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Introducing Fractional Numbers (V)

© Vidya Narayan Wadadekar

In the previous article, we were talking about teaching 4/2 as a fraction. In the first place, I would like to teach this fraction as 4 times ½. To do this, I would give children square pieces of same sizes, cut exactly into half. I would ask them to take 4 half pieces and ask them to find out how many complete squares they make. Children are usually able to tell that they make 2 squares. We write it as 4/2 = 2.

After ensuring that children understand 4/2 = 4 times half = ½ + ½ + ½ + ½ = 2, we can introduce the third meaning of fraction, which is as a division of whole numbers. They are familiar with the notation 4/2 as a division of 4 by 2. To give this sense, take 4 squares of the sizes we have used in the earlier activity. Ask children to divide them between two groups of equal sizes. Ask them to find out the number of squares in one group, which is two squares. Thus, 4 ÷ 2 = 2.

In the above example, the numbers involved in the fraction resulted in complete division. Therefore, take examples wherein the whole numbers involved result in incomplete division. For example, take the fraction ¾. We must repeat the different meaning of ¾ learned so far in order to develop clear-cut understanding of fractions.

As a Part of a Whole: The expression ¾ implies dividing the whole into a given number of equal parts, shown by the denominator. Thus, we divide one square into four equal parts. Each part we name as one-fourth. Next, consider the number of those parts, shown by the numerator. Thus, we take three (times) one-fourths. This is the concept of fraction as broken numbers. See figure 1.

As a part of a Group: We give them, suppose, 12 beads. We represent them in four rows having an equal number of beads. We take four rows, as the number in the denominator of ¾ is four. Thus, each row gets three beads. See figure 2.

Now, we select three rows, as three is the number indicated in the numerator. The total number of beads we have thus selected is nine. Thus, ¾ of 12 is 9.

This use of fraction to express parts of groups larger than one is more difficult for the child to understand. However, it is necessary to comprehend parts of a group.

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