For a reasonable sum you can order multi-sided dice from various online sites.  Try Amazon.com for example.
Or you can look in the game section of thrift stores.
You can buy dice with various numbers of sides depending on how large your class is.

12-sided
14-sided
16-sided
20-sided
24-sided
30-sided
34-sided
There is even a 100-sided die that I hope you will never have to use in an ASL class.

I recommend you keep a couple sizes in your teaching bag.
Then you can assign students each a letter or number corresponding to a side of your die and use a roll of the die to choose your next victim, ...er, I mean participant.