Tuesday, February 11, 2014

Analyzing Exponential and Logarithmic Graphs

As I was looking ahead in my unit of exponentials and logs in Algebra II, I opened up a lesson plan whose first page read, "Note to self: This lesson sucked. Kids were totally bored."

Must have written that a year ago and forgotten...until now.

This is a topic that I teach in PreCalc also, so I was motivated to change this boring lesson.  But worse than being boring, my lesson honestly did not have kids exploring interesting mathematics.

What I really wanted was for kids to understand the inverse relationship between exponential and logarithmic functions before we talked about solving equations.  I wanted them to start to understand what happens graphically before we explored the analytic implications.

So, I made this matching activity.  I really broke it down for my Algebra II kids, but I think PreCalc students (or advanced Algebra II students) could dive right into it with little to no instruction on the teacher's part.  I limited the transformations of the graphs to shifts only, but, for more advanced students, it could be nice to show reflections also (though I might stay away from stretches/shrinks...).

I had my Algebra II students work ONLY with the exponential graphs first.  They shared a deck of cards with a partner, but each student was to fill in his/her own chart. Once they were done with that side, I had them figure out which log graph was the correct inverse for each exponential graph.  Lastly, I had them analyze the log graphs.

The activity is designed so that students can see the similarities/differences of exponential and log functions, beyond just "x's and y's switch."  Ok, so they switch...what does that mean?  If I have an exponential graph that shifted to the right 2 units, which direction will its inverse graph shift?  Why?

I think this was a considerably more interesting way to get kids more comfortable with log graphs.  And they were definitely noticing the types of patterns I was hoping they'd notice.  The nice thing is that since a lot of the patterns are obvious, kids can quickly check their own work for errors once you've had a discussion as a class about all the similarities that should occur in their charts.

Chart to record results (and key):

Deck of cards (6 exponential functions and their corresponding logarithmic inverses)--thanks as always, Desmos!:

A couple of the matches