Introducing Division (I)

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Dec 4, 2002

Of all the basic arithmetic operations I find the division operation most interesting one to teach. When I teach this operation children's involvement is more and every one is eager to discover his answer to the given problem. The variety of activities demanding children's participation for understanding division operation is literally endless.

Teaching division to children involves giving them understanding of the two meanings attached to it. These two meanings arise because of the two types of situations we have to handle requiring division operation.

One meaning of division is the partitive meaning. We apply this meaning when we are asked to find out how many objects will be in one part when the given number of objects are distributed in some number of equal parts.

Suppose, we have 12 picture-cards and we have to find out how many each of the four children will have, if these were distributed equally. In this situation we will be using the partitive meaning of division. As the word partitive suggest, we actually distribute the picture-cards one at a time turn by turn to all the four children, till we finish all the cards. Then we count the number of picture cards received by any of these children. Thus, we find out how many objects are in one of the four equal parts of the picture cards we have made. This is the partitive meaning of division. The answer of the given division situation is "three picture cards". This is shown in the figure above to your left-hand side.

The other meaning of division is the measurement meaning. We apply this meaning when we are asked to find out how many groups we can have, if we take out given number (measure) of objects at a time from the given set of objects.

Let us again take the example of 12 picture cards. However, let us now find out the number of children, to each of whom we can give a set of four picture cards from the 12 cards. As the word measurement suggests we take out four picture cards at a time making one group. We repeat this procedure till we finish all the cards. Then we count the number of groups. This is the measurement meaning of division. Answer of the given division situation is "three children". This is shown in the figure to your left.

It can be easily seen that in the partitive meaning the focus is on the number of objects in each group whereas, in the measurement meaning the focus is on the number of groups. However, it is worth noting that in both the situations answer remains the same. Children should know these two different meanings of division very clearly, to avoid confusions in solving specifically word problems related to division. Of course, they need not be told the terms partitive or measurement.

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