Numeracy

Numeracy

Teaching Numeracy at Teaching Numeracy at KS2KS2

Calculations done horizontally first

Emphasis on mental calculation

Emphasis on place value

Core Principles

Two key pointsTwo 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 means the value of digits depending on the column they are in

Place ValuePlace Value

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 ….How would you work out ….

23 + 24 =

45 + 46 =

68 – 34 =

101 – 59 =

AdditionAdditionAt 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…Addition continued…

Children are introduced to ‘partitioning’

Early stage:

38 + 27 =

30 + 20 = 50

8 + 7 = 15

38 + 27 = 65

Then:

38 38+ 87 + 87 110 15 15 110 125 125

Lastly:

Subtraction at KS2Subtraction at KS2Children are taught to subtract by finding thedifference between the two numbers.This method involves counting on from the smallerto the larger number and is called ’complementaryaddition’

85 – 57 _85 57 3 (60)

25 (85) 28

Subtraction with larger numbersSubtraction with larger numbers

326 – 178

326- 178 22 (200) 126 (326) 148

Subtraction at KS2Subtraction at KS2Finding the difference continues to be an important informal method

When children are ready, they are introduced to ‘decomposition’, which involves partitioning

Leading (eventually) to:

MultiplicatiMultiplicationonEarly 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:

Multiplication – children move on to Multiplication – children move on to the ‘grid method’the ‘grid method’7 x 237 x 23 = = 161 161

x 20 3

7 140 21

Multiplication - Multiplication - continuedcontinued

The following method of recording istaught to children when they are ready

534 468 x 6 x 52

DivisioDivisionnEarly 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 thisusing practical apparatus (counters

arebest as they can be placed in ‘arrays’

– see previous)

Division – the ‘chunking Division – the ‘chunking method’method’

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

Next children are encouraged to understand division as building up multiples (chunking)

Division continuedDivision continuedChildren who are ready, are taughtother methods of recording267 ÷ 8 =

… and, only after much work on the value of fractions:

In conclusion …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