As a southern hemisphere school we have just had our mock exams, so I thought about way to return them for the biggest impact. I put the question to twitter and got some great responses (given that it was the summer holiday for UK teachers).
At lunch today, a colleague and I were talking about Trig, and one thing that came up in conversation was that if a+b=90 then sin(a)=cos(b). Not that this was something that we did not know, but it certainly was a case of the curse of knowledge as neither of us could think of a time we actually taught this to our students. We both felt this was a useful thing to explicitly teach them.
I had a good lesson (as far as it can be judged at the time) with my IB Higher Level class this week where we started implicit differentiation.