Education Technology

Take the Train

Published on 10/17/2008

Activity Overview

In this activity, students collect information about the stops made, time taken, and distance covered by a train on one of Amtrak's routes. They find a mathematical model that can best track the train. Student understand concepts related to direct variation and linear functions.

Before the Activity

  • Open a new TI InterActive!™ document
  • Find Amtrak's timetable for the route from Chicago to New Orleans from the website
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 15 - 19 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Note the arrival times of the train at different cities and the distance covered as the train travels from Chicago to New Orleans
  • Convert the time to a decimal format and calculate elapsed time
  • Plot elapsed time versus total distance traveled
  • Observe that the data can be modeled by an equation y = kx where y is the distance, x is the time, and k is a constant, and both y and x are directly proportional to each other
  • Find the slope of the plot by the guess-and-check method
  • Find the average speed between stops separately and find when the train was traveling the fastest and when it was traveling the slowest
  • Use the linear regression function to get a line that best fits the data and record the linear equation y = ax + b and values of a and b
  • Compare the values of slope and y-intercept from the linear regression model with that from the guess-and-check method
  • Note the value of b from the linear regression model should be equal to zero
  • After the Activity

    Students complete the analysis and answer questions.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary