I agree with runs-with-dogs! ALL of you should have the opportunity to eat at a sensible lunchtime! If you're not going to eat at lunch or as soon as school finishes, then at least eat something proper at morning break - sandwiches and some fruit.
I wouldn't advise the 7-8 bagels a day option - that's basically like eating a loaf of bread - but some sandwiches and fruit at least. I would also experiment with things that you CAN eat straight after school. Sandwiches might be out - possibly depending on the filling - but can try a slice of malt loaf, some rice cakes etc...
Agree to more protein, and also think you should eat more/more substantial breakfast if you are only going to graze - add some toast to the cereals, or switch cereal to porridge.
Also, are you one of the overworked teachers who suppliments their diet with endless cups of coffee?
You're basically going from 5am until 8.30 without eating properly.