Last week I had an idea about how I could introduce average value in calculus next year. When I've taught average value in the past, I felt like students just memorized a two-step procedure and several didn't see the connection to the definition of average that they've been using for years. I know I won't be teaching this concept until...mmm...December?...but when you get excited about a lesson/idea, you just gotta follow through with it, right?
What I like about this little packet:
- It starts with an application to motivate the discussion and the why should we study this?
- It recalls previous knowledge.
- It applies the fundamental 3-step process of all calculus topics: (1) Start with a non-calculus idea, (2) apply a limit, (3) arrive at the calculus concept.
- It lets students practice a FRQ from a previous exam, but forces them to search through the problems to find which one would require their new tool.
- Students discover a main idea of calculus using what they already know, each other, and the text (not me).