Education Technology

Get Your Numbers in Shape (TI-73 Explorer)

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