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Introducing Fractional Numbers (III)

© Vidya Narayan Wadadekar

To check if children have correctly grasped ideas about the fractions taught so far we can ask story-problems. It could be like: Tom said, "I ate half pizza, today. Steve said, "I also ate half pizza, today!" Then Tom said, "but I ate more pizza than Steve has". Is that possible?
We can construct many such problems for understanding their idea of one-fourth and one-third. Once we are sure that children clearly understand that if there are objects of different sizes (e.g. squares, circular objects) their halves will also differ in size, we can introduce very many fractional numbers and their names.

We can tell them that half is written as "one, below it a small horizontal line, below the line two" (See the notation in the left). Using this notation the convention followed for reading this fractional number is like this: the number above the horizontal line is read as a cardinal number and the number below the horizontal line is read as an ordinal number. Accordingly, we should read this as "one-second". However, this fractional number is used frequently in our day-to-day activities and hence has received a special name "half". Is it not very simple to read or write?

This number could be read as "one-third". Let children note that the word names for the fractional numbers are hyphenated.

When the mathematical model is a set of discrete objects like beads as shown in the figure here, we check the set to see that its number is divisible by the number of the subsets required. For example, we want to know one-third of twelve. We check if twelve is divisible by three (the "third" in one-third suggests that there are three subsets).

Teacher can hand over additional sheets of paper to children for folding as many times as they wish and help them in identifying ways to write the fractional numbers and their word names. Some of the fractions and their names are indicated in the figure below:

After giving children experiences with fractional numbers less than or equal to one, we can extend their ideas to include fractional numbers greater than one. At this stage the most appropriate teaching aid is the number-line segment. However, special care need to be taken when the number-line segment is introduced. We should relate the concept of division of whole numbers to the definition of a fractional number as the quotient of two whole numbers.

Remember that the divisor should never be zero. For example, 4 ÷ 2 can be interpreted on the number-line segment as two backward jumps of equal lengths from 4 to 0.

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