Election Math, by Michael Naylor

Statistics, percentages, graphing and all manner of math skills come into play once the polls are closed

Election time is a great time to look at statistics, data gathering and representations and to examine the mathematical quirks in our country's election system. You can hold a classroom election and use the results in these activities.

Graphing the vote (Grades K-2)
Have students write their votes on index cards. After tallying the votes, tape the cards to the blackboard in columns according to the vote marked on the card.

How can we tell who won this class election, without counting the index cards? How many more votes did the winner get? If one student changed his or her vote, would the results change? What if two students changed their votes? What are some other ways we could arrange the cards?

Next, supply paper and colored squares and have your students glue the squares to the paper in columns that match the graph on the board. Students will be learning to make and compare bar graphs as well as creating visual representations of numbers.

Make a human pie graph by grouping students according to their votes.
Artwork: Laura bethel-sehn

Human pie graph (Grades 3-6)
Go outside or move your classroom's desks so that all your students can stand in a circle, grouped according to their votes. Place string or ribbon on the floor, stretching from the center of the circle to the points between the groups to form a giant, human pie graph.

Ask your students to look at the areas into which the circle is divided. Can they tell at a glance who won? Connect the ideas to fractions – approximately what fraction of the class voted for each candidate? What angle is formed by the strings in the center of the circle?

Afterwards, ask your students to sketch the graph and write down what each section of the graph means. Include percentages!

Pie graph percents (Grades 5-6)
Older students can make an accurate pie graph using a protractor and a calculator. Have them use their percentages for each candidate to calculate the percentage of degrees in a whole circle. This degree measurement indicates the size of the "slice of pie" each candidate won, from 0 to 360°. Have the students draw a circle and then construct these angles in the center of their circles.

Complete the graph with an explanation and key.

For example, suppose Candidate A got 9 of the 26 votes. 9÷26 = 34.6% of the votes, and 0.346 x 360° is about 125° of the full circle. Students would draw a radius of the circle and use this as the first side of a 125° angle.

The popular vs. electoral vote paradox (Grades 6-8)
Three times in our country's history, a presidential candidate has won more popular votes than his opponent, but ended up losing the election. This happened when Andrew Jackson lost the election to John Quincy Adams in 1824, when Grover Cleveland lost to Benjamin Harrison in 1888 and when Al Gore lost to George W. Bush in 2000.

One reason this happens is because a presidential candidate is elected by electoral votes, not popular votes. If a candidate receives the most popular votes in a state, then he or she is awarded all of the state's electoral votes, even if the state is evenly divided between candidates. This system serves to protect our smaller states and gives them an important role in the election, but it sometimes can lead to problems.

This idea can be hard to understand, which makes it a great problem-solving opportunity for your students! You can begin to make it clearer for them with the data chart below. This chart lists the states beginning with "A," but feel free to use states from your region. You can get a list of state populations and electoral votes for the 2004 election at: www.thegreenpapers.com. Also get a list of electoral votes by state for the 2008 election at: history.howstuffworks.com.

Challenge your students to decide the election results for each state for two candidates, A and B. They can allocate as many popular votes as they wish for either candidate; the winner of a state's popular vote receives all of that state's electoral votes. Is it possible for Candidate A to win the election by getting the most electoral votes, even though Candidate B gets more popular votes? You can help your students organize their work by giving them a data sheet like the one below.

Here's one of many possible solutions: Candidate A could win slightly more than half the popular votes from Alabama and Arkansas each and get 15 electoral votes to B's 13. Candidate B could get most or even all of the votes from Alaska and Arizona. Candidate A would win the election, even though he or she would only have about 3.7 million popular votes to Candidate B's 9.3 million.

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.