Insert Clever Math Pun Here

I think this is maybe the tenth time I’ve taught trig graphs, and I think I FINALLY like it. Almost. Except for tangent.  But who likes him anyway, amirite?

Here’s what I used to do, and it worked ok. Some years we started with this ferris wheel group work:

 

File link. Except I’m not sure if I ever made the connection well enough between the Ferris wheel and the sine graph the next day, and some years we were short on time, so I would usually just jump into this:File link. Basic plan: know the pattern of sin (0, 1, 0, -1, 0) and cos (1, 0, -1, 0, 1), find the period, divide by four to find the “exciting spots” divide your x-axis as needed, graph the pattern, connect. Repeat.

The nice thing is that the divide period by four, graph exciting spots worked for tangent, too:

File link. And my kids usually did pretty well.  But I had tried a little bit of windowpane graphing in Precal earlier this year and wanted to give it a shot, so I came up with this:

File link. Basically: know the general shape of one cycle, then repeat it.

Things I would like to do differently:

• Have them watch a desmos or gif animation of extending the sine wave past 2 pi.
• Have them extend the cosine graph past 2 pi.  A lot of their cosine graphs looked like UUUUU instead of “gentle rolling hills” no matter how many times we talked about how sine and cosine look the same! Just moved over!
• Spend one day (1/2 day? homework? assignment after quiz?) before this on (non-trig) periodic functions and “picking out the smallest cycle that will give you the whole graph” and “stretch this to be twice as long/three times taller/moved to the left”  Also maybe patty paper?

BUT!  The thing that was definitely on the verge of something great was, don’t give them the equations to start with.

“Hey kids, I know you’ve never seen a periodic function before or had to deal with a b value stretching or shrinking horizontally, and we’re going to measure in radians because that’s normal and you love fractions, and now find all this crap from a weird looking equation…why are you all looking at me in terror?”

So the back of the first day was this:

And ok, some of them still looked at me in terror. I think this is where the patty paper would help tracing one pattern. And I ended up switching the order and graphing 7-12 first, which helped a lot.

Then the next day was a breeeeeeeeze with equations!

File link. The next day was *slightly* less of a breeze.  Patty paper would also help-many students have trouble with moving the period with the origin.  As in, if you move back to -pi/2, they would still have the period end at 2pi, not 3pi/2.

File link

We then spent the rest of the day and the next practicing. I was down with some pretty big allergies, so instead of walking around, I had them come to me, which was a bit fairer than usual (didn’t get stuck at one table), but also a few kids never came up to get checked, so I still need a system where everyone can get checked equally.

Then I did something foolish.  It’s AP testing season and state tournament season and hey-why-don’t-you-just-take-a-day-off season, so I should have ended there and done another practice day with one of my favorite worksheets:

File link.   Or maybe done a day with biorhythms or some such, but instead I decided to be completionist and talk about tangent.  Where the window pane graphing doesn’t really work as well.  And all the wheels fell off…

File link.  Just no.  Especially no need to phase shift tangent, goodness, what was I thinking?  And yes, DEFINITELY need patty paper on this.  Not sure how to make it better/easier to understand.  The students were having trouble placing asymptotes at the end of the period instead of the middle or vice versa (making the period end where the asymptote should be).

But anyway, except for tangent, most of the grades were pretty good on the test.  They even did pretty well writing equations, which is always tricky.  And maybe they’ll remember it a little bit better next year in Precal?  At the very least, they can tell me the shape of each, which is what the AP teacher says they need to know.

My Thing

My thing this week is British Dramas That Are Not Downton Abbey. Have you tried Call the Midwife? Gracepoint? Broadchurch? Orphan Black? If not, you’re missing out on some fine, fine television. All of them are shows that never get backed up on our DVR because both my husband and I want to watch them RIGHT NOW PLEASE.  Midwife and Gracepoint are both great period pieces, in about the same time frame (vaguely after World War II). Broadchurch was a great police procedural the first season and a great courtroom drama the second season. And Orphan Black is totally modern with 5 clones played by the same actress (#TeamAllison). Who cloned them? Why did they clone them? Why is somebody after them? So many questions!  Go check any of these shows out if you’re looking for some summer binge watching!  Or let me know that you like them so we can bond!