Whole & Part

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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 &ldquo;same&rdquo; quantity as &ldquo;different&rdquo; fractions when they are part of different &ldquo;wholes&rdquo;.

The top horizontal row contains different sets of tokens (1, 2, 3 &amp; 4) which can be considered as &ldquo;wholes&rdquo;. The left vertical column contains the same sets of tokens (1, 2, 3 &amp; 4) which are to be expressed as fractions of these &ldquo;wholes&rdquo;.

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 &ldquo;interpreted&rdquo; unless the whole is known.

Constructing a Whole from the Part 

The above table can also be used to &ldquo;find&rdquo; 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 &ldquo;intuitive&rdquo; meaning to fraction operations &amp; finding the result of operations, without relying only on the rules of fraction operations.

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