# Activities

• • • ##### Subject Area

• Math: Algebra I: Linear Functions

• ##### Author 9-12

60 Minutes

• ##### Software

TI InterActive!™

• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
TI InterActive!™ Data Collection and Analysis

Take the Train

#### 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.

• 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