Day 155: Coneheads
There are so many cool ways to help students get the ideas behind the geometry of conic sections, that it’s hard to choose. At one of my TI User Group sessions, we explored the conic sections using patty paper, led by Art Mabbott, to develop the locus definition of various conics. We then followed it up with a really neat Nspire activity called Introduction to Conics and Patty Paper Ellipses.
This year I decided the tactical approach would be fun, so out came the patty paper. The students followed a guided exploration and they were amazed when the parabolic shape emerged out of their folding. We compared what happened when the focus moves closer to the directrix and further away. Using geometry, they determined the actual geometric definition of a parabola on their own. Very cool!
As a side note, I was observing my colleague as he had his students explore the ellipse construction using string, tape, and the white boards. I thought it was quite ingenious using the white boards rather than pushpins. Watching the students draw the ellipses was fun, but the development of the relationship between the foci and any point on the ellipse through questioning was really well done. When the students determined the relationship, it was also so interesting to watch the students talk through their formal definition, revising and cleaning up the language.