I'm a mentor for FIRST Team 4095 Team RoXI of Pius XI High School out of Milwaukee WI. It was our rookie year this year and we didn't do all that well, but we were there with more than a plywood box (but close though). I was also a student on FIRST team 13 of Johnsburg IL 1996 through 1998.
FIRST is a great project for those interested in STEM and Business and Marketing students too.
Our team was a team of 12 kids and 2 mentors. While most teams are double or triple the number of participants.
When starting, most of our team didn't even know how to use a drill. After the very short and intense 6 week build season, they all have that figured out, and have better learned the engineering portion of the event. They also got into mathematics of projectile motion. All to build a robot that is 28"x38"x60"tall and max weight of 120lbs. The event changes every year, and the size constraints change a little bit every year.
The other interesting thing with FIRST Robotics is the way they made the event more than just cheering on your own robot. You are teamed up with two other teams for the event. For this last year a game of 3 on 3 basketball. So teams cheer themselves on along with 2 other teams who earlier were opponents to them.
There is a lot of opportunity to volunteer being a mentor to a local team as well or even sponsor a team.
I know our team is looking for all types of mentors and sponsors, ME, EE, Machinists, CS, programming, Business, Marketing.
If you're even a little bit interested check out http://www.usfirst.org/roboticsprograms/frc/get-involved
for more information.