Prior to the lesson, attempt to obtain a ticket for a toll road in your state. Ask a toll booth attendant while traveling, or write your state’s department of transportation or turnpike commission. Explain that you are an educator who will be using the ticket for a classroom activity. (The Federal Highway Administration maintains a list of
State Transportation Web Sites.)
You can also find information about toll rates via the Internet. Most states have a turnpike web site. A few are listed below; if yours is not, enter your state name and the word "turnpike" or "toll road" into a search engine such as Google, Yahoo, Webcrawler, or Ask Jeeves.
Several states do not have state toll roads. Other states have toll roads that charge a constant fee, regardless of distance. If this is the case in your state, you may wish to use the data from a neighboring state for this lesson, or you can use the Pennsylvania Turnpike Toll Rates overhead to provide data for your class.
Another effective introduction is to pose the following problem:
The [State] Turnpike Commission is planning to add a toll plaza in [City]. They have asked for your help in determining the amount of the toll that should be charged at this exit.
Of course, this introduction could be embellished to include reasons why an exit is being added, such as the construction of a new sports stadium, easier access to local shopping, and so forth.
Assign students to groups of three. Make all materials easily accessible, and designate one member to get the Taking Its Toll activity sheet, while another member gets calculators, rulers, and graph paper.
Students should then gather data for the Toll Data Recording Sheet in either of two ways:
- Many states include a toll calculator for their turnpike on a web site. These calculators often give both the amount of the toll as well as the distance between toll plazas. Use a search engine to find your state’s turnpike web site; then, use the toll calculator to gather the data, or allow students to use the web site to gather data on their own.
- Alternatively, students can use the state’s toll ticket in conjunction with a state map to find the necessary information. The ticket will provide toll information, and the map will provide distance. Discuss with students how to determine the necessary information from the ticket. There may be different tolls for travelers depending on the state vehicle classification system that is used.
Have the students work together in their groups on the student activity sheet. If necessary, have them record data on the last page of the activity sheet, or have them enter the information into the Toll Data (Excel) spreadsheet. The first column is only needed to identify each exit. In the second column, students should record the total distance from the start of the toll road. This information may be easily obtained if the exit numbers correspond to mileage; if not, students will need to determine this information from another source. In the third column, students should record the cumulative toll.
Beware of common student errors when recording data. Computation errors often occur in the third column. In addition, some plazas do not have a toll, so students may be confused as to how the cumulative total is affected. Be sure that students verify their data before proceeding.
Using their data, students should then create a scatterplot. Students can create this scatterplot on the graph of Question 3 of the Taking Its Toll activity sheet, or you may wish to have them use the chart feature if they entered their data in a spreadsheet program.
Results will vary from state to state, but the scatterplot for most toll roads generally indicates a linear pattern with a positive slope. For instance, the tolls on the Pennsylvania Turnpike result in the following:
After gathering data and making a graph, students should analyze the results. Gathering the data and creating graphs are skill-based tasks. While it is important for students to develop these skills, it is more important for students to conduct an analysis of their completed graphs to develop conceptual understanding of rates of change.
Questions 4-10 on the activity sheet require students to analyze the graph, and you may wish to have students work on these questions in their groups. After they complete these questions, conduct a follow-up discussion to review their answers and to ensure a high level of student understanding. Allow each group to present their line of best fit and how it was determined.
Alternatively, you may wish to have students consider Questions 4-10, as well as other questions that you devise, as part of a whole-class discussion. If you choose this option, do not distribute the second and third pages of the activity sheet. Instead, ask these questions one at a time, and allow students to discuss them as a class. The conversations that occur between students are often beneficial. (To ensure that all students participate in this discussion, and to prevent just a few students from monopolizing the conversation, use a random selection technique to call on students, such as putting all student names in a hat and drawing them at random.)
