At the end of every semester the students in my undergraduate math, science and engineering class have to make a rubber band roller. It's a great activity. Here's a sophisticated one on Youtube. I prefer to have my students use "found" materials so that they can develop their resourcefulness, creativity and stamina!.
It's a great engineering activity because it never works first time. You have to adapt and improve the design based on your observations of where you need more friction and where you need less friction. The activity is not graded but can take a student quite a bit of time to complete. Despite this every semester every student always completes the roller and takes part in the three competitions we have. (I always think it's great when students do assignments that are not for a grade). The three competitions are distance, speed and creativity and were won by Shelly, Lila and Katie respectively.
The competition at the end of last fall was especially memorable as Mallory, one of the students, made an incredible rubber band roller cake. Not only did it look amazing but it was really good to eat as we all found out. Many thanks to Mallory and everyone else for making this a memorable class.