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We will now present an activity which clarifies that the part (fraction) and the Whole are relative. It also helps to see the “same” quantity as “different” fractions when they are part of different “wholes”.
The top horizontal row contains different sets of tokens (1, 2, 3 & 4) which can be considered as “wholes”. The left vertical column contains the same sets of tokens (1, 2, 3 & 4) which are to be expressed as fractions of these “wholes”.
Each cell expresses the set (from the left vertical column) as a fraction of the set from the top horizontal row.
For example if the whole is a set of 3 tokens (on the top row), then a set of 4 tokens (left vertical column) can be expressed asor 1 . The same set of 4 tokens, however, is expressed as or 2 if the whole is a set of 2 tokens.
This activity will give a lot of understanding of the fluid relation between a whole and a part and how it gets expressed as different fractions. It also drives home the point that a fraction cannot be “interpreted” unless the whole is known.
Constructing a Whole from the Part
The above table can also be used to “find” the whole when a part is given as a fraction. IF a set of 2 tokens is 2/3 in relation to a whole, then we can deduce that the whole must be a set of 3 tokens! These exercises provide “intuitive” meaning to fraction operations & finding the result of operations, without relying only on the rules of fraction operations.
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