Introducing My Thinking Classroom

 I just started my 28th year teaching high school math and I had the best first day(s) ever!  I teach in a block schedule, so last week I had two classes on Thursday and three on Friday.  I am teaching AP Calculus BC and Algebra 1.

In my calculus class, students completed two tasks at the boards.  I modified two lessons from MathMedic. The first was to find an estimate for an instantaneous rate of change based on a free fall by Austrian Felix Baumgartner, starting with a video of his accomplishment.  Instead of completing the entire MathMedic lesson, I had the students use the graph from the lesson to come up with an estimate of his velocity 30 seconds into his freefall.  We discussed how to make the best possible estimate since a rate of change is (generally) over time.

In the second lesson, I used a graph that showed the velocity of a motorcycle over time and asked the students how far the driver (me) travelled.  They were able to determine that they had to find the area under the curve and were able to estimate using geometric shapes.

The two activities were designed to introduce them to differential and integral calculus and we had a discussion of what calculus is all about.

In Algebra, students started with The Tax Collector.  Then we did some housekeeping items and moved into The Answers Are.  Both activities, found in the book, were great!  Students were engaged, getting ideas from other groups and having some great conversations.  We debriefed after both activities.  I asked the students three questions.  First, why did we use dry erase boards and not paper?  Paper just feels too permanent so we all feel better when it's easy to erase things we don't want to keep.  Second, why were the groups created randomly?  Some good conversation here about getting to know others as well as my explanation that it goes beyond the social.  Sometimes our classmates simply understand something better or can explain it better than Mrs. Swift.  The third question was about standing up.  One young lady shouted out "blood flow!"  Awesome!  Yes, standing allows us to move a bit and gets our blood flowing.  That, in turn, means our brains are more engaged and we think better.

All in all, a great first day!