# Activities

• • • ##### Subject Area

• Math: Algebra I: Sequences and Series
• Math: Algebra I: Quadratic Functions

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Other Materials
This is Activity 11 from the EXPLORATIONS Book:
Activities for Algebra with the TI-83 Plus.

The following materials are required for this activity:
• Small cubes or candy
• ##### Report an Issue

Get Your Numbers in Shape (TI-83/84 Family)

#### 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 141 - 154 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to your class.

• 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
• Re-teach concepts as necessary