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?
I 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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