Learning equivalent fractions using a fraction wall:
The uppermost strip of the fraction wall shows 'one whole unit'. This strip can be numerically represented as 1. If we want to represent it in terms of fractions, we can write it as 1/1.
Next, let children find out the way to express 1/1 by using strips labeled as ½. Children will identify that lengths of two strips together, labeled as ½ , make a strip labeled as 'whole' or '1'.
We write this in words, as 'two times half are equal/equivalent to a whole.' Using arithmetic language we can write it as: 2 x ½ = 1/1 The same expression also can be written in a different way as: 2/2 = 1/1
Let them now find out the way to express 1/1 by using strips labeled 1/3. Without experimenting, some children can quickly tell that lengths of three strips together fit into a strip labeled as a 'whole'. Allow them to note down this observation first into words and then using the language of arithmetic as shown below: Three times one-thirds are equivalent to a whole. 3 x 1/3 = 1/1
The same expression also can be written as 3/3 = 1/1
If at this stage children have difficulty in accepting 2 x ½ = 2/2 or 3 x 1/3 = 3/3 allow them to experiment using squares of equal sizes required. How to check 2 times half is equal to 2/2 is explained in an article titled "Introducing Fractional Numbers (VI)" .
Using the method explained above, children will continue to identify many more equivalent fractions of 1 or 1/1. They will know that 1/1 = 2/2 = 3/3 = 4/4 , and so on.
In the next activity, let children find out how ½ can be represented using strips of smaller sizes. By experimenting, children will observe that using strips labeled as '1/3' or 'one-thirds', ½ cannot be represented by using the method explained above. However, if two strips labeled as ¼ are taken, their combined length can fit into a strip labeled as ½. This they can express in words, as "Two one-fourths are equivalent to one-half". Arithmetically, this is expressed as 2 x ¼ = ½ or 2/4 = ½. Using some more strips in the fraction wall, of lengths smaller than that of the strip labeled 1/4th, children should be lead to work out some more equivalent fractions of ½.
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