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Introducing Fractional Numbers (VI)

© Vidya Narayan Wadadekar

We discussed how children could be shown different meanings of the fraction ¾ in the article "Introducing Fractional Numbers (V)" . We can take it as three-fourths as three parts of one-fourths of a square or we can take it as one part of three squares divided into four equal parts. If you take a look at the three parts in Figure 1 and try to check if they match with the three-fourths in the Figure 3, it cannot be done directly. Therefore, we need to stick to some method of dividing the square into the required number of equal parts, which will make comparison of different parts of the squares very easy.

See how we have divided the three squares attached to each other in a row (figure 3). We have folded them lengthwise twice. Then one part of it is 3/4th. In a similar way, we can take a single square and fold it twice to get four equal vertical portions rather than triangles. This is shown in the figure below:

In this case, a child can take three separate one-fourths or directly take three one-fourths together, leaving out only the one-fourths of the square shown in the left. Then he can overlay these three one-fourths on the colored portion in the figure to the right.

Such comparisons help children grasp a very important idea: Three times one-fourths is equal to one-fourths of three squares together.

Here, point out the important condition we have that the squares used should be of the same size (congruent).

Take many more examples like: 3/2, 5/8 where the denominator is easier to handle. Children can easily make two or eight equal parts of a square by just folding it.

Next, you can take fractions like: 2/3, 4/5 etc., where the teacher may have to provide help in folding out the squares to get three or five equal parts. Another way to improve class work is to provide squares with three or five grooves on opposite sides, as shown in the figure below:

Using these grooves as points for folding, children can obtain equal portions of the given square. This method of understanding meanings of the fractions may appear as slow, but it tremendously increases children's understanding of fractions. This kind of understanding later increases the speed of understanding of addition, subtraction, multiplication and division of fractions.

When children master different meanings of given fractions, using actual objects, they should be taught to draw figures. In drawing figures to represent fractions, children should be taught to follow a particular method.

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