Neil Sinhababu (aka the Ethical Werewolf) lays out one approach to making an impression in a job interview teaching demo:
Before giving my job talk, N[ational] U[niversity of] S[ingapore] had me give an hour-long presentation to the graduate students and advanced undergraduates to prepare them for the talk and also evaluate my teaching abilities. Since my talk was on the Humean theory of motivation, I taught them about the puzzle involving cognitivism, internalism, and the Humean theory — if you accept all three, you end up having to say that humans can’t make moral judgments, so you’d better deny at least one of the three. I’d planned the talk to include about 20 minutes of student questions, but a third of the way through, the students hadn’t asked me anything.
So I looked at them and tried a trick that I had spontaneously come up with in the previous session of the lecture I’ve been teaching at Texas. I said, “If someone asks a question, and it’s a good question, I’m going to dance.” Amid lots of giggling, a brave young man raised his hand and asked a question — I’ve forgotten what it was now, but it was good, and the students laughed again when they saw me dancing. After that, good questions flowed freely. When students see that their teacher is willing to do comical and mildly embarrassing things to reward student participation, they get the idea that class really is a place where they’re suppose to participate.
I wondered at the time what the NUS faculty evaluating me thought of that stunt. They didn’t express emotion in any obvious way, and it seemed kind of high-risk, high-reward — would I look like a dynamic, exciting teacher, or a maniac?