mathematical explorations classroom-ready activities The Electoral College Kimberly A. Markworth and Lara M. Willox Edited by gwen Johnson, gwendolyn.johnson@unt.edu, University of North Texas, Dallas, and James dogbey, jdogbey@clemson.edu, Clemson University, South Carolina. Readers are encouraged to submit manuscripts through http://mtms.msubmit.net. dduring 2004 s presidential election, voters could choose between incumbent George W. Bush (Republican) and John Kerry (Democrat). That year, I had the opportunity to work with several classes of eighth- dwith several class dgrade students on an Electoral dcollege investigation. My dstuden students prior knowl- edge of this institution was limited. During our first discussion, they were surprised to discover that their home state of North Carolina was historically a red state and that all its electoral votes would go to a single candi- date on Election Day. After working through a series of tasks on the topic of the Electoral College, my students were prepared to make sense of Election Day. Their enthusiasm the day after the election was palpable because students had understood the process as it unfolded. I remember one student saying to me, I saw all those red and blue states come up, and I knew what it meant! Two class periods had not only empowered my students but also made them aware of an important political process. An overarching goal of education is to prepare students to be informed and engaged citizens. Currently, more than one-third of Americans do not understand the Electoral College and the role that it plays in the election process (Ross 2009). The 2000 election was notable for its controversy: Although Al Gore won the popular vote, George W. Bush won the Electoral College vote and, therefore, the election. Although the 2004 election was not similarly notable, a knowledge of the Electoral College enabled my students to engage in the presidential election. As a result, they understood the mathematics of the process and became better-informed citizens. Engaging in these tasks with your students will prepare them for Election Day, even though they are too young to vote. exploring electoral college Math Activity sheets 1 and 2 guide students through thinking about the Electoral College and the Election Day process. Activity sheet 1 is more accessible for students in grades 5 and 6. The goal 118 MatheMatics teaching in the Middle school Vol. 18, No. 2, September 2012 Copyright 2012 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM.
is to understand the computation behind each candidate being able to procure enough electoral votes to win the election. This activity requires simple addition, subtraction, and comparison of whole numbers. Calculator use is probably warranted; there are several numbers to add, and students could potentially lose track of them. It is impossible for us to predict with certainty how the election map will appear close to Election Day. In addition, various sources may predict states voting differently, so answers will depend on the individual state analyzed as well as the source used in the classroom. Regardless, it is important to present data that do not produce a landslide win for either candidate so that students can consider the multiple ways that the election may be won or lost. The target quantity is 270; the candidate earning 270 electoral votes will win the election. Question 5 on activity sheet 1 gives students the opportunity to use the data they have analyzed to suggest candidates campaign strategies. They may consider which states are most likely to swing toward one candidate or the other as well as the electoral vote weight of individual states for launching a final campaign push. Of course, there is no right answer, and the staff of each campaign will surely consider additional factors when making these decisions. This thread of discussion can be pulled in class to identify additional information or variables that might be significant to campaigns. If adequate time is available, ask students to consider the possibility of a tie between candidates, with each garnering 269 electoral votes an unlikely but possible scenario. Students might search for combinations of swing states that would create an electoral vote tie; parsing electoral votes from Maine and Nebraska can also assist with this endeavor. Finally, it would be worthwhile for Basics of the electoral college Every four years, U.S. citizens go to the polls to vote in a presidential election. This November, voters will either re-elect President Barack Obama (the Democratic candidate) for a second term in office or elect Mitt Romney (the Republican candidate) to succeed him in the White House. The popular vote does not decide the election because the United States adheres to the tenets of the Electoral College, which grants to states a specific number of electoral votes. This quantity is determined for each state by summing the number of representatives in the House of Representatives (which is