Continuity has been the topic of discussion the past week. Even though my kids learn about the Intermediate Value Theorem in PreCalculus, I wanted them to be able to do more with it than just find a couple of y-values. They could have done that in Algebra 1. Let's get to some more interesting questions. So, we worked through a version of these questions. They hated it. I loved it. I will use it again, no doubt.
The next day, I showed them this slide. Again, it's nothing you can't find elsewhere, but the kids were amazingly into it.
I had the students discuss the questions with their partner before I took a class poll (thumbs up/down). I would ask a thumbs down student to defend his position, and then a thumbs up student to defend hers. The kids got into a couple debates, which made me super super happy. I love it when they argue about math because then I know they're invested in the problem and they're using higher levels of critical thinking.
The most interesting one for us (I think) was the population of the earth. The fascinating part was that even the students who said it was not everywhere continuous did not come up with the correct reasoning (or, at least the vocal ones didn't). So, that one's a keeper for future years.
Anyway. Some seriously good results here.