Objectives
Students often identify almost any U-shaped curve as a parabola, however, parabolas have distinct properties. The first part of this series aims to provide students a much better understanding of these properties. A CAS environment allows us to de-emphasize procedural content around expand, factorise and graph; and replace it with understanding.
Vocabulary
- Perpendicular
- Bisector
- Envelope
- Parabola
- Model
- Focus
- Directrix
About the Lesson
The paper folding component of this activity provides a simple way for all students to engage and see a parabola form. The calculator environment replicates the physical folds in a very dynamic way and provides a platform on which students can model the curve using a dynamic parabola. At this point the curve is being modelled. The next activity provides a simple proof of why this series of folds (envelope) is an actual parabola.