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Why Is California So Important?

6-8
2
Number and OperationsData Analysis and Probability
Kimberly Morrow-Leong
Gainesville, VA

In this lesson, students learn about the mechanics of the Electoral College and use data on population and electoral votes for each state. Students calculate the percentage of the Electoral College vote allocated to each state, and use mathematics to reflect on the differences. Several questions are provided to strengthen understanding of measures of central tendency and fluency with decimals and percents.

Ask students:

Who elects the president of the United States?

[The Electoral College, not the general voting public.]

Describe the mechanics of the Electoral College to students. If time permits, you can also have students 2821 picture voteresearch how the electoral college works. Many resources are available online.

Tell students how many electoral votes their state has. Ask them whether it seems like a lot or a little. Discuss what they've learned to get them excited for the upcoming lesson. Tell students that they are going to be gathering data about the number of electoral college votes in each state and discovering interesting facts. By the end of the lesson, they will know if their state has many or few electors, and what that means to a candidate running a presidential campaign.

To get students started on the activity, distribute the Why California? Activity Sheet. The first task is to complete the table in Question 1. Have pairs of students collect the data. Or, to save time, divide the table into sections of 5–10 states, and assign a small group of students to each section.

pdficon Why California? Activity Sheet 

If using computers with Internet access: 

There are many websites that provide the most current census data on population and the number of electoral votes for each state.

If computers are available, but not an Internet connection: 

Have students record the data in the Electoral College Spreadsheet. Then have students complete the remaining cells using spreadsheet functions, such as sum and average. Using the sort function, you may choose to have students sort the states by number of electors and make observations about the data.

spreadsheet Electoral College Spreadsheet    

Have students gather the data as a collaborative group and record it in the table.  Or they could collect data on one day and complete the rest of the table on another day. You could also assign students to collect the data at home as a family activity. 

As students begin collecting the data, monitor their progress. Adding large numbers can be problematic for some students, but it shouldn’t prevent them from completing the rest of the lesson. This is an ideal task for the use of technology such as calculators or computer spreadsheets.

Question 2 should be completed individually to allow students to make their own observations of the data. When you see a student writing an observation on the activity sheet, ask them to record their responses so that they can share them with the rest of the class. Once everyone has made at least one observation, discuss the observations as a class. Observations to look for are the great variability in the data, the fact that each state has a minimum of 3 electoral votes regardless of the population, and estimates of the mean of the data, since it is a good indicator of students’ understanding of the data. Do not share the actual mean at this time; wait for it to come up in Question 6.

Questions 3 and 4 can be completed individually or in small groups depending on your class’s level of confidence. As you circulate, look for students using mathematical ideas, such as divisibility, to solve Question 4. With some students, you may choose to address the topic further. If the number is divisible by 2, does that necessarily mean a tie is possible?

[No. There has to be a way to group the data. For example, if there were 2 states, one with 3 votes and the other with 5, a tie would be impossible, even though the sum is divisible by 2.]

Question 5 can be completed during the lesson or used as a take-home assessment. While counting the number of states above and below 2% of the electoral votes is straightforward, the mathematics of expecting 2% to split the states might be confusing to some students. If the problem is answered during class, take the time to discuss it with students.

Questions 6 - 8 require reflection before responding. Before performing the calculations, ask students to estimate the median and mode and record them in pencil. Students should have estimated the mean previously in Question 2. Have them record their 3 estimates together. This will reveal whether they understand the degree to which California’s 55 electoral votes skew the mean relative to the median.

To make the calculations, have students use a spreadsheet utility or the LIST function on a graphing calculator. If students use a standard calculator, have them work in pairs and compare answers with another pair before continuing. A list of 51 data points is more prone to errors, so build in this self-checking strategy. Some students may need to be convinced that there is only one correct answer for each measure. Follow the calculation exercise with a discussion of the answers. Students should recognize that the mean is higher than the median, and the mode is the lowest possible value. Encourage students to make generalizations about the data based on the measures of central tendency.

Introduce Question 9 with “On average, how many electoral votes does each state have?” Students may initially struggle with this idea. For many of them, average is only the mean. Encourage students to come up with a reason why each of the 3 measures of central tendency might be useful. This will give students the opportunity to explore the differences between the mean, median, and mode. This is a difficult concept to understand, so encourage students to explore the answers without expecting the "right" answer.

Question 10 is a good lead-in to the remaining questions. Students will likely be interested in discussing their state. The median is a good measure to use since it physically divides the states into two equal groups. Also, with the exception of California, the states are more likely to be close to the median than to the mean or the mode.

Question 11 is a good class discussion topic because it addresses the key idea of the lesson, which is how influential states with a large number of electoral votes are in a presidential election. You may choose to enrich this question with follow-up questions such as the following:

  • How many less populous states would a candidate have to visit in order to reach the same number of voters as California? as Texas?
    [A presidential candidate would have to visit the 16 states with the least electors to reach a total of 59 electors, just 4 more than California alone. For Texas, the candidate would have to visit the 13 states with the least electors.]
  • If a candidate could only visit 10 states in the week before the election, which states would you schedule?
    [The 10 states with the most electors, which are California, Texas, New York, Florida, Illinois, Pennsylvania, Ohio, Michigan, Georgia, and North Carolina are good choices. This will come up again when students plan a campaign in Question 13, but you can get them started early with this question.]

Question 12 is also a good assessment question because it reveals whether students understand the importance of a state having many electoral votes and asks students to consider their own state in the data list. Is your state “average” or is it further from the median? It’s important for students to understand that a state with a higher percentage of the electoral votes is more “valuable” to a candidate.

