 Compete against other teams to strategically place colors to make the least expensive maps possible. To play this game, you need 90 tokens, 20 each of the first, second, third, and fourth colors, and 10 of the fifth color. You also need three maps, one each of Canada, South America, and the USA, per team. Separate the tokens into five different piles, one per color, and around one use a map of Canada, around two use a map of South America, and finally around three use a map of the USA. The object of this game is to color a map using the least number of colors possible. Regions that share an edge may not be the same color. For example, if you place a blue token here, all of the surrounding regions cannot be marked with a blue token. Regions that share only a vertex may share a color. Now let's play with the map of Canada. There are seven steps. To assure that no two regions sharing a border are colored with the same color, using the first color places many tokens of this color as possible. Record how many tokens you used. Using the second color places many tokens on the map as possible. Record how many tokens you used. Repeat for the third, fourth, and fifth colors. The values of the tokens are based on their color as follows. First color is worth $1. Second color is worth $2. Third color is worth $5. Fourth color is worth $10. And the fifth color is worth $25. Determine how much your map costs. Try to make your map less expensive. Find your new total. The team with the least expensive map wins that round. A helpful hint is if you realize a color is misplaced, pick it up and replace it with the correct color. Repeat the steps for South America and then the USA map. Record the cost of each map. The team with the lowest total after three rounds, all three maps, wins. Here are some things to think about after a round. How did your map coloring compare with other teams' maps? How did the price of your map compare to the prices of other teams' maps? Can you find a way to make your map less expensive? What regions of your map are easier to color? What about the regions makes the coloring easier? What regions of your map are more challenging to color? What about the regions makes the coloring more challenging? Is it possible to use fewer colors on your map? Is it possible to use fewer tokens on your last color on your map? How many colors are necessary to color a map? Why do you think so? A variation of this game is to find your own maps of two color. Look for two maps to color. One that you think will be simple to color and one that will provide you a challenge. Play the game with your maps. Another variation is to use adjacency maps. In graph theory, a map coloring is an important topic. Graph theorists use lines and vertices or circles to show which regions share a border with other regions. Study the adjacency map for Canada. Notice how the circles are noting each province or territory is connected by lines to another province or territory if they share a border. Play the game with the adjacency map. Compare your cost to the amount you found using the map. Choose your last challenging map from the previous variation making adjacency map for it and play the game again. Find an adjacency map for the USA at the link on the screen. Play the game with this adjacency map. Compare your costs. How helpful are adjacency maps? What do they help you see more clearly than typical maps? Click on the instructions links on the Regional Math Science Center website to read the game rules or just re-watch this video pausing as needed. Thanks for playing!