After the AP Calculus exam every year (of the 4 I've taught it), I've done different things. The first year I did a volumes of cross section project with foam and hot glue and a ton of grief. That was the year I had a screaming match with a student outside of class. The 2nd year I took a break from that and did various other snippets of math topics with mini quizzes. No screaming matches. The 3rd year I revamped the volumes project and tossed in a volumes of revolution project with foam and hot glue and stricter guidelines. That year I had a child sit in class with his pants unzipped and then tell me later that HE WILL DECIDE what is socially acceptable.
This year I'm teaching snippets of advanced calculus to my 2 classes with "easy" quizzes at the end of each class that should be ace-able if they simply pay attention. So far I have one class being good about it, and I've even had one student finally perk up and get out of his morose I-suck-at-math state and pay attention to be able to pass the quiz. The other class was great for one day (when the loud students were gone for other AP exams).
There are students in that 2nd class though that are enjoying things. They come up to me after class to discuss the topics some more.
So far we've "covered" (just given them a taste of) double integrals used for calculating volumes of weirder shapes, surface area calculations, and Gabriel's Horn Paradox. I think I also want to do Fourier Series with my BC class and centers of mass and .... who knows what else. I have a great resource ... the Smith calculus book. It's the THICK blue one, and it has amazing problems and historical snippets and ideas. Anyhow, busy busy busy trying to learn things right before I teach them.
I was also intrigued by the Hubble Telescope news of late, so I assigned my precalculus class an assignment of bringing back 3 facts in their own words about anything to do with "Hubble". I told them that I wanted to learn about it, too, since I didn't know much about it, and I would also do the homework. I told them that we couldn't just exist in our own little bubble of everyday existence. We had to be informed about the world. Then a student said, "we'll bring Hubble into our bubble."
I told them to explore the "what,when,where,who,why, & math" of the situation. Anyway, I went on a particular website, and WOW, the pictures it sent back from space are breath-taking. Can't wait to see what they find out.