Conic Sections are an unfortunate part of Pre-Calculus and Algebra II. Typically the most difficult part is explaining where simple things like circles and ellipses come from. You and I know they come from the oh so familiar double cone, that you know, we see everywhere, all the time. And think about circles when we see it...you get the idea. So I've tried website animations, I've tried holding a model in my hands and letting them visualize slicing through and seeing the shapes. This year I let them do the slicing for themselves.
Materials: case of Play-Doh, dental floss
Play-Doh is cheap, 10 mini cans can be had for $5. And the kids love the colors. I split my classes into groups of four and handed out two cans per table. If the class was small enough I gave each kid a can (I had 20 cans of the stuff). I have them role out their own cone, either modeling it myself with my own can or using a big plastic model of the double cone. Then we walk through the four shapes. Each kid has a strip of dental floss and I explain how to slice. Then we crack open the cone and I see if they can guess the shape. I get "oval" instead of "ellipse" but that's easy to correct. After we get through all four I ask if they see evidence of them around the room. It's impressive when a kid says they've found a hyperbola. Then we go through some other examples. I explain how satellite dishes work, then we dive into the equations.
Here's my case of Play-Doh and an example of a cone:
An added bonus is that you now have Play-Doh in your room for those days when 70% of them are on a field trip or you have some random time to kill during standardized testing week or finals week. Kids love Play-Doh. Count how many times they say "I haven't touched this since I was 5."