The Electoral College

Context:
In this rural adult learning center, Max teaches an ABE math class, a basic reading/writing class, and a pre-GED class. The program is open entry and attendance is very inconsistent, so Max tries to limit his lessons to one class period. If they spill over to a second session, he builds in time for students to explain what they’ve been doing and learning to those who missed the first class.

In both classes that include math, Max tries to make use of the numbers all around us in daily life. Once a week, he asks students to bring in a “number in the news” – some number that helps us understand what’s happening in the world. It could be (un)employment figures, price increases or decreases, poll numbers, interest rates, etc. Whatever the number, the class discusses:

a) what the number tells you (or doesn’t tell you)

b) how the number might have been calculated and how precise it is

c) how you might use the information

Recently, students have brought in numbers that relate to the electoral college along with questions about how the whole system works . Max develops a lesson to address their questions.

Lesson:
Max found a brief explanation of the electoral college in the shared lesson files of the program. The original lesson was intended for reading practice, so Max drafted questions that would involve students in manipulating numbers to get answers to real civics questions about how our electoral system works. He checked the Use Math to Solve Problems and Communicate standard to make sure that his lesson addressed the full standard and also checked the performance continuum to make sure that the math strategies required to answer the questions fell within the range of knowledge of his students (basic operations for his ABE math students and more complex strategies – extending from benchmark fractions (such as 1:2 and 1:4) to larger, messier ratios; use of formulas - for some of his pre-GED students. Then, each of Max’s two math classes followed these steps:

  1. They read and discussed the text. As they read the text, they underlined any terms that they did not understand, especially math-related terms. (15 minutes).

  2. They looked at an electoral college map and a list of the electoral votes by state in 2000 and 2004 and discussed what these materials were telling them (15 minutes).

  3. Max explained their assignment (to manipulate the numbers to find out various facts about how the electoral college works). In preparation for the more challenging questions, he reviewed how to change large, “messy” numbers into friendlier numbers. They practiced rounding large numbers with Max asking them what they thought they should round each number to given a particular situation. He also did a review of ratios, ensuring that all the students could double or triple ratios to build up (and halve by building down). Students could see that a ratio of 1:2 was the same as 2:4, 4:8, etc. Together they then explored how to build up using larger numbers, such as 1:20,000 equaling 2:40,000, etc. This skill would be helpful in comparing electoral representation by state (such as 6:40,000 compared to 10:50,000). They read over the questions and were invited to add others, and Max made sure they understood each one (20 minutes).

  4. Before they began, they talked about how they would know if their answers were right (besides Max telling them). They had already learned about looking for “reasonableness,” so they would do that. They would also explain and compare how they came up with their answers so that they could check each others’ work (5 minutes).

  5. Pairs worked on the list of questions (getting as far as they could and then skipping down to the opinion questions 8 through 10). Max expected the ABE students to only get through question 4, but invited them to go as far as they could. The ABE students went beyond question 4, getting stuck on the idea of “writing a rule” in question 5, although they did know some simple “rules.” They were interested in the answers to 6 and 7 and insisted that Max take the time to explain the underlying concepts by using words and simplified numbers. (55 minutes) Students were quite surprised at what they were discovering about how we elect our presidents and wanted to know why the system was designed this way. Max suggested that they bring this question to their other classes (GED social studies, ABE reading/writing) or have one of the teachers come into their class to be interviewed.

  6. For homework, the students were asked to write math questions about the electoral college for each other. The pre-GED students were asked to write multiple choice questions to practice the kinds of questions found on the GED.

  7. The election was around the corner and the students were eager to return to this topic to check their predictions, at least. Some also wanted to see how the popular vote would compare to the electoral vote.

For a word file of the following reading and questions, click here.

The Electoral College

Contrary to popular belief, the president of the United States does not get elected by counting up everyone’s vote to directly decide the winner. Instead, we have an indirect system, whereby each state counts the winner in that state and then sends representatives (electors) to Washington D.C. (the electoral college) to cast votes for that winner. Here’s how it works.

After we vote in November, each state counts their votes and figures out the winner in that state. Then the state gives all its electors to the winning candidate (except Maine and Nebraska , which divide their electors according to the winner in each congressional district). The first candidate to reach 270 electoral votes wins.

The states do not all get the same number of electors. The number of electors for a state equals the number of Senators (two) plus the number of Representatives from that state. The number of Representatives in a state is based on the number of people who live in the state. Since each state has at least one Representative, every state has at least three electors. Big states with a lot of people, such as California , have many electors. Since the last election, the number of electors for many states has changed because the population of the state either went up or down. For example, in 2000, Illinois had 22 electors. But, because of a decrease in the population, it will only have 21 electors in the 2004 election.

It is the electors from all the states who actually elect the president. If no candidate gets a majority of the electoral vote, the House of Representatives elects the president, with each state having one vote. This happened in 1800 and again in 1824.