Question 13 wraps up what students have learned during the lesson. Ask students to write their answer in a complete paragraph, using supporting details from the data in their writing. As you discuss students' answers, reflect on arguments using the information from the previous questions.

pdficon Why California? Answer Key 

Assessment Options

  1. Create a take-home assignment that includes participation from students' families. Consider asking students to recount how they explained the data to their families, to provide a short summary of the observations they made and heard in the class discussion, and to make a list of any new observations made by or information learned from their families.
  2. Ask students to plan a candidate’s campaign by creating a campaign schedule for the election season (August–October) or for the period from the time of the activity to the election. Have students use data collection and analysis to justify their decisions.

Extensions 

  1. Have students make a scatter plot of the number of electoral votes to the population of the state of the 13 least populous states. They can then find the correlation and analyze the relationship. Have students repeat the exercise for the number of electoral votes to the population of the 17 most populous states. These are the states with electors over the mean.
  2. Add an additional column to the table on the activity sheet and have students create a fraction representing each state’s part of the 538 electoral votes. Have students find the factors of 538 first to facilitate the calculations.
  3. Students can research the process for determining a winner when no candidate reaches the 270 votes needed to win.
  4. The question of 2- and 3-way ties is related to the topic of bin-packing. Have students research bin-packing to explore different ways in which ties or near ties are possible.
  5. Make a connection to social studies. Involve students in a school-wide election, including voter registration and a school electoral college. Allocate electoral votes according to class population, run the election, and analyze the results from both a social studies and math perspective.
  6. Move on to the next lesson, How Could That Happen?
 

Questions for Students 

1. How could the votes be split between the states to create a tie?

[There are several possible answers. For example, one candidate wins Virginia, New Jersey, North Carolina, Michigan, Ohio, Illinois, Pennsylvania, Florida, New York, Texas, and California, while the other candidate wins all the other states.]

2. Why do candidates spend so much money and time in California?

[California is an outlier with respect to the number of electoral votes — it represents over 10% of the electoral college.]

3. Do the presidential candidates come to visit your state often? Why?

[Answers will vary by state. The reasons may be tied to the electoral college, but also encourage students to consider other factors, such as historical voting trends.]

4. Why do many states have exactly 3 electoral votes?

[This has to do with the way electors are assigned. A state with 3 electors is a state with 2 senators and 1 representative. The number of representatives a state has is determined by its population. Therefore, all states with 3 electors are states with low populations.]

5. How are electoral votes related to population? Do you think this a fair system?

[This revisits the concept in the previous question, but from the perspective of population instead of electors. The fairness of the system is highly subjective and can be used to start an interesting discussion.]

Teacher Reflection 

  • Did students use a divisibility rule or any other mathematical concept to address the question of a tie?
  • Did mechanical tasks like copying data make the activity difficult for some students?
  • Were student observations insightful or superficial?
  • What kinds of difficulties did students have with calculations?
  • Did students understand the role of the electoral college in the campaigning schedules of candidates?
  • Will students understand the importance placed on California, Florida, Ohio, New York, Texas, Illinois, Michigan, and Pennsylvania during election night coverage?
 
2825icon
Number and Operations

How Could That Happen?

6-8
This problem-solving lesson challenges students to generate election results using number sense and other mathematical skills. Students are also given the opportunity to explore the mathematical questions in a politically challenging context. Calculations can be made using online or desktop tools or using the data gathered on the Lesson 1 activity sheet, Why California?  Additional resources are introduced to extend the primary activity. 
2833icon
Measurement

A Swath of Red

6-8
A political map of the United States after the 2000 election is largely red, representing the Republican candidate, George W. Bush. However, the presidential race was nearly tied. Using a grid overlay, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.
2983icon
Data Analysis and Probability

There is a Difference: Histograms vs. Bar Graphs

3-5, 6-8
Using data from the Internet, students summarize information about party affiliation and ages at inauguration of Presidents of the United States in frequency tables and graphs.  This leads to a discussion about categorical data (party affiliations) vs. numerical data (inauguration ages) and histograms vs bar graphs.
2539icon
Data Analysis and Probability

Will the Best Candidate Win?

9-12
This lesson plan for grades 9‑12 is adapted from an article in the January 2000 edition of Mathematics Teacher. The following activities allow students to explore alternative voting methods. Students discover what advantages and disadvantages each method offers and also see that each fails, in some way, to satisfy some desirable properties.

Learning Objectives

Students will:

  • Collect state-level data on population and electoral votes.
  • Calculate each state’s share of the electoral college votes as a decimal and a percentage.
  • Use divisibility rules to decide if a 2- or 3- way electoral tie is possible.
  • Use the mean, median, and mode to determine which measure of central tendency best describes the number of electoral votes per state.
  • Use the data collected to make conjectures about the behavior of presidential candidates during an election.

NCTM Standards and Expectations

  • Work flexibly with fractions, decimals, and percents to solve problems.
  • Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
  • Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

Common Core State Standards – Mathematics

Grade 4, Algebraic Thinking

  • CCSS.Math.Content.4.OA.A.3
    Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Grade 4, Num & Ops Base Ten

  • CCSS.Math.Content.4.NBT.B.4
    Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Grade 5, Num & Ops Base Ten

  • CCSS.Math.Content.5.NBT.A.3
    Read, write, and compare decimals to thousandths.

Grade 6, Stats & Probability

  • CCSS.Math.Content.6.SP.A.3
    Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.