Ugh ... that's one of my pet peeves too.

I get paid to write, but I make mistakes that look like that - the wrong versions of words - pretty often. I catch most of them. I type definitely when I mean definite, etc. There's a disconnect between thinking and typing and seeing. I type too fast. Proofing is vital for me.

Even if the teacher had written, "You are to explain to Bill ..." it would still be a bad sentence. "You are" is superfluous. The sentence is passive and effete.

Bill is overweight and wants to lose 40 pounds. Explain nutrition to Bill with this goal in mind.

So when did they become the Browns?

That jumped out of the page at me.

Now then, the problem really is do you criticise the teacher in front of the student?