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Introducing Division (IV)

© Vidya Narayan Wadadekar

We have seen many ways to introduce division operations to children in the last two articles. Here is an even more important way to introduce the concept of division which involves use of the Number Line. The Number Line model gives the teacher a good device for interpreting division both with partitive and measurement meaning.

The teacher may draw/paint a number line on the classroom floor as shown in the figure here. The question could be framed as, "How many jumps of three it takes to go from 6 to 0?" In this case the number of jumps (two) of a given length (three) is the answer to the question.

Entire class can participate in this activity and hence is enjoyed by children. In this type of activity we use the measurement meaning of division. There is another benefit in teaching division using a number line. The jumping activity involved gives true sense of repeated subtraction in the concept of division. Every time the child jumps, he gets to know the remainder. Because the various stopping points on the number line correspond to the remainders obtained.

For example, when finding the number of sets of three that can be divided out of a set of six, we will have three left when we have measured out 1 set of three. Zero of six are left, when we have partitioned out two sets of three. This is shown in the figure here.

On getting to know the meaning of division, children should be introduced to the notations that represent division. There are four basic notations to represent division. These are shown below.

It is very useful to use all these notations from time to time, as all mean the same and each one them is useful in a specific situation. I have found that majority of the teachers and the text books use the fourth notation. However, division and fraction are closely related and hence familiarity with the third notation proves a useful link in smooth transition from division to fraction. The first type of notation in the figure is useful in recording the division problem statement. The second notation is space saving while typing or printing the reports. So, teaching all these notations is necessary and helps children in identifying the division operation involved.

After introducing the notations used for recording the division, you may introduce the mathematical sentences and the terms used for referring the numbers involved. The related mathematical sentences for 12/3 = 4 are:

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