Tuesday 26th February 2013

Minishant Primary SchoolParental Workshop

Class 1

Mental Maths and

Decomposition

Mental Maths

The ability to calculate ‘in your head’ is an important part of

mathematics and an important part of coping with maths in

everyday situations.

MENTAL STRATEGIES FOR

ADDITION AND SUBTRACTION There are many different ways of adding and subtracting; to do both efficiently ‘in our head’, children need to be able

to use and apply the following strategies:

•Counting forward and backwards•Reordering•Partitioning•Bridging•Compensating•Using doubles and near doubles•Number bonds

Counting forward and

backwards The image of a number-line helps children to appreciate the idea of

counting forward and back, it allows them to recognise patterns and relationships too.

E.g.

Count up in one’s from 8 to 28Count up in three’s from 0 to 30Count up in five’s from 5 to 55

Count back in one’s from 100 to 77Count back in two’s from 40 to 20Count back in ten’s from 80 to 10

Partitioning

It is essential for children to know that numbers can be partitioned into, for example, hundreds, tens and units.

In this way numbers are seen as wholes rather than a collection of single digits in columns.

E.g.

30 + 47 = 30 + 40 + 7

78 - 40 = 70 – 40 - 8

Bridging

AdditionFor example: 8 + 7How many more are needed to make 10? 2If the 2 is taken from the 7, how many are left

over? 5 So, 8 + 7 is 10 + 5

56 + 17 - The ten from 17 is added to 56 to make 66Then from 66 the 7 units are added = 73

BridgingSubtraction:

For example: 63 – 37First subtract the 3 tens 63- 30 = 33Then subtract the 7 units in 2

sections33 – 3 = 3030 – 4 = 26 7

Compensating

Compensation is one of several efficient written methods for addition of larger numbers. It involves adding too much and then taking the extra off that

you have added.

For example: 744 + 86Round 86 up to the nearest 100: 86 → 100 744 + 100 = 844 We have added 14 too many (100 - 86 = 14) so we must take it away 844 - 14 = 830

744 + 86 = 830

DecompositionConsider the following subtraction:

TU 56 -12 __

When subtracting one number from another, we start with the units in the right hand column and then move on to the tens in the left hand column. In each column we subtract the bottom number from the top number and write the result below. In this sum, we subtract 2 from 6 in the units column to get 4.

56-12 4

Now we move along to the tens column and subtract 1 from 5 to get 4.

56-12 44

This is an easy sum because each number in the bottom row is smaller than the number in the top row.

What happens if that’s not the case, as in the following example?

Decomposition34

-19

___

The problem is that we can’t take 9 from 4 in the units column. If you have only 4 apples, your friend can’t take 9 away from you. What we need here is something called decomposition. Decomposition happens when we borrow an amount from the number on the left to give it to the number on the right. We only do this in the top row.

Decomposition What this means here is that we can’t take 9 from 4 so

we exchange a ten from the next column along (the 3).

We will take 10 off the left hand number (3) and give it to the right hand number (4).

The 3 is in the tens column, so it represents 30. Taking 10 off 30 leaves 20 (2) and adding 10 to 4 gives 14.

Decomposition We can now subtract 9 from 14 in the units column to

get 5.

Next, we subtract 1 from 2 in the tens column to get 1.

And that’s the answer: 34 – 19 = 15.

Task

Now it is your turn to have a go, using decomposition.

W.A.L.T.: To subtract tens and units, using decomposition.