We can use the past to precede a date in the future if the decision or consideration of a potential activity took place in the past.
For example, someone asks me if I'm free to go to the cinema tomorrow. I look in my diary but there's nothing in there. However, I feel sure that I had arranged something. As I'm looking in my diary, I might say:
"I'm just looking at my diary for tomorrow. That's strange, it's empty. That doesn't seem right. What was I supposed to be doing tomorrow?"
However, before I open my diary I might say:
"I'm going to look in my diary to see what I am supposed to be doing tomorrow."
With the statement about the classroom teacher, the connotation can be that he says "What were we supposed to do today?", the children say "Shakespeare!" and he says "Well, I've changed my mind. We were going to do Shakespeare but actually we're going to do Chaucer". Later in the day, a colleague asks him about his morning class. The teacher can say "We were supposed to be doing Shakespeare but I'm a bit bored with that so I did Chaucer with them instead."
The problem I'm having with explaining this is that not everyone would say "What were we supposed to do ...", some would say "What are we supposed to do ..." As with all spoken English, there's a lot of personal choice and a lot of things can be said which don't follow any particular grammatical rule but make complete sense nonetheless.