Classroom use of a limited port scan in the wild?
I taught a Cisco networking class for a couple of years and we had to stay off of the district network any time we were doing networking stuff. 

What I did was build a separate network in the middle of my room with old computers. Ran network drops from there to the racks in the back of the room so we could hook into switches, routers, and stuff. 

Once we got to the point where they knew how to program routers over IP instead of wiring directly in I started messing with them. For one of the labs I closed the ports they needed on the router. One student figured it out and started scanning ports on the router to see if I had changed it. I had. 

We spent a lot of time going over the reasons you would want to do certain things like port scanning. When it's the right thing to do and when it's not. I also posted links to several articles about people getting arrested for computer crimes each week. 

Since our network was segregated, we could do pretty much anything we wanted to on it though. A couple of times I setup a web server and had them try and break in. My personal favorite though was having a student put their iPhone on our network and had about 20 computers constantly pinging it. You could watch the battery meter dropping and by the end the phone was seriously hot.