based on population) and the two senators in the United States Senate. State legislatures determine who serves as an elector; an elector cannot be a member of Congress or hold a federal office. In December, the electors of each state meet to vote for president and vice president. The electors use the results of the popular election to determine their vote. With the exception of Maine and Nebraska, which can split their votes between candidates, all states grant all their electoral votes to a single candidate. A candidate needs 270 electoral votes to win the presidency. If no candidate receives a majority of electoral votes, the House of Representatives elects the president from the 3 candidates who received the most electoral votes. States are typically dubbed blue states (predominantly Democrat) or red states (predominantly Republican) on the basis of how their electoral votes will most likely be cast. Mandating the Electoral College system was one of the most difficult decisions made by the Constitutional Convention in 1787 (Rothwell 2001). By using electors to vote, the founding fathers were hoping to avoid voting by mob rule as well as for favorite sons (a locality s nominee). In addition, smaller states were hesitant to endorse a direct popular election because it would limit their power and voice in the election. Turner (2007) has argued that the current Electoral College system promotes compromise and government moderation. Some people, however, want to abandon the Electoral College and adopt a purely popular election, pointing both to advances in wider communication and greater knowledge and the fact that a candidate can potentially win the popular vote and not win the election (Clayton 2007). Changes to the Electoral College process have occurred over time, particularly with the passing of the 12th Amendment in 1804 (Rothwell 2001). Before 1804, electors could cast two votes, with the expectation that they would use one vote for the president and one vote for the vice president. This proved problematic in the 1796 and 1800 elections when electors used both votes for the president and there were too few votes cast to elect the vice president (Turner 2007). Currently, electors cast one vote for president and one vote for vice president. Since 1804, many proposals for changing the presidential election process have been introduced, such as a direct popular election; to date none have been passed by Congress and sent to the states for ratification (Clayton 2007). Thus, it is important for all citizens, including students, to understand how the electoral system works. students to research what would happen in the event of an electoral vote tie. The website About.com clearly describes what happens if a tie throws the election into the House of Representatives and the Senate (see http://usgovinfo.about.com/od/ thepoliticalsystem/a/electiontie.htm). Activity sheet 2 explores how the number of electoral votes is determined for each state. This activity is more appropriate for students in grades 7 and 8 because it involves creating a scatterplot, sketching a trend line, and making predictions on the basis of the trend line. Vol. 18, No. 2, September 2012 MatheMatics teaching in the Middle school 119
Consider the resulting scatterplot for the 25 states (selected for question 1) in figure 1. The individual data points demonstrate a remarkably linear relationship. It is not challenging for most students to sketch a trend line for the data points. Because of the substantial numerical variation in state populations, using the trend line to predict a state s population from the number of electoral votes is difficult and inexact (question 3). However, using a state s population to predict the number of electoral Fig. 1 A scatterplot using the population and electoral votes for 25 states shows a direct relation that can be represented by the linear equation y = 0.0014x + 2.0039. Fig. 2 The numbers in this cartogram, illustrating electoral votes by state, were based on 2010 census data (Colley and Gott 2011). votes is more precise, and students ought to be able to generate a prediction within a few electoral votes (question 2).The actual line of best fit generated by Excel for these 25 states is y = 0.0014x + 2.0039. The model demonstrates some meaningful connections to how the number of electoral votes is determined for the individual states (see fi g.1 ). Consider first the slope of the linear equation, 0.0014. In context, this is the number of electoral votes awarded to a state for every 1,000 residents. Therefore, for every 1,000,000 residents, approximately 1.4 electoral votes are awarded. Basing electoral votes on population alone would diminish the influence of states with smaller populations. Consider 2.0039, the y-intercept of the equation. In this equation for the line of best fit, this number refers to the Electoral College votes that are awarded in addition to those based on the state s population. Note how close this value is to 2, which is the