I'm loving this unit more and more each year. It's a chance for the students to practice their ever-waning algebra skills (hello completing the square, I love you). It's also a chance to do some hands-on stuff. AND it's a chance to see some cool applications.
One year (not this one, because ... well, just because) I saw an application that you could build a pool table in the shape of an ellipse, and then if a ball was at one focus point and you hit it, then in an ideal world, it would pass through the other focus point. I then just had to try it. I had the kids construct an ellipse (lots of string and a large piece of paper. Then I had my patient/loving husband carve this out of some wood and hollow out the inside to be the "pool table" in the shape of the ellipse. I brought it to class and we recreated where the foci were and we tested it out. It worked most of the time and was cool.
This year for ellipses, I just had them create ellipses on paper with a partner and a loop of string and 2 sharp pencils held down for the foci. Then they took their notes on this creation. Every student had 2 ellipses, one on each side of the paper, one with vertical foci, and one with horizontal. It worked well.
I'm having them do a project of searching for practical uses of each conic (circles, parabolas, ellipses, and hyperbolas). Let's see what they wow me with.
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This is such a great idea! Would you mind sharing what kind of practical uses of the conics that the students came up with?
ReplyDeleteI was introduced to how conics can be introduced by paddy paper...and it also literally applies the definition of each conic. For instance parabola is everywhere equidistant between a point and a line. So on patty paper, students draw a line and then draw a point. Then they fold the paddy paper as many times so that the point they drew falls on the line...and do it for a while until a parabola appears. Same works for circles, ellipses, and hyperbolas. Hope this sparks another idea :)
Happy New Year!
Hi Jdao. Unfortunately, it's been soooo long since I did this that I don't remember what the kids came up with. ... I love the patty paper idea, though. It's hands on and the kids can see how things come about.
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