Activity for exponential functions

The continuing story of my flipped classroom, in which I try to make the best possible use of that f2f time:

I spent yesterday working on this activity for tomorrow's Science Math gr 11 class. It's another one that was inspired by Malcom Swan's Improving Learning in Mathematics, and I think it would fall under the category of  "Interpreting Multiple Representations", on page 19.

What I'm really looking forward to is the part where I ask them to reflect on what they learned doing this. I am giving them the option to do so either in private, via this week's checklist: (4th item):

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or on their blogs. I'm hoping to get more blog action this way, but I do plan to share the private reflections, and keep them anonymous. I just want them to know what each other is thinking!

Here's the activity: We're just finishing up with the exponential function, and I wanted to tie up a few loose ends, and give them time to chew on things. For instance, that when something gets doubled every hour, it gets root2'd every half hour. You didn't know that "to root2" was a verb, did you? It means to multiply something by the square root of 2. (In my world it does, anyway.)

I'm going to give them this jumbled up slide of exponential things (I just couldn't think of another noun....) and ask them to sort them by which ones are equivalent. Lots of  "things" here - graphs, function rules, sentences. I plan to put the kids into small groups, then gather them back every few minutes. I'll ask them to use the nifty new highlighter pens in our virtual classroom.

But this is what I'm really getting at. Equivalent situations, ie. that you aren't locked into a base of 2 just because the problem says something doubles. The next sequence of slides is all about getting them to be able to move easily between these equivalent representations, not only from algebra to english, but from algebra to algebra, and english to english.

Here's the full set of slides, with answers. I'm thinking that I will go over the answers to the first jumble, but then let them sleep on the next set. We'll see how it goes. The thing about these types of activities is that they sometimes go in a direction you hadn't thought of. And they as a result end up taking either way less or way more time than you had anticipated. It certainly keeps me on my teaching toes!

Equivalent Exponential Things by amcsquared