How to teach subtraction
Counting on - a useful mental method for subtraction
Children usually can learn to add with few difficulties, even where there is the difficult "carrying over". Many have difficulties with a formal written method for subtraction (or taking away). The mental method of "counting on" gives a good representation of one of the meanings of subtraction that children may find difficult, namely "find the difference between two numbers" I find that this is a much more difficult concept than "here is a number, now "take away" this number from it"
The method known as "counting on" needs children to have a basic idea of a number line. To do the sum 134 - 27 put down both numbers on this line.
27 ............................................................ 134
Now ask what is the next whole number. Answer "30" How do we get from 27? Add 3.
How do we get from 30 to 130? Add 100.
How do we get from 130 to 134? Add 4
How do we get from 27 to 134? 3 + 100 + 4 = 107
This method is so simple that a child can do quite complex subtraction, including numbers where "borrowing" would be needed in a written method, in their heads and even counting on their fingers. Children who really struggle with maths could manage with this method even if they never master a formal method. This is not, of course, ideal but as a life skill it could do! I have found that children in Years 5 and 6 (age 10 and 11) really like this method, and with mathematically challenged pupils in Years 7, 8 and 9 it builds confidence, particularly when they can do the sums in their heads.