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Four Color Theorem Activity

One of the end-of-year activities I did with my statistics students was to explore the four color theorem. One of my students had been begging for weeks for me to let them color. I don’t think this was what she had in mind…

Of course, I didn’t tell them the name of the theorem. I wanted them to discover that part for themselves! I told them that there had been mathematical research about how many colors were required to properly color a map. It was there job to discover the fewest number of colors you could use to color any map.

In June of 2016, I attended a Math Teachers’ Circle Summer Institute where we played with the four color theorem using large posters and colored bits of paper. I decided to recreate the experience for my own students.

What is the Four Color Theorem?

The Four Color Theorem states that no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Regions that meet only at a corner may be the same color.

The theorem has some pretty cool history behind it. It was the first major theorem to be proved using a computer!

Four Color Theorem Activity

I printed five different designs off on 11 x 17 cardstock for them to “color.”

Four Color Theorem Activity

These first two coloring designs were pretty basic. That was intentional.

I recreated them based on some of the four color theorem practice problems in the 8th edition of A Survey of Mathematics with Applications by Angel, Abbott, Runde (Pearson).

Four Color Theorem Activity

The last three designs were all maps. I included a map of Oklahoma’s 77 counties since we are in Oklahoma, a map of Australia since my husband is Australian, and a map of the United States (West of the Mississippi River).

Four Color Theorem Activity

I gave each group of students some strips of cardstock that were leftover from building Columbus Cube Towers. They cut the strips into small squares to use to “color” the maps.

Four Color Theorem Activity

Originally, I had planned to chop the cardstock into uniform squares with my paper chopper. I started, but I quickly realized it was much too tedious of a task!

Four Color Theorem Activity

I challenged my students to color each map using the least number of colors possible.

Four Color Theorem Activity

They found the map of Oklahoma to be especially tricky to color!

Four Color Theorem Activity

The more basic designs did not require as many colors. This flag-like design ended up only requiring three colors.

Four Color Theorem Activity
Four Color Theorem Activity

I’m glad I included these simpler designs before jumping into the maps.

Four Color Theorem Activity
Four Color Theorem Activity
Four Color Theorem Activity
Four Color Theorem Activity
Four Color Theorem Activity
Four Color Theorem Activity

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