Math Adventures - Voting

My school had a mathematician visit this week and develop a parent-child seminar on math concepts. These are hands on activities for parents and children to do together. They're wonderful and I'm glad to share them! Here are some of the activities that we did at the Elementary level:

The first was an exercise that demonstrated the importance of how district lines are drawn in voting. This has become a big issue in our neighboring state of Virginia, following the most recent Census.

To first demonstrate the "popular vote" she passed out colored index cards with letters on them. Each person got a card. We were voting on chocolate, strawberry, or vanilla ice cream. Ignoring the colors of the index cards, we tallied the votes by letter. More people had a "C" on their card than any other letter so the popular vote was in favor of Chocolate.

Now we organized our voters into districts. The people with yellow cards went to sit at a table together (Yellow Town). Green Town and Violet Town were also quickly formed. Now, within each town, a vote was once again taken. Whatever flavor was the majority choice would be the vote of the entire town. The students were amazed to see that two towns voted "V" for vanilla and only one town voted "C" using this method. Even though Chocolate would win in popular vote, using the district system resulted in a win for Vanilla.

The mathematician shared some classroom (or at home) follow up ideas for this activity: Talk with your students about what it means to have a representative democracy as opposed to a true democracy. Have them explain to you potential benefits and drawbacks of each system. Discuss other ideas for voting. Instead of voting for someone, you could vote against someone. We could rank candidates and give three votes to our top choice, two votes to our second choice, and one vote to our third choice. We could be given three votes to cast and distribute them as we wish (all three to one candidate or split the votes across two or three candidates). Test these ideas... do you always get the same winner? Which one is most "fair"? What does it mean to be "fair"?

To reproduce this activity in your classroom with 12 students, the directions to prepare the cards are as follows:

Cut four cards out of green cardstock. Label three C, one S.
Cut four cards out of yellow carstock. Label two V, one C, one S.
Cut four cards out of violet cardstock. Label two V, one C, one S.