Activity Overview
Students use sample data to approximate models with the Transformation Graphing Application. They are introduced to the idea of discrete data sets being used with continuous function models. They also identify non-zero asymptote form of an exponential function.
Before the Activity
Install the Transformation Graphing application on the students' graphing calculators using one of these two methods:
TI-Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
TI-Navigator™ "send to class" feature
See the attached PDF file for detailed instructions for this activity Print pages 89 - 96 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Record the number of dice used for the trial
Roll the dice
Remove from the set any dice that shows a 6 on its top face
Record the number of remaining dice in the set
Use only the dice left, roll these dice, and remove any dice that shows a 6
Repeat until no dice remain, or the dice have been rolled 15 times, whichever occurs first
Enter the number of rolls and number of dice left as lists
Plot the graph and select an appropriate value for A
Change the value of B and use the guess-and-check method to find a reasonable model for the data
Observe that the decaying curve does not reach zero, but tends to zero
Write an equation for the exponential function
Determine when y < 0.5, and when there are no dice left
Use the calculator to get a rough estimate of the location of the asymptote
Repeat the activity with non-standard set of dice
After the Activity
Students will complete the Student Worksheet and answer questions.
Review student results
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary