Instructional Unit: Properties of Circles

Arielle Alford

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 GeometerŐs 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 oneŐs 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.

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 |