Category Archives: trig

End of 3rd Quarter

Hi everyone.

It’s the end of 3rd quarter, and we’ve got a grading day. Actually half-day. So I thought I should blog since I got the time! No kids! It’s some sort of miracle. I’m fortunate at my school to have a prep period and a department planning period… but during my prep, I can expect to supervise 8 to 10 up-to-no-good-but-so-lovable seniors. Up-to-no-good is definitely putting a positive spin on it. During my plan period, I can expect to supervise two or three accelerated freshmen for whom school comes easy and are mostly bored with it, and two or three sophomores who care, but need me to give them 1-1 tutoring in Geometry.

In short, having some time to myself in my classroom is some sort of miracle. It never happens. Now if only I had something interesting and substantial to blog about.

The kids are the best part of the job though. Forget grading, planning, and prepping. I do what I do because I believe in those little punks. They’re beautiful, lovely, funny, and smart. They deserve the best.

OK, here’s something worth blogging about. I just taught right triangle trigonometry to my Geometry kiddos. I love introducing trig. This year it conveniently followed a similarity unit, so I introduced it with a quick lab measuring sides of triangles and computing SOHCAHTOA ratios. Huh, weird, for any 30 degree angle in a right triangle, the ratio of the opposite side and the hypotenuse is the same. Huh, weird. (Similar triangles, anyone?)

Then we do some boring, but straightforward practice. Then the next class we go on a field trip. I love to advertise this next bit as a field trip, even though we only go down two floors to the Commons.

I start by having them estimate the height of the ceiling in the Commons (we regularly do Estimation180 in Geometry). Then I have them take out their telly-phones and download a free clinometer app. The only issue is the kids who say, “but I don’t have any room on my phone”. Maybe if you deleted some of those dang selfies, kid.

I crappily, but enthusiastically, model what they’re supposed to do. (My teaching career is a work in progress, OK? Year two is better than year one, at least.) I pass out the awesome, giant tape measures that the math department owns. We disperse down to the Commons. Chaos ensues, naturally, but we’re on a field trip in math class, so it’s a good thing. Tape measures are being stretched out, kids are pointing their phones at the ceiling, and most kids are sketching a triangle and writing down some sort of trigonometric equation. It’s my favorite day of the year.

Eventually we return to the classroom. My least-focused kid (one of those with an ADHD star next to his name in Infinite Campus) happily sits down and gets to work solving trig equations. How could he not? I just let him run around the Commons for 10 minutes.

They’re beautiful creatures, ya feel?

IMG_1956

8.4 trig lab

8.5 trig invest how high is ceiling (I think this was adapted from something from Tina Cardone @ drawingonmath ??? Not sure. But I definitely stand on the shoulders of giants. Thank you all.)

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Filed under fun, Geometry, grading, trig

Why Do We Memorize the Unit Circle?

Let me preface this blog post by saying I teach a “lower-track” Alg 2/Trig class. (The school tries to spin it as “we have many options for math classes, blah, blah, blah, so that students can be successful”, which is great, but it’s also silly not to call it what it is.) Almost all of my students are seniors, and the average student is going to a 2-year college. Some will go to a 4-year college. They’ve got a lot of potential, but they’re not particularly motivated by academics.

So keep in mind I’m thinking of my students, not a group of juniors in Pre-Calculus who will take Calculus AB next year; however I think the following question applies to those students as well.

Why do we make students memorize the unit circle?

Isn’t it more important to understand what the unit circle is? Memorizing a few selected values didn’t help with conceptual knowledge of the unit circle, and I ultimately felt like I was making them memorize it simply because I could. And then I could give them a quiz. I almost feel dirty about it because instead of making sure they actually know what the unit circle is and why it works, I had them memorize a bunch of numbers.

I love trig and love teaching trig, but I’m not sure memorizing the unit circle is helping any of my students actually learn trig.

Any feedback is appreciated! Thanks!

 

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Filed under FST / Algebra 2, trig