If you read enough teacher sites, you might get the impression that anyone who has one creates a magical experience during any lesson they teach. It's like Pinterest guilt or something. But, this is not true. I screw up, all the time. Just a couple days ago something I thought that would be great blew up in my face within 15 minutes of handing it out. How you adapt to failure of this kind is usually a quick way to know how long someone has been in the business. My first year of teaching, we'd be talking Level 5 FREAKOUT. Is this why some people use a worksheet for 10 years? Maybe.

### Good Intentions

Because I get bored easily, I have been toying with the curriculum. I have this harmonics lesson I added last year, but wanted to set it up with some talk about trigonometric transformations. And with Desmos, it should be easier than ever, right? I generated a bunch of random sine waves and altered them in different ways, the intention being to give the students the pictures and have them poke around until they could come up with a sin x AND cos x function that would reproduce the picture.

I thought it was pretty straight forward. I did a demonstration, trying to model the thought process about how to address things like amplitude, vertical translations, etc. I passed out iPads and set them loose. Everyone figured out A. Then they ran into C and the whole process ground to a halt. Classic kid move. This is hard, me stop now.

Why? Well, C is the first one with a modified period. It's possible in setting up the activity I failed to mention this as a possibility (I definitely didn't demo it). Also, in true math fashion, for whatever reason, no matter how good a student is at determining the period with the equation present, they have their own Level 5 FREAKOUT trying to read it off a picture. Or never think it's something you could even do. Remembering that for next year.

### Intervention

After about 20 minutes I took the temperature of the room. Again, A wasn't a problem, but beyond that was a crapshoot. Around 10 were able to determine several of them. But not the kind of percentage I want. So quickly, after a little lecture about giving up at the first sign of trouble, we concluded the lesson together. I made up a sine function (leaving the equation visible), and they had to determine the cosine version. We discussed what properties are the same, what's different, and how to source values for horizontal transitions (most had ignored my hint about unit circle values).

This also helped to show that there isn't a single right answer. It also gave me my warm up tasks for the next groups. You know, right after I readied a new batch of functions in 6 minutes...

### Pay No Attention to the Graphs Behind the Curtain

I figured it was the period changes that were screwing this up, in addition to the short introduction. I drew up four new functions (reason 347 you need a printer in your room):

This time, no period changes. And I started each successive class with the activity I used to save the sanity of the kids in my first class. I created a sine wave, they fiddled with finding the cosine wave. We discussed what should be different. We discussed how to determine amplitude, how to determine a vertical translation, and in more explicit terms what works for horizontal translations.

Greater success this time. Everyone got at least two of them, and a significant percentage were able to get three. Given more time they'd probably get them all. Lots of interesting things this highlighted: the difficulty of open-ended tasks, the evidence that students are incredibly far from being experts, and how bad students are at reversing information (deciphering the period changes).

I'm going to keep the original batch of functions. I can make it succeed next year. Plus, I laminated them and stuff.

On the whole, this is a great activity. I would recommend it. Despite the audible, it turned transformations into a puzzle and there was genuine excitement from students as they solved them. Far better than a lot of scripted drawing.