# Activities

• • • ##### Subject Area

• Math: Algebra I: Sequences and Series

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Other Materials
This is Activity 8 from the EXPLORATIONS Book:
Activities for Algebra with the TI-83 Plus.

The following materials are required for this activity:
• Red and green colored pencils
• Metric ruler
• Compass
• Tracing paper and graph paper

## At a Snail's Pace

#### Activity Overview

In this activity, students plot a mathematical relationship that defines a spiral. They use technology to create a spiral and to plot a set of ordered pairs.

#### Before the Activity

• Set up the calculator for data collection using the procedure described in the attached Appendix file
• See the attached PDF file for detailed instructions for this activity
• Print pages 101 - 108 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Draw a square and record the coordinates of its vertices
• Construct a congruent square to the left of the original square to form a rectangle
• Construct a square above this rectangle with the side of the square equal to the length of longer side of the rectangle
• Continue adding squares in a clockwise direction
• Record the length of the sides of each square and the coordinates of its vertices
• Using a compass, make a quarter circle inside the square
• Repeat this step with each square
• Record the coordinates of the center-points and lengths of the radii for the circles
• Observe that the construction resembles a spiral
• Construct a Fibonacci spiral using the calculator and the data for the center points and radii
• Compare the spiral formed on the calculator with the spiral drawn on the graph paper
• Observe that Fibonacci sequences can be seen in the lengths of the sides of the squares, widths of the rectangles, lengths of the rectangles, and radii of the concentric circles that form the spiral
• #### 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