Extending, Formulating, and Refining Conjectures with GeoGebra: The Pentagon and Its Medial Pentagon

Abstract

In this paper, I describe a classroom experience on how I guided a group of preservice secondary mathematics teachers to extend, formulate, and refine a conjecture about the ratio of the area of a pentagon and the area of its medial pentagon: The ratio of the area of a medial pentagon to the area of the outer pentagon lies between 1/2 and 3/4. The use of GeoGebra facilitated the discovery and visualization of the conjecture.