In my honors Algebra II class of sophomores, I always look forward to doing a culminating project on quadratics. We start at the beginning of the chapter with introducing the project and having the kids break up into groups of 3 and 4 and start designing and building a catapult outside of school.
Meanwhile, in school, I teach them everything they need to know about quadratics. They have a due date to bring the catapults to school to showcase them, to test them, to compare theirs to the other students and to decide on how they might improve their own. Next, they bring it home and get it ready for target shooting day. We spend two class periods on the lab. Day 1 is launching M&Ms from the catapult and timing the landing to come up with the equation of the path. They need to use their equation to determine where their target (a bowl) should be placed. They shoot from floor to floor. Then, they are asked to translate it up onto a desk. Day 2 is the "for real" target shooting. The kids get 1 practice shot from the desk and then 3 real shots.
They really enjoy this and get to see all of their quadratic knowledge put to work.
I will try to include the lab with directions and rubric here. I am not sure of the best way to attach a word document, but I will try: (okay, I put it on google docs and linked to it but it is way at the bottom.
Here are some pictures.
Hint: smaller is better, we are going for accuracy, not distance or height and I don't recommend allowing students to use mouse traps (too fast to time) or to build a trebuchet.
Catapult Quadratic Lab