Nothing amazing with this little project, but it's something to get started and you guys can run with it.
In geometry we're talking about ratios of similar shapes. Comparing a 2x2 square with a 6x6 square, we see that the side lengths triple, but the area increases 9-fold. I had them discover this by doing a number of different shapes and finding their areas then comparing. Similarly, for volume, the shape whose sides have ratio N has a volume that is N^3 times as much.
Anyhow, with The Hobbit movie coming out this week, I thought I'd tap into that excitement a bit and have them do a little map reading. I found this map online: http://mearth.lords-of-blah.nl/ It's huge, but printable. There are other online maps, but not with a scale and with different resolution screens or whatever, I thought I'd give them all a print out so we can be a little consistent.
Then I typed up these instructions on what to do with the map. I couldn't think of how to incorporate volume into the instructions at the time, but now I think I might include making a scale model to the same proportions of the map. Maybe how wide and tall a mini-Isengard should be made to fit on the map or something.
Anyways, feel free to steal and/or enhance this lesson for yourself.