Last year I did this, and afterward wrote about how it didn't have the impact I had hoped for. So immediately after that class, one year ago, I created another series of slides, thinking, this is what I'll do next time. I did it this week, and it did exactly what I had hoped for, at least for some kids.
A little background:
Kids often make the mistake of thinking that if something is doubled every hour, then it's multiplied by half of 2 every half hour. I can easily show them the faulty logic of that, but I'd rather not teach by telling them no, you're wrong, I'd much rather get them intuitively to the right place, so they can see that every half hour, it gets multiplied by root 2. The discussion about why two exponential functions are equivalent algebraically is different from the one about why they're equivalent realistically. Both are worthwhile, just different. Up till now, I feel like I've only ever dealt with the algebraic part with my students.
So here it is, my second time at bat with this lesson. I uploaded the pdf to slideshare so that it wouldn't mess up any of the formatting, but you're welcome to the editable ppt and the notes underneath this slideshow:
I also gave them a ggb that dealt with the algebraic equivalence better than I ever could by blathering on. Here are all the downloadable and editable versions if you'd like to use and tweak anything:
Slides with answers
Notes version for students
This week, I'll try another version of the equivalent exponential THINGS activity from last year, and see how it goes. It's got not only situations, but also graphs and rules. Here goes nothing!
Feedback hysterically welcome.