Hobbit Ratios

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.