If your instructor expects you to use opamps, then use them as comparators.
Following is a circuit which uses comparators to do what what you want, but you could just as easily substitute opamps.
I'll post it now so you can study it, and I'll add a circuit description sometime later today if I can get to it.
in the meantime, here's an LTspice .asc file you can use to simulate the circuit if you want to play around with it