actual number and based on the number of senators allotted for each state. Of course, error is associated with the line of best fit. From these equations, it might be interesting to examine which states benefit with a greater number of Electoral College votes, as well as which states lose out. An intriguing extension is provided at the end of activity sheet 2. Cartograms depict statistical information in a distorted, diagram-like representation. The cartogram in figure 2 represents Electoral College votes by numbered and colored squares. This map of the United States is distorted because population (rather than land area) is a substantial contributor to the size of the state on the cartogram. For example, examine Alaska and Montana, two of the four largest states in the United States by 120 MatheMatics teaching in the Middle school Vol. 18, No. 2, September 2012
area. Both appear quite small in the cartogram because they have very low population densities and each has only 3 electoral votes. In contrast, Rhode Island is the smallest state by area, yet appears larger than Alaska or Montana because of its high population density. Other cartograms are equally intriguing as depictions of 2008 election results (e.g., explore the website http://www-personal.umich.edu/~ mejn/election/2008/). conclusion Preparing students mathematically to make sense of the Electoral College engages them in a process that is vital to our democracy. Although they are unable to vote, they will like my own students eight years ago watch the results with enthusiasm and understanding. These tasks will prepare them not only for this presidential election but also for future elections in which they are able to vote. This activity will also help them understand how individual votes influence a larger process. We encourage you to team up with your students social studies teacher to do a two-day mini-unit on the Electoral College. By examining the pros and cons of the Electoral College, your students will develop their own informed opinions about this important political process. ReFeRences About.com. US Government Info: What If the Presidential Election Is a Tie? http://usgovinfo.about.com/od/ thepoliticalsystem/a/electiontie.htm Clayton, Dewey M. 2007. The Electoral College: An Idea Whose Time Has Come and Gone. The Black Scholar 37 (3): 28-41. Colley, Wes, and J. Richard Gott. 2010. 2010 Electoral Cartogram. http://en.wikipedia.org/wiki/ File:2010ElectoralCartogramGott.png#metadata. extensions Mathematical extensions abound that are related to the Electoral College. We have identified additional possibilities for extending students work, the first two of which would contribute to students enthusiasm for the election process and results as Election Day approaches. Research the candidates final days on the campaign trail. In which states are they spending their time and money? Follow the voting predictions as they change and the voting results as they come in. Were the pundits correct in their predictions? Research the 2000 presidential election between Al Gore (the Democratic candidate) and George W. Bush (the Republican candidate). Why was this election controversial? Why did some people question the use of the Electoral College following this election? Learn more about the workings of the Electoral College. Historical information, current practices, and frequently asked questions are found at http://www.archives.gov/federal-register/electoral-college/. What is your opinion of the Electoral College? Newman, Mark. Maps of the 2008 US Presidential Election Results. http:// www-personal.umich.edu/~mejn/ election/2008/ Ross, Tara. 2009. The Electoral College s Thankless Task. http:// www.utsandiego.com/news/2009/ may/17/1e17ross1155333. Rothwell, Jennifer Truran. 2001. Prospects for the Electoral College after Election 2000. Social Education 65 (1): 8-17. Turner, John J. Jr. 2007. One Vote for the Electoral College. The History Teacher 40 (3): 411-16. 270 to Win. www.270towin.com. United States Census Bureau. Population Distribution and Change: 2000 to 2010. http://www.census.gov/prod/ cen2010/briefs/c2010br-01.pdf U.S. National Archives and Records Administration. U.S. Electoral College. http://www.archives.gov/ federal-register/electoral-college Ed. note. For more Electoral College and election-related articles and information, see the September 2012 Student Explorations in Mathematics and the October 2012 issue of Mathematics Teacher. Kimberly a. Markworth, kimberly.markworth@ wwu.edu, is an assistant professor of mathematics education at Western Washington University in Bellingham. She taught middle school mathematics in North Carolina at the time of the 2004 presidential election. lara M. Willox, lwillox@westga.edu, is an assistant professor of education at the University of West Georgia in Carrollton. She taught for twelve years in North Carolina public schools. Download one of the free apps for your smartphone. Then scan this tag to access the solutions to Mathematical Explorations that are online at http://www.nctm.org/mtms028. Vol. 18, No. 2, September 2012 MatheMatics teaching in the Middle school 121
