The Web Site of Jeanne Wilson

Software Lesson for TI-Interactive

Pennsylvania Turnpike

Grade Levels:  Algebra 1/Algebra 2

Focus of the Lesson:  Real World Application for Linear Functions

 

 

Introduction

 

The Pennsylvania Turnpike site has a toll collector calculator that enables the student to choose a starting interchange and an ending interchange to calculate the toll charge for the mileage traveled.  Students will determine that real data models linear functions.  The lesson is appropriate for all levels of students who study linear functions.  Students will use the TI-Interactive software to display their data, graph their data and interact with the graphics to find an appropriate linear equation to model the mileage and toll data.  TI-Interactive software provides the opportunity for graphic representation of a real world application.  The software enhances the study of linear functions for the visual learner by enabling the students to use transformations of linear equations to curve fit the data. 

 

Lesson Objectives

 

The students will:

  • Use real world data from www.paturnpike.com to create a list.
  • Create a scatter plot on a TI-Interactive document using their data using an appropriate WINDOW.
  • Define the independent and dependent variables. 
  • Determine if their data represents a linear model.
  • Determine by curve fitting the equation of the line to represent their data and graph it on his TI-Interactive document.
  • Use all appropriate labels for graph i.e. title, axis, intervals on the axis.
  • Calculate a linear regression using TI-Interactive menu.
  • Describe the meaning of the slope (m) of the line of best fit.
  • Write a comparison of the slopes and y-intercepts of the regression calculated from TI-Interactive and the line of best fit.
  • Print their document.  

 

Instructional Materials

 

Computer wired to the Internet

Software:  TI-Interactive

Pennsylvania Turnpike data sheet

Activity packet - directions for TI-Interactive

Projector (optional)

Printer

Pen/pencil

Lesson Sequence

 

The class time is 45 minutes.  Students in the honors level Algebra 2 class will be able to finish the assignment in one class period.  Students in lower levels of Algebra 2 or in Algebra 1 may need an additional class period to successfully complete the lesson objectives.  Student will work on their individual computers but may confer with other students beside them as they curve fit their data.

 

Collecting Data:

Students will complete Pennsylvania Turnpike data sheet by accessing www.paturnpike.com.  They will use the toll mileage calculator to calculate 5 tolls with the corresponding mileage.  The students will use the same starting interchange 5 times with a different ending interchange for each.  (approximate time: 5 minutes)

 

Graphing Data:

Students will open TI-Interactive, enter their data in the lists, graph the data with the appropriate WINDOW, curve fit their data with their own line of best fit, save to document.  Students will calculate the linear regression using the Stat Calculation Tool and save to document.  (approximate time: 25 – 30 minutes)

 

Analyzing Results: 

Students will define the dependent and independent variables, write a description of the slope of the line of best fit, and compare the two equations of the lines that model the Pennsylvania Turnpike data.  (approximate time: 10 – 15 minutes)

 

Evaluation/ Assessment

 

The students will print their document which will be evaluated for the following:

  • Lists with the appropriate headings
  • Scatter plot with axis labeled and title, student’s line of best fit, and the line of TI-Interactive regression equation.
  • Linear regression calculation.
  • Definition of the dependent and independent variables.
  • Statement describing the meaning of the slope of the line relative to the tolls and mileage.
  • Written comparison of 2 equations modeling their data.

 

Supplemental Materials

 

 

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                  ©JWilson | Last revised April 25, 2007 | jwilson@hamden.org