key stage 2 numeracy -
Addition & Subtraction & the Number Line
In the early years of maths teaching the emphasis is now on mental maths rather than written work. The belief is that a thorough mental picture is essential. Some countries with a very high maths attainment do not start written methods of calculation until the age of nine.
The Number Line
This is very useful to illustrate addition and subtraction and is used extensively in early years. Find the point corresponding to the first number and then count on (addition) or back (subtraction) to the second number.
The Law of Commutation
a + b = b + a
It is important that your child fully understands this. When doing the sum 3 + 58 it is much easier to convert it to 58 + 3 and move three spaces on the number line from 58 rather than move fifty eight spaces on from 3.
The law of commutation also works for multiplication but not for subtraction as (a-b) does not equal (b-a).
58 + 29 = difficult
58 + 30 - 1 or 58 + 2 + 27 = easier
When doing mental maths we do this without thinking about it, but it needs to be taught. Changing a number to a round number or one which creates a round number when added to or subtracted from the other (e.g. 29 to 30 or 28) and then compensating makes the calculation much easier. For instance (33 + 99) is much easier when thought of as (33 + 100 -1).
The Number Square
The number square is an excellent visual tool for addition and subtraction. Move across to add or subtract units and up or down for tens.
This is very useful to illustrate addition and subtraction and is used extensively in early years. Find the point corresponding to the first number and then count on (addition) or back (subtraction) the second number.
Using Multiples of Five
Perhaps as a result of counting on their fingers, young children find counting using multiples of five and 'some more' relatively easy. For instance, 8 + 6 can be thought of as 5 + 5 + 3 + 1. This confidence can be used for larger numbers such as 24 + 32. 20 + 30 = 50. The 4 and 2 can then be added to make a total of 56.
Children often find calculating doubles easy. So (5 + 6) can be thought of as (2 x 5) + 1. We can also use doubles for larger number calculations such as 31 + 29 = (2 x 30) + 1 - 1 = 60.