Your omni mic idea might work better if you seat the students in anc arc rather than a straight line. If they are equidistant from the mic each will sound about the same (assuming they all speak at the same relative level). Using 2 mics might be better. You still might need a mixer to optrimize performance. It’s also possible the omnis will pick up your voice as well.
You are correct in thinking a shotgun will have a tight pattern. These patterns vary among different mics. Also, good ones are expensive.
Is there an av dept. in the school? It’s possible they’ll have some equipment you can use.
John
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