How to gauge someone's chess strength quickly? I plan on teaching a chess class (5 classes in a sequence, each building off the previous, 1 hour each) to high schoolers, with emphasis on applying chess principles to real life. Now, it'll be unproductive to have players of maybe &lt;1200-1300 strength, since they won't quite understand positional and tactical ideas well, and will likely find the class advanced/unproductive. 

Given the short time frame, I'd like to somehow assess their playing strength at the beginning of the first class in as short amount of time as possible, so as to make the rest of the sessions most productive for the rest. Any suggestions?

I thought of tactical puzzles, and someone suggested multiple choice format for guess the move, but both will require a good 10 minutes for the students to have a good chance at getting them right.
Perhaps show them positions and ask them to assess them and analyze the various salient features (i.e., king safety, piece mobility, central control, weak squares/color complexes, etc.). Naturally, novice players likely won't be able to formulate a cogent response, but if you're looking to identify at least reasonably strong/experienced players, then I would imagine that kind of approach would be more efficient than presenting them with tactical puzzles.

Tactical puzzles are also slightly scattershot; a strong player can occasionally overlook a tactic, but classic positional motifs are typically readily apparent (as long as the positions you select aren't either overly subtle or purely tactical in nature). I wouldn't expect them to formulate concrete positional plans on the spot and in a short amount of time, but I think the mere ability to identify positional imbalances is a sufficient indicator of some chess skill.

I think you could present a few tactical puzzles as well, as long as they comprise common motifs and don't require overly long combinations. Puzzles that would take ten minutes strikes me as excessive. As an indicator of playing strength, the (in)ability to solve a few fairly simple puzzles in a short amount of time would be relatively conclusive. If the puzzles are short, you can also administer more of them, which is apt to yield more accurate data than the results from a smaller number of more complex puzzles that each require deep thought.