# Day 17 – iPhone Prices and the Intermediate Value Theorem

I am so thankful we are almost done talking about limits in AP Calc. Not my favorite subject. I introduced the Intermediate Value Theorem today by showing them a video of a speedometer with a chunk from the middle cut out. I asked them “What speed must we have gone in during the cutout part, and then what’s a speed that we could have gone but are not sure?” Then I showed them the iPhone prices from two years apart and asked a similar question, “What price must the iPhone have had during that time and what’s a price it could have had but you aren’t sure?” We talked about why these two situations are different and how it relates to continuity. I love introducing new concepts with problems like this, as I feel it gives them a conceptual hook to connect the crazy notation to.

Then we broke up and worked on Whiteboarding problems having to do with the Intermediate Value Theorem. For some students it was a struggle to realize why we do this because the ideas are common sense, but I tried to express how we need to formalize logical things into a mathematical language that we can all understand.

One student drew this picture of me today. My AP class can be a bit behavior-ly challenged, so I made them take an oath that they would remain focused during group work so I wouldn’t go crazy. I think this is a picture of me crazy?