IF you're cutting the strips at class the traditional way, you'll want the fabric folded so you can easily and accurately cut it there. Fold selvage to selvage - in half and then in half again. You'll end up with 3 creases in the strips you cut. You can either press them out easily or sew with creases.
Check with the instructor to see if she wants the fabric pieces pressed wide open...but I can't imagine she does.
I'd probably gently fold the lengths of fabric at the last minute and place them on top of everything else I'm bringing. A few gently wrinkles won't hurt anything....and I'll bet there's going to be an iron or two there!
Remember to post pictures!
Nan - Indiana