This task seeks to make the connection between pupils understanding of fraction as an operator “half of…” and formal multiplication of fractions.
For each question the pupils are to compare against the “whole” which is shown and draw bars, in turn. The middle bar is relative to the top bar, whereas the bottom bar is relative to the middle bar.
So, in the complete example given, the middle bar is half of the top bar. The bottom bar is half of the middle bar. The second fraction is always relative to the middle bar, in order for the model to work.
We then reinterpret the bottom bar with respect to the top bar. So while the bottom bar is 1/2 of the middle bar it is only 1/4 of the top bar. 1/4 is the product.
Of course order isn’t important and we could do the questions in reverse. 1/2 x 1/3 = 1/3 x 1/2. It doesn’t which fraction we place down first. We just need to remember that on the bottom bar, it is that fraction of the middle bar we are concerned with.
A couple of examples on the board, to ensure pupils are familiar with the model might be helpful. After this, I can imagine using this task to help pupils establish the rules fo multiplication of fractions by themselves. The important result about reciprocal fractions multiplying to give 1 is considered in the final row.
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