## How to Teach Coloring Maps and Map Coloring Theory

Most folks don’t know (or care) about coloring maps or map coloring theory, but today’s elementary school students are forced to take an interest.  For some reason, these subjects are often stressed on state achievement tests.  However, few textbooks provide practice or assessment for the skills.

What’s a teacher to do?

Turn to the Internet.  That’s what I did, and I found some resources that I hope will help others.

Back up and explain: coloring maps questions usually go something like this: what is the fewest number of colors needed to color this map so that no edges are touching?  (A squiggle of lines forming a “map” accompanies the question.)

Teachers and students were left to fend for themselves, drawing their best guess at sample maps, coloring them in, and trying to figure out how many colors were needed.  We never really knew if we were doing it right.

Someone already did this work for us, apparently.  My research showed that four colors are enough for any map you can draw.  Two two mathematicians, Ken Appel and Wolfgang Haken, figured this out in 1976.  If that’s not enough to convince the kids, I invite them to read about the four color theorem.  (Here’s the short version: four colors are enough!)

So, I taught my students a few things:

a)      It’s never more than four colors, according to mathematicians.

b)      On our practice tests, the answer is almost always three colors.  Ergo, this is most likely the answer to any coloring maps question life will throw at you.

c)      If the answer is only two colors, it will usually be pretty clear because the picture will look more or less like stripes.

I found an Internet tutorial on the subject that lets students practice coloring in the maps.   In our era of standardized testing, the ability to actually color in the map isn’t important, since it can’t be reduced to a bubble sheet answer choice.  However, the act of trying to color in the maps helps students understand why you never need more than four colors, and why three colors will usually suffice.

Click here to use the tutorial, from subtangent.com.  I highly recommend the tutorial as a computer lab exercise for your students.