I just had to share the neatest activity that I saw at the California Math Council conference at Asilomar last month. And I loved it for more reasons than just because it was created at my old haunt, the Exploratorium.
You know those clear plastic trays that you get your salad bar goodies in? You can use them to do math, too. They stack very neatly on top of one another, with just a slight separation between each tray. So, if you draw a single outline from a contour plot on each one, when you stack them together you get a three dimensional contour map. It really has to be seen to be believed — the contour just pops out at you, it’s quite impressive. The one linked on this page is of a paraboloid, but I found the one of a saddle function (sorry, no picture!) to be more impressive. It gave me a 3D understanding of the shape that I think I couldn’t grasp by looking at plots on two-dimensional paper.
Here is a link to the deli-tray math activity. Note that you can also use this to plot constellations, like the big dipper and orion.
Or, obviously, topographic maps for geology!
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