My whole campus is divided into 3 separate schools, so the other 2 schools know little or nothing about our team. My separate school is supported by some of the other students. They sometimes ask questions about what our team does (the question I get the most is "So do you guys build fighting robots?"). The staff at my school, though, find our team to be quite interesting and love the idea of it all. So I can pretty much say that, overall, my school is quite supported.
