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