UPDATED POST. I used this task at my workshop at #mixedattainmentmaths on Saturday. I asked all teachers to have a go at this task but to do it in what they thought was the most obvious / simplest way. An interesting experiment: what is obvious to some is not to others. Of the solutions that I managed to take in, these were the choices:
This looks like a very useful open-ended task which provides an opportunity for creative solutions and rich discussion. I have produce some printouts here.
In my view, the value in this activity is in representing each area as a fraction calculation.
According the Australian blog where I first read about this task, this is one of the most common first solutions
I’d be looking for some rationalising as to why the red area is a quarter. For example:
There are 100 solutions posted here!
And on a Prezi here enabling you to zoom into each one individually.
This is potentially very high ceiling. If students are struggling to come up with suitably challenging solutions of their own, you could always ask:
Show why this is a quarter:
Have a go first yourself. I think this is a pretty mammoth task! This one caught my eye, but you might want to have a look at the 100 solutions to find something a bit easier!
Since this post was originally written back in January, I have used this task a couple of times at conferences and had some really good discussions on this example. If you want a rather big hint, scroll down to see an animation. Or you can find the Geogebra file here.