This activity uses a voting situation with one vote per class. Similarly to the families with computers, three classrooms need to share three votes. The vote for the class is whichever choice wins a majority in the class election. Students discover that this system is unfair because a class voting heavily for one choice counts for the same as a class barely voting for the choice (“yessiness”). They use division to try to devise a more fair system. Monitor for different ways to assign votes. As students evaluate the fairness of the principal’s plan and propose alternatives, they are creating and working with models of the situation (MP4).

Note: A banana slug is a bright yellow snail without a shell that lives in redwood forests. In 1986, students at the University of California Santa Cruz voted for the banana slug as their mascot. The administration thought sea lions were more dignified.

If students are confused about the two-step process (each class votes, then the representatives vote again), consider asking:

• “Who is involved in the final vote?”
• “How do they know how to represent their class?”

Invite students to share their ways to assign votes and the reasons for their system. Select students who have different methods.

Students should recognize, after discussion, that the system the principal proposed is unfair. A majority in a small class voting for banana slugs can overwhelm a larger number voting for sea lions in a larger class.

A more fair system should take the sizes of the classes into account.

This activity includes two problems of assigning representatives proportionally, with schools sending students to advise the school board. In the first problem, school sizes have been carefully planned so that each school has the same number of students per representative as the district as a whole. In the second, this is not possible, in part because of a very large and a very small school.

The mathematics is the same as in the previous activity distributing computers to families. It is also the same as in the problem of assigning congressional representatives to states. Some states have very large populations, and others have very small populations. As students grapple with finding a fair representation they reason abstractly and quantitatively (MP2).

Invite previously selected students to present their plans for assigning advisors.

If not brought up by students, highlight that the ideal number of students per representative is 85, an average. The Dr. King School is very close to this ideal. The other schools have much higher or lower numbers.

Make sure that students understand that the big idea here is that it’s impossible to be completely fair. The students from Trombone Academy will have more influence with their representatives than will the students at the bigger schools because their advisor is representing only 10 students. On the other hand, if the Trombone Academy gets no advisors, then their views aren’t represented at all, which also isn’t fair.