Presidential elections provide opportunities to teach about power, proportions and percentages

The complex voting system in the U.S. requires a sophisticated understanding of math. bamlou/DigitalVision Vectors

To American voters, the process of electing a president and other officials may be difficult to explain and understand. For America’s math teachers, the system represents a gold mine for real-life lessons on ratios, statistics and data.

And by basing the lessons on elections, teachers can help put students on the path to becoming informed and engaged voters later in life, according to a 2020 survey of 2,232 young adults ages 18-21.

Americans don’t vote directly for the president. Instead, a group of electors vote for the candidate who wins the popular vote in that state. In most states, whoever wins the most votes wins all the state’s electors, or “electoral votes.”

Not all states have the same number of electors. Each state starts with two electoral votes, based on the two U.S. senators in each state. States receive additional electors based on the number of representatives they have in the House of Representatives, which depends on a state’s population. The number of representatives in the House, however, has been set at 435 since 1929, despite a huge and varied increase in the population. This means the number of people represented by each member of the U.S. House – the ratio of people to representative – varies considerably, as shown in a table from the U.S. Census Bureau.

Armed with this background, math teachers can use the census data on population and ratios to teach students the following math – and voting – topics.

Topic 1: Ratio

To calculate a state’s representative ratio, the number of people for every one representative, divide the population by the number of the state’s representatives in the U.S. House. In 2020, for example, Montana had two congressional representatives and a population of 1,085,407. The representative ratio was 542,704:1 – 1,085,407 divided by 2 – or 542,704 residents for each representative.

Topic 2: Minimum and maximum

In any set of numbers, the minimum is the smallest number in the set and the maximum is the largest number. For example, using the representative ratios from the 2020 census data, Montana’s ratio of 542,704:1 is the smallest – the minimum – and Delaware’s ratio of 990,837:1 is the largest, or the maximum.

Topic 3: The shape, center and spread of data

Shape means how data, such as the ratios of residents to representatives, looks on a chart or graph. Teachers can use a histogram, a kind of graph used to illustrate how data is distributed: evenly, skewed to one side, or with some numbers as outliers, at a distance from the other numbers.

The ratios can also be used to explain how to find the “center” of data, its mean or median. The mean is the average, found by adding all the numbers in the set and dividing by how many there are. For example, adding the ratios for all the states and dividing by 50. The median is the middle number when all numbers are placed in order from minimum to maximum. Simple spreadsheet formulas are available online to help students find both.

Students can examine ratios of residents to representatives for all 50 states.
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The “spread” of a set of numbers tells how much the numbers are different from the center. One measure of spread is called the range, which is the difference between the maximum and the minimum. For example, the range in representative ratios among the states is 448,133: the maximum, Delaware’s 990,837, minus the minimum, Montana’s 542,704.

When students understand how ratios – and elections – work, teachers can ask questions such as, “Montana has fewer people per representative than Delaware. Where would your vote count more?” Answer: Montana, because fewer people per representative means each vote counts more.

Topic 4: Gerrymandering

Each state is divided into districts; residents of each district vote for their state and federal representatives. Gerrymandering occurs when the borders of voting districts are drawn to favor one party at the expense of another. The political party in power often draws these district lines to make it easier for that party to win in the future.

Imagine a state has 10 representatives, and Party X gets 60% of the votes. With 60% of the votes, it seems fair that Party X should get 6 of the state’s 10 seats for representatives.

There is no rule that says the percentage of votes cast for a party in a state has to line up with the number of seats the party wins. And Party X wants more. To keep control of as many seats as possible, the politicians in Party X would like to manipulate – or gerrymander – each of 10 districts to make sure it would win 60% of the vote in each. With a majority in each district, Party X would win all 10 seats. Gerrymandering to this extreme is not always possible because districts must consist of adjoining areas, and voters who favor one party might not live in areas that can be easily connected.

Lessons on gerrymandering can vary by grade level. For example, elementary students can get hands-on experience manipulating borders with the Julia Robinson Mathematics Festival “puzzles” tool. The puzzle, which can be tied to lessons about shapes, percents and area, allows children to change boundaries on a graph to increase or decrease the number of yellow or green squares – representing voters – in each “district.” There are fewer green squares than yellow squares in each puzzle. Students win when they successfully gerrymander, changing the borders so the green voters are in the majority in most, or all, of the districts.

High school students, who already understand the basics of gerrymandering, can use a tool called Districtr to draw real voting districts. The site uses actual data about where voters live and which political party won in which area. Using this tool, students cannot only try to gerrymander districts, they can also try to create districts that are more fairly balanced. After trying to draw their own “fair” districts, students might be interested in some states’ use of independent groups to draw fairer district lines.

By using elections as a learning tool, students can gain a better understanding of ratios, means and range, and they might also start thinking about what they can do to improve the process.

The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.