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 141 - 154 from the attached PDF file for your class

During the Activity

Distribute the pages to your class.

Follow the activity procedures:

Enter the stage number data and the value (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 find the 100th and 75th terms in the sequence

After the Activity

Students will complete the Data Collection and Analysis page and answer questions listed on it.

Review student results

As a class, discuss questions that appeared to be more challenging