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|