Activity Overview
Students produce a sequence, explore patterns and find a linear or quadratic equation for a given pattern. They use inductive reasoning to make conjectures about patterns. Students also find the Y-value of a function if the X-value is provided, and vice versa.
Before the Activity
Set up the calculator for data collection using the procedure described in the attached Appendix PDF file
See the attached PDF file for detailed instructions for this activity
Print pages 151 - 164 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the activity procedures:
Enter the stage number and the value for the first eight stages of the triangular numbers (data for a sequence)
Find the first difference between the successive terms
Observe the differences are not equal, and the sequence is not linear
Find the second difference between successive terms
Observe the differences are equal, and the sequence is quadratic
Set up a scatter plot using the data
Perform a quadratic regression to find a best fit equation that describes the sequence
Observe and graph the quadratic function
Develop recursive and explicit formulas for the sequence and use them to generate the successive terms in the sequence
After the Activity
Students will complete the Data Collection and Analysis page and answer questions.
Review student results
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary