# Fraction Spiders

This task was inspired by Don Steward’s tasks on Percentage Spiders, which in turn was based upon an idea from Dave Hewitt.

I have provided the structure, but fully expect teachers to create further instances. The first version starts with the value of one whole and then pupils have work out the other values.  The second version starts with the definition of 1/15, so pupils have to work backwards in order to work forwards to many of the other fractions.

The final image is of a blank grid.  A value can be palced into any cell.  Pupils can then be asked to complete the spider.

On the bottom right of each of the spiders there is the curious move from 7/18 to 14/3.  That is a doubling of numerator and a sixth of the denominator.  This is meant to be possible using logic, rather than having to step to other calculations.  It may serve as a good discussion point.  Similarly, 7/6 leads to 21/2 by multiplying numerator by 3 and dividing denominator by 3.  In effect this is a scaling by 9.

I’ve always liked this structure and had meant to formally type up a fraction version for several years, rather than sketchily drawing it on my whiteboard.  Now I have!