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.
Follow the Activity procedures:
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