Education Technology

# Move My Way--A CBR Analysis of Rates of Change

Math: Calculus: Other Functions
Math: AP Calculus: AP Calculus
9-12
60 Minutes
TI-83 Plus Family
TI-84 Plus
TI-84 Plus Silver Edition
CBR 2™ motion sensor
This is Activity 8 from the EXPLORATIONS Book:
Calculus Activities.
Lessons

# Move My Way--A CBR Analysis of Rates of Change

Activity Overview

In this activity, students' use the motion detector to collect position data and study the relationship between position and velocity. They explore the relationship between functions and their derivatives. Students' learn to connect mathematical relationships to real-world phenomena.

Before the Activity

• Connect the CBR 2™ unit to the calculator
• Start the Ranger program
• See the attached PDF file for detailed instructions for this activity
• Print pages 77 - 82 from the attached PDF file for your class
• During the Activity

Distribute the pages to the class.

• Set up the CBR™ to collect position data every 15 seconds
• Move back and forth in front of the CBR and collect distance versus time data
• Identify regions on the graph where the velocity is positive, negative, and zero
• Make a sketch of the predicted velocity versus time graph
• Determine the instantaneous velocity
• Use the stat plot for velocity as a function of time to sketch velocity versus time graph and compare it with the prediction
• Sketch a velocity versus time graph for a given position versus time graph
• Use the RANGER application to collect velocity data, and match the sketched graph with the actual graph of the data
• Observe the derivative graph as the function graph changes
• After the Activity

Students' will collect data and analyze the results.

Review student results:

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