‘chunking method’
Next children are encouraged to understand
division as building up multiples (chunking)
305 ÷ 7 =
(estimate: 40 x 7= 280 so the answer is a bit
more than 40.)
305
- 280 (40 x 7)
25
- 21 ( 3 x 7)
4
305 ÷ 7 = 43 r 4
Division continued
Children who are ready, are taught
other methods of recording
267 ÷ 8 =
… and, only after much work on the
value of fractions:
In conclusion …
Children are always encouraged to think
which is the most appropriate and
efficient method for the numbers
involved
 An understanding of place value is vital


Mental methods should be the first
resort