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.

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