Explanation and Rationale

This series of nine lessons is designed as a technology-aided student exploration of the geometry of circles. Implemented as a unit, this set of lessons incorporates a majority of the circle geometry included in Euclidean Geometry textbooks. However, each lesson is also designed for easy implementation outside of the context of the unit. That is, one should find that incorporating a single lesson into her course is a simple task.

Technology is infused through this unit. In particular, heavy use of the Geometer’s Sketchpad software is accompanied by elements of spreadsheet, presentation, and graphing software. While the majority of lessons are written for environments in which all students have access to a computer, not having these extensive technology resources should not be seen as an immediate signal that this unit is not applicable to one’s school. The majority of the explorations outlined in these lessons can be accomplished in an alternative, more teacher-driven form. With access to only one computer equipped with appropriate software, a teacher can create and manipulate the dynamic sketches described and promote student hypothesizing, conjecturing, and proof.

Timeline

The timeline below is based on one-hour class periods. Completion of the entire unit is estimated to require 11 days.

Lesson 1: Circumference of a circle	1.5 days
Lesson 2: Area of a circle	1.5 days
Lesson 3: Parallelogram, circles, vertices	1 day
Lesson 4: Tangents and Secants of a Circle	2 days
Lesson 5: Inscribed Angles	1 day
Lesson 6: Quadrilaterals inscribed in a circle	1.5 days
Lesson 7: Parallel Chords	1 day
Lesson 8: Length of Chord, Distance from Center	2 days
Lesson 9: Intersecting Chords	1 day