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Course, Subject

Algebra I (NYS P-12 Common Core), Algebra I (Next Generation), Math, Science & Technology, Mathematics (NYS P-12 Common Core), Mathematics (NYS P-12 Next Generation)

Description

In this lesson, students will investigate the cost of tolls in a given state. The students will determine the average cost per mile for passenger vehicles. In addition, the students will model, analyze, and make predictions for adding a new toll plaza in their given state.

Website(s)

Massachusetts Toll Calculator
Pennsylvania Toll Calculator
New York Toll Calculator

Duration

Three 45-minute classes

Learning Objectives

Students will be able to: determine the line best fit based on given data, determine the average cost per mile for passenger vehicles, and model, analyze, and make predictions for adding a new toll plaza.

Materials

Paying for Tolls worksheet

Toll Recording worksheet

computer for internet access (one computer for each group of students - 4 students per group)

websites for state toll road(s)

graph paper (one for each student)

rulers

Paying for Tolls worksheet

Toll Calculator

Step-by-Step Procedures

Put the students in groups of 4. Assign each group a state.

Hand out Toll Recording worksheet to each student. Each student in the group is responsible for recording all of the data.

Explain that the state website(s) given include a toll calculator for their turnpike or highway. The calculators give the amount of the toll and the distance between the toll plazas.

The students will use the toll plaza websites to gather data. Explain that the students must always begin at the same location when using the toll calculator.

The students are to use the Toll Recording worksheet to record the data that they find. Explain the different columns on the worksheet and how to fill them in.

Once the group has recorded all of their data, hand out a piece of graph paper and a ruler to each student. Go over the instructions on how to make a graph (located on the back of the Toll Recording worksheet). The students will be making a scatter plot and drawing in a line best fit. (They should have a positive slope.)

After the students finish making the graph, hand out Paying for Tolls worksheet. The students will continue to work as a group to answer the questions.

Have the students show their graphs to the class and discuss any pattern(s) that they saw.

For homework, the students are to answer the homework question.

Assessments

Collect the graph and Toll Recording worksheet.

Paying for Tolls homework question

Related Academic Standards

New York State

7.RP.2.c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★

MST3.8.PS.6 Students represent problem situations verbally, numerically, algebraically, and graphically.

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