180 Days of Ideas for Discussion in Math Class.
(as of 9July2014, we're in overtime!)
Shading is disturbingly close to 3/4: 76%.Let them chew on THAT for a while.
There arel visual proofs of this and the last one: it's not too hard to see that the bottom left triangle can be used to (almost) tile the whole shape. The only leftover part is the top triangle, which is half of the bottom left one. Counting the tiles, there are 9.5 shaded out of 12.5, or 76%
Visual explanation of the 3/5 version that applies here too:http://imgur.com/L3iP1g9