Representing Fractions 2

Each representation of fractions has advantages & disadvantages. Let us see them one by one.

Area Representation

It is the best suited for introducing the idea of fractions to children. It can easily be mirrored by sharing many daily-use items between friends.

It introduces children to the idea of the conditions under which a fraction increases or decreases. While sharing a roti, the more the number of shares, the smaller is the size of the share! It can lead to the logic of the numerator (shares considered) and denominator (total number of shares).

It can also lead to the idea that 2 fractions can be compared only if both of them are of the same size and are divided into the same number of parts. ½ of a big roti actually looks bigger than ¾ of a small roti! The concept that a fraction is actually a relation takes time to take root.

For the same reason, area representation makes it difficult for children to see fractions as a number. It is quite alien to their understanding of whole numbers.

Developing Logical Thinking

At the same time, the area representation, using suitable models, is excellent for developing logical thinking and flexible thinking about fractions.

1. While talking of equal parts, the focus is on the area of a part and not on its shape. In many cases, to figure out the relation between 2 different kinds of figures, principles of geometry would need to be used.

Look at the above figures. Both show a rectangle divided into four quarters. Some may hesitate to accept this in case of the second figure. But the area of the triangle and the smaller rectangles are the same!

1. The focus is also on the total number of the parts (I.e total of the area of the parts) and not their being contiguous to one another. Without this clarification, children always tend to draw the parts joined to one another.

2. In some cases, the idea of a whole being divided into “equal” parts may not be directly visible. The whole may have to be divided actually or mentally to proceed with the problem.

3. In many cases, the parts may be separated from each other, thus making it easier to guess their area in relation to the whole. But many a time, the parts can be mentally rearranged so that the answer literally jumps out.

   1. Two triangles which are in different parts of a figure, could be combined into a square which may bring out the relation of the area in relation to the whole area

4. When several parts of a whole are in separate locations, it may also lead to solving the problem in terms of set representation

Misconceptions in Area Representations

First misconception is that the various parts should not only be equal but also similar. In this representation, shape does not matter. Only the magnitude of the area matter.

Second misconception is that the lines separating the parts should always be straight line. A curved line is correct, as long as it divides the areas equally.

Difficulty with Operations

While area representation is easy to understand, it is difficult to demonstrate fraction operations like addition & subtraction.

While demonstrating fractions with area representations the whole gets obscured. In computing ½ + 1/3, if we take a roti and take ½ of it, then where is the whole from which we have to take the 1/3 from?

The Set representation is suitable for demonstrating fraction operations.