activity sheet 1 Name the electoral college Every four years, the United States has a presidential election. In November 2012, the primary contenders will be the incumbent Barack Obama (the Democratic candidate) and Mitt Romney (the Republican candidate). The election is not decided strictly by popular vote but by the Electoral College. States are granted a specific number of electoral votes, which are then cast for a candidate. This vote count is the sum of the number of U.S. representatives (which is dependent on population) and the two U.S. senators in each state. directions: Work in pairs or groups of three to answer the following questions. (You may use a calculator.) Your teacher will provide maps of current predictions of the presidential race or online access and suggested websites for finding this information. (Note: The map used must provide information about how many electoral votes each state is given.) 1. Use a recent online map that illustrates which states are solidly red or blue at this point in the campaign. a. If these predictions hold true for the actual election, how many electoral votes will Obama receive? b. How many electoral votes will Romney receive? 2. A candidate needs 270 electoral votes to win the presidential election. From your answers to questions 1(a) and 1(b), how many more votes does each candidate need to reach the majority required to win the election? 3. Several states are called swing states because no single candidate has overwhelming support and the voting can go either way. Identify the states that are neither red nor blue on the map. What combination of these states could go to Obama and secure him a second term? Identify three different combinations of states. 4. What combination of these swing states could go to Romney to secure his win? Identify three different combinations of states. 5. With the election just months away, in which states should each candidate focus his campaign efforts? Support your reasoning with calculations from questions 3 4. 6. With 538 electoral votes available, is it possible for neither candidate to reach the 270 electoral votes required to win the election? Do you think this is likely? Why, or why not? from the September 2012 issue of
activity sheet 2 Name determining electoral college Votes Work in pairs or groups of three to answer the following questions. Use the data provided in the table on the next page for population and number of electoral votes for each state. 1. Population is one factor that contributes to the number of Electoral College votes awarded to a state. Make a scatterplot of the population (x-axis) and Electoral College votes (y-axis) for the following states: AK, AZ, CT, CA, CO, FL, GA, KY, LA, MA, MN, MO, NC, ND, NE, NY, NV, OH, PA, RI, TX, VA, VT, WA, WY. What trend do you see? Sketch a line of best fit. 2. On the basis of your line of best fit, predict how many electoral votes a state will receive if it has a population of 1,316,000 people. 3. On the basis of your line of best fit, predict the population of a state that has 20 Electoral College votes. 4. Check your prediction for question 2 with New Hampshire (NH). Check your prediction for question 3 with Illinois (IL). Was your prediction for question 2 or 3 closer to the actual data? Explain why. 5. Use a graphing calculator or Excel to calculate a line of best fit. Interpret the slope and y-intercept in relation to how the number of Electoral College votes is actually determined. (Note that the y-intercept is remarkably close to 2.) 6. Research cartograms for the distribution of Electoral College votes in the United States. How and why are cartograms distorted? What do the distortions represent? (Check out http://www-personal.umich.edu/~mejn/election/2008/ and http://en.wikipedia.org/wiki/ File:2010ElectoralCartogramGott.png for intriguing examples.) (Continued on the next page) from the September 2012 issue of
activity sheet 2 (continued) Name table of state PoPulation and electoral college Votes state (abbreviation) electoral college Votes Population (in thousands) AL 9 4,780 AK 3 710 AZ 11 6,392 AR 6 2,916 CA 55 37,254 CO 9 5,029 CT 7 3,574 DE 3 898 DC 3 602 FL 29 18,801 GA 16 9,688 HI 4 1,360 ID 4 1,568 IL 20 12,831 IN 11 6,484 IA 6 3,046 KS 6 2,853 KY 8 4,339 LA 8 4,533 ME 4 1,328 MD 10 5,774 MA 11 6,548 MI 16 9,884 MN 10 5,304 MS 6 2,967 MO 10 5,989 state (abbreviation) electoral college Votes Population (in thousands) MT 3 989 NE 5 1,826 NV 6 2,701 NH 4 1,316 NJ 14 8,792 NM 5 2,059 NY 29 19,378 NC 15 9,535 ND 3 673 OH 18 11,537 OK 7 3,751 OR 7 3,831 PA 20 12,702 RI 4 1,053 SC 9 4,625 SD 3 814 TN 11 6,346 TX 38 25,146 UT 6 2,764 VT 3 626 VA 13 8,001 WA 12 6,725 WV 5 1,853 WI 10 5,687 WY 3 564 The population, rounded to the nearest thousand, is based on 2010 U.S. census data from http://www.census.gov/prod/cen2010/briefs/c2010br-01.pdf. from the September 2012 issue of