Are you teaching in German or in English?
One of the problems is that historically, aktionsart simply meant aspect. The two terms are virtually interchangeable in the old grammars. And to that extent, its less helpful to use them both in the classroom. In terms of the modern distinction, the easiest way to show it would be to do something like this:
I go/went (perfective) vs. I am/was going (imperfective)
take (non-telic) vs. take off (telic)
bring vs. bring up
follow vs. follow up
knock vs. knock down
If you're teaching in German, it shouldn't be hard to find parallel examples. Using prepositions/adverbs in conjunction with other verbs is quite common for Indo-European languages.
ἔρχομαι (imperfective) vs. ἦλθον (perfective)
ἔρχομαι (non-telic) vs. εἰσέρχομαι (telic)
ἦλθον vs. εἰσῆλθον
Of course, Aktionsart gets far more complicated than this. In Linguistic jargon: the English non-telics are all Activities (knock is probably better labeled a semelfactive). The English telics above are all causative accomplishments. But for simply showing the distinction between the two, this is basically it.
Here's a professor at Simon Fraser University in Canada's summary of aktionsart (a lot of more recent linguistic work prefers to use the term "event classes" or "predicate classes": Event Classes
Note: in undergraduate linguistics programs this stuff normally isn't touched on until the third or fourth year.