There are a lot of times in Calculus where stuff that you want to be true is (like the limit of a sum is the sum of the limits) but then there are a lot of other times where sadly your intuition just doesn’t work (like the derivative of a product is NOT the product of the derivatives). This is a random little thing, but I’ve been doing “Wannabe Math” in thought bubbles on the board to distinguish between rules we know that work and ones that we don’t know are solid:

I want to encourage students to try things (so encourage them to use their intuition to explore) but give them tools to be able to test to see if they are correct. I did this for the product/quotient rules and then used it to derive the chain rule with the class – with the Wannabe Math on one side and the actual math on one side, we could easily see what was “missing” and come up with the whole derivative of the inside part of the rule.