1. Numeracy

2. Teaching Numeracy at KS2
Core Principles
Calculations done horizontally first
Emphasis on mental calculation
Emphasis on place value

3. Standard written calculations are delayed until pupils have firm working ideas about place value and have a bank of mental calculation strategies
Firstly . =
before

4. 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:

5. Place Value
Place value means the value of digits depending on the column they are in

6. How many of these are there in £20? How many 5p make this?
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?

7. How would you work out ….
= = 68 – 34 = 101 – 59 =

8. Addition At Key Stage 1 calculations are usually written horizontally
Number lines are often used to support informal methods and help build up imagery =

9. Addition continued… Children are introduced to ‘partitioning’
Then:
38 38
Children are introduced to ‘partitioning’
Early stage: =
= 50
= 15
= 65
Lastly:

10. 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 – _85 57
3 (60)
25 (85) 28

11. Subtraction with larger numbers
326 – 178
326
178
22 (200)
126 (326)
148

12. 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:

13. Multiplication
Early work on multiplication involves images of groups and arrays:
26 x 7 =
20 x 7 = 140
6 x 7 = 42
26 x 7 = 182
Next children use partitioning
for calculations:

14. Multiplication – children move on to the ‘grid method’ 7 x 23 = 16120 3 7
140 21

15. Multiplication - continued
The following method of recording is taught to children when they are ready x 6 x 52

16. 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)

17. 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
(40 x 7) 25
( 3 x 7) 4
305 ÷ 7 = 43 r 4

18. Division continued
Children who are ready, are taught other methods of recording 267 ÷ 8 =
… and, only after much work on the value of fractions:

19. 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