One of the things I find challenging to balance is convincing kids of mathematical truths without overwhelming them. Sometimes, I know, there is a time and a place for a bit of hand-waving. And, sometimes, I know, there is a time and a place for formal proofs.[1] But I think most of the time the sweet spot is somewhere in between a formal proof and "this is how it is--just memorize these rules."

In search of that happy medium, I created decks of 12 cards (6 with the graphs of the basic trig functions {orange} and 6 with the graphs of their derivatives {blue}). I had students match them up with a partner.

Matching a function to its derivative using only graphs is new for my kids, so I knew this would be a challenge if I didn't lead them quite a bit. However, gathering data from a graph is so heavily tested on the AP exam that I figured it wouldn't hurt to start making some connections.

After they matched them up, I followed up with these questions:

Here are the cards I made, if you're interested (thanks, Desmos!).

6 basic trig functions (enough for 16 decks):

6 derivatives (enough for 16 decks):

[1] Although I'm beginning to think I show proofs more for myself than my kids.

My calculus course being at college, I suppose it makes sense I prove more with them. I made a 4-page handout proving that derivative of sine is cosine. They fought their way through that jungle admirably well.

ReplyDeleteI like these cards. I want to use them. Maybe on Thursday we can use this as a review activity for the upcoming test.

Definitely...when I taught calc at the community college I proved substantially more...but I'm still not certain how many of the students really followed. I remember reading your handout for the derivative of sine and thought it was awesome. I should use it as a follow up--especially for my more advanced kids.

DeleteJust as a warning--I included the the equations on the bottom of the cards, which would probably be a dead give away if your students already know their derivative formulas...so you may want to chop that part off the cards. :) Let me know how it goes!

Maybe I'll make my own - as a handout. It should take under an hour.

DeleteIt took about an hour. I'm not happy with the quality yet, but I'm using it as-is for now. I used desmos to draw the graphs (struggled to get the right labels on the x-axis), and jing to save them. I can email you my handout if you want, but your stuff is nicer.

DeletePlease send it my way when you get a chance! My email is rebecka dot peterson at gmail

DeleteI have always sworn by flash cards for so many different subjects, but I have never tried them with something like a graph on them. It may take a bit of effort to prepare, but I can see how useful that would be, if for nothing else than purely quicker recognition. And that in itself is useful when it comes to testing!

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