Wednesday, October 7, 2015

Average Velocity vs Instantaneous Velocity

In Calculus, I wanted to start my unit on Derivatives by getting the students to conceptualize the limit definition of the derivative.  I decided to use an idea from @ThinkThankThunk that he blogged about here.  Now, I didn't start by doing this on day 1, but I really liked the idea of somehow demonstrating the difference between average and instantaneous velocity.

Day 1 & 2:  I went outside and we had one of the students run/walk/jog at varying speeds for 200 ft.  I timed her first for the 200 ft, then every, 50 ft, then every 25 ft.  We discussed the difference between average and instantaneous velocity and how we could go about determining instantaneous velocity.



Day 3, 4, & 5:  We used the CBR2 to do a ball bounce activity to help develop the limit definition of the derivative.  Handouts are here, here (Activities 1.3, 1.8, and 1.9), and here. And a little Desmos demo thrown in.


Overall, I felt like the lesson went well.  Yes, it took quite a few days, but the understanding of what a derivative is, what it is measuring, and how it measures that will be invaluable as we move on to more difficult topics.  

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