Coloring

New year, new math. I'm tired of origami (the three-headed dragon took a very long time), so we're moving on.

Right now we're working on coloring "maps." The "maps" are drawings with various shapes, and each shape is considered its own country - no funny stuff like Alaska not being attached to the rest of the US.

When coloring, two countries that share a border aren't allowed to be the same color. If two countries only touch at a corner (like Utah and New Mexico in the 4 corners), they are not considered to share a border, so they are allowed to be the same color.

The challenge: given a map, how many colors do you need to be able to color it following the rules? Use the smallest number of colors you can get away with.

Here's an example:

We can't color this following the rules with only 1 color, or with 2. What about 3? Maybe we need 4, or 5.

I gave the kids a bunch of maps (this was the hardest one) and for each map they figured out the smallest number of colors they could get away with. Then they drew their own maps and started figuring out how many colors they would need for those.