Concerns about the electoral college system

Many people think that there are problems with this way of electing the president. First, the candidate who receives the most popular votes can still lose the election (which happened in 1876 and 2000). This is because most states give all of their electors to the winner in their state, even if the candidate only won by a few votes. This is called winner-take-all.

Second, since every state gets 2 electors for their 2 Senators, low-population states have proportionally more political power than other states. For example, Montana has a population of 917,621 and 3 electors. If you divide the population by the electors, you find that each elector represents about 305,874 people. If you compare that to Ohio , where the population of 11,435,798 gets 20 electors (or one elector for every 571,799 people), you see that the residents of Montana have greater representation in the electoral college than residents of Ohio .

Questions (with teaching notes)

  1. Looking at the electoral votes list , how many electors will your state have in the 2004 presidential election? How does this number compare to a state that abuts your state? Are you surprised at the number of electors in your state vs. a neighboring state? (level 1 students need to find the number on a list)

  2. Based on what you know about the number of electors, how many Congressional Representatives does your state have? (level 1 students have to subtract 2 from the number of electors)

  3. Look at the electoral map. What is the smallest number of states a candidate needs to win in order to win the election? What are those states? What is the total of their electoral votes? (level 1 students only need to count the number of electors until 270 – would encourage the use of a calculator to help with the adding of states’ electors; would also suggest using the electoral map so that students can color in states as they add on).

  4. How many states have either gained or lost electors since 2000? Based on how the states voted in 2000, which party (Republican or Democratic) could benefit from these changes? How many electors could that party gain? (level 1 students are adding and subtracting – could use manipulatives to keep track of actual electors)

  5. Find the population of your state. About how many voters does each elector represent in your state? Explain how to figure this out. Then write a rule for it. (level 2-3 – students should be encouraged to round first (especially because the numbers are so large); then they can compare their estimated answer with the answer using a calculator. If students are exposed to patterns and rules at a very early level, they could begin to create simple rules by level 2 (using rounded numbers rather than exact numbers). In any case, students should be allowed to use a calculator rather than have to do long division to figure out these answers.

  6. Consider these two states. Arkansas has a population of 2,725,714 and 6 electors. The state of Washington has 6,131,445 people and 11 electors. Which state has stronger representation in the election of the president? Explain why. To determine about how many voters each elector represents, you may want to first round each state’s population. Think about how to round the number so that it is easily divisible by the number of electors. How does the representation of those two states compare to your state? (level 2-3 – see note for #5)

  7. The electoral vote system is winner take all. That means that in NY, for example, if 60% of the voters voted for Kerry and 40% voted for Bush, then Kerry would win all 31 electoral votes. Explain – or using 5 states as examples, show - how a candidate that wins a majority of the popular vote can still lose the election. (level 2 possible if students are given opportunity to work in a group so that they can help each other, and if they are encouraged to use friendly whole numbers (e.g. 20,000 vs. 23,402). A visual would be helpful – a line map of the U. S. or a chart so that students could jot down the number of actual votes vs. number of electors going to a particular candidate)

  8. Who do you think the electors from your state will vote for? What makes you think this?

  9. Which candidate do you predict will win the election? By how many electoral votes? Use a U. S. map or chart similar to the one here to show how you got your answer. (level 1 – if working with a partner or team; also, should be able to use a calculator to keep track of tally)

  10. What did you learn about our electoral system that you didn’t know before? What other questions do you have about it? How effective do you think the system is?

Use Math to Solve Problems and Communicate

How the lesson addressed the Standard

Understand, interpret, and work with pictures, numbers, and symbolic information.

Students had to choose and work with numbers from lists, charts, and maps

Apply knowledge of mathematical concepts and procedures to figure out how to answer a question, solve a problem, make a prediction, or carry out a task that has a mathematical dimension.

Students used a variety of math operations (counting, adding, subtracting, rounding, comparing ratios, writing rules) to make sense of the numbers. They applied an understanding of ratio (of voters to electors) to determine strength of representation and used the concept of “total amount needed” in order to determine the states needed to win the election.

Define and select data to be used in solving the problem.

Students had to find the numbers they needed from authentic materials (e.g. a census list) provided by the teacher and from website provided.

Determine the degree of precision required by the situation.

Students were assumed to be using precise, whole numbers for most problems. Students rounded total voters to reasonable, usable estimates in order to determine representation for questions 6 and 7.

Solve the problem using appropriate quantitative procedures and verify that the results are reasonable.

The problems required students to use math to understand the workings of our electoral system and to draw conclusions and make predictions. Students had to show, explain and check their answers, using estimation and calculators to check for reasonableness of answers.

Communicate results using a variety of mathematical representations, including graphs, charts, tables, and algebraic models.

Students wrote explanations, shared “rules” for finding electoral representation, and used visual representations such as U. S. maps and charts to communicate predictions.