Precal Files: Dude, I told you I love Trig.

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tl;dr: Notetakermakers, homework, and study guides for trig sum/difference/double/half angles, trig identities, and solving trig equations.  Part of my ongoing series of posting all of my files; see more and FAQs on this page.  Plus I tell you about an awesome book at the end!

Yes, I love trig. I love that I there’s always new ways to think about and teach it. I love that it’s so elegant. And I love that it’s one of those topics that looks scary and is scary and new but eventually most kids get it and feel so smart about it.

Now, check out the middle box of the “three fraction hints” above. If it’s the first time you’ve seen this multiply-by-the-common-denominator-of-the-small-denominators, then be sure to read this post about it.  It’s totally awesome and is so handy in Precal and Calculus!

Now, don’t worry, we don’t do all of those in identities in one day!  We do the first six together:

This is also the first time I talk about Q.E.D and I tell them they could use any symbol to show “YES! I DID IT!” such as a check, smiley face, corgi, or unicorn.

Then I have them work on the rest of the first column for homework with the rule: if you’ve been on a problem for more than 5 minutes without getting anywhere, stop and move on. Since I teach honors, I know some of them would get trapped in a problem for 20 minutes and then just get frustrated with the whole thing. Then we work on the others in class on group whiteboards for a day, and finish them up whenever we have a few minutes throughout the week.

Another reason I like trig is because there’s ACTING! involved. Sure, you could just show the powerpoint of Sinbad and Cosette when you teach the sum and difference formulas. But why tell it, when you can get four chairs at the front of the room, make some nametags (write the names really big, put them in page protectors, then tie some string through the holes of the page protector), and then act out the whole thing with 3 volunteers?  I even bring in a tie and a scarf for when I’m playing each driver. And yes, as Cosette, I wear sunglasses so I can do this move:

and say, “we do not have the same sign.”  Although, confession: I have no idea how the story is supposed to help memorize the tangent sum/difference formula–please let me in on the secret if you know it!  Another confession: Crazy Stupid Love is one of my favorite movies of all time.

FOCUS!  Back to sum and difference:

File here. We also decided this year not to do the problems like 7 and 8 so I will allow you to skip those as well.  You’re welcome.

File here.  If you do skip 7 and 8, also skip 12, 13, 18-20 on the homework.

Some double/half angles:

File here. Fun tip: have them derive the double angle formula of sin and cos from the sum formulas and then everybody gets to feel smart.

File here.  Now’s a good time to consolidate all our knowledge:

File here.  (omit #19 if you’ve been omitting stuff) And then begin solving trig equations!

Check out that awesomeness about sin 2x having twice as many answers, but 1/2x could have the same number of answers or even no answers between 0 and 2pi.

Yeah, I was really clip-art happy when I was making all these.

File here.

And then some quadratic and mixed equations!

Cute and cuddly, boys, cute and cuddly….

File here.

It’s only one section, but worthy of its own study guide and test.

File here.  There’s even a couple showme videos for the study guide: #1-9 and #10-16

My Thing

My thing this week is Simon vs. The Homo Sapiens Agenda. I read about 50 pages of it the night before last, then spent all afternoon yesterday finishing it because I HAD TO KNOW WHAT WAS GOING TO HAPPEN TELL ME TELL ME TELL ME.  And it’s obvious that the author works with teenagers because the dialogue is spot-on.  And they’re normal teenagers doing normal teenager-y things which is a rarity in YA. And it’s just a nice pleasant story where no one dies, not even the dog. 🙂

Sunday Summary

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3 things to share

1. Man, don’t you hate it when you figure out a better way to teach something the day after you teach it?  Although trig equations went pretty well this year (well, we’ll see tomorrow on their quiz), I think next year I will structure it differently. Here’s where we started:

Next year, I’m going to start at the end with the calculator/desmos, with a -4π to 4π window to discuss the general form.  Then do some examples with θ between 0 and 2π, then non-calculator examples.  Then on day 2, graph 2θ (or θ/2) on the same graph to discuss getting more/less answers.  If you’d like to modify this for me (doesn’t hurt to ask, right?), or if you want to use it as is, here is the .doc file (with bonus homework at the bottom!)

2. Now, day 2’s note-taker-maker, I’m kind of in love with. (ok, technically this was day 3 because I ended up teaching day 1 slowly)

The only thing I might change is super-reinforcing the ZERO product property rule is not the “ZERO or sometimes 2 or 3 or -7 product property rule” because some of my students are still having issues with that. (btw, Snoops is dancing because it’s already factored.  Also, it is super fun to have a kid ask later, “How can we solve this?” and you reply, “Cute and cuddly, boys!”  File link.

3. I finally figured out about 3 years ago how to make linear programming less painful…get the mechanics of it out the way first!

Let them spend a day finding the feasible region, vertices, and max/mins.  Then the next day you can focus on the finding the equations from those long scary problems and the rest is the same as these notes.  Much less stress than trying to introduce all of it the same day.  File here.

2 good books I’ve been reading

We took a quick weekend trip to Chattanooga last week where I started David Benioff’s City of Thieves and could not put it down!  It’s like a buddy cop movie set in the absurdity of World War II.  It reminded me of Anthony Marra’s Constellation of Vital Phenomona, one of my favorite books of the last few years.

Hector Tobar’s Deep Down Dark is the reason I haven’t gotten anything done today!  How did he make this so compelling when I already know the outcome?  I’m about to go draw a bath and try to finish it tonight; it’s such a page turner!  And don’t worry, he does a really good job making sure the reader doesn’t get lost with all the people in the story (I’m horrible at remembering names in both book and real life.)

1 thing I’m meh about

I have to write a unit plan about complex, polar, and parametrics using some premade lessons (and adding others as I see fit). The premade lessons are really expecting a lot from our students and I’m not sure if I will get the outcomes desired by using them (unless the desired outcomes are tears and frustration).  But I’m having trouble finding a lot of great stuff that I can easily replace them with (I have a few things thanks to @mrdardy and @crstn85).  So if you have some cool stuff to share, please do so!  The state of Alabama will thank you!