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Intermediate Value Theorem

posted Jul 30, 2013, 7:54 AM by Kathryn Behling
Sometimes, it seems like AP Calculus is just theorem after theorem after theorem.  My students have some trouble keeping all of them separated in their mind.  They particularly had trouble with the Intermediate Value Theorem.  One day, I figured out the perfect way to explain it.  I stood on one side of the classroom and then told my students to close their eyes.  I quietly moved to the other side of the classroom and told them to open their eyes.  I told them I had done a magic trick and appeared on the other side of my classroom.  They all adamantly deny that I had done a magic trick.  So I ask them what they know I had to cross in front.  They then start listing things left and right that I had to pass to make it to the other side of the classroom.  I make them justify everything until one student finally says, "Well, we know you can't disappear and we know you can't fly!"  Exactly!!  We then talk about what it means for a function to be continuous - it can't "disappear" and it can't "fly".  

If anything, my students always remembered that it was the theorem where I did my magic trick!!