The reason you need this post is because Math Teacher Mambo has unlocked the secret to teaching radians so kids will understand. YES IT IS TRUE. She posted this fabulous idea on cutting out radian pieces to use, like this:

How can I describe using them in class? Well…

Exhibit A: After two days of working with both, I informally polled all three classes about whether they prefer radians or degrees. At least 25 – 50% raised their hands for radians, and many of them said it didn’t matter to them. That’s right, a class where *kids prefer or at least do not actively dislike radians.*

Exhibit B: In one of my classes, after the poll, I told them I was so excited because this was a new way of teaching it and it actually worked. One of the students asked, “so how in the world did you teach it before?” “We just thought about it.” Their reaction:

Exhibit C: After that reaction, another student said that they were great to start with, but then after a while *they didn’t even need them. *Woohoo!

Since I use NoteTakerMakers® instead of INB, I modified my NTM from last year to accommodate Shireen’s circle files:

We started with degrees. By “bow-tie triangle” I mean reference angle (we had done trig values at a point the day before and practiced drawing our bowtie) and by “type” I tell them short, medium, or tall. We did the first five together and then I sent them on their way. Yes, with greater than 360 and negative angles, which was great because everyone had a different way of thinking about where they were.

Ok, just so I’m not kicked out of the #MTBoS, I would *love* to do a radians activity where we discover what they are, and that one radian is the same for every circle, and it takes 2pi of them to go around, lalala discovery learning, but I have 13 class periods to go from 0 to translating sine and cosine graphs, so I showed them a quick animation from Sam and pi, 2pi, pi/2 and 3pi/2 using Math Teacher Mambo’s empinadas analogy. (except with quesadillas because our Moe’s actually asks if you want them cut in half or fourths). We had just enough time at the end of class to cut out radians out, label them, and put them in a pocket (hint: Give each student a third of a piece of paper. Fold strip into thirds. Tape two sides and you got a pocket with flap. You can even tape it down to the NTM between the two circles, but it does over lap the chart a bit. I could probably make it pretty so it doesn’t, but I didn’t.)

The next day we talked about the radian examples at the bottom of the NTM. After the examples I asked them about what type of triangle we will have with denominator 6, 4, 3, and 2. I think next year, I’ll have them cut out the pieces like this:

Because lining up 7 or 11(!) of the wedges was time consuming and easy to land on the wrong space. Plus hopefully this might help them think, “is this more than a whole quesadila?” when they are deciding which pieces to use.

After the examples, I let them loose on this page:

I stamped the first five and ten as they were working to make sure they were on the right track. They didn’t even balk at the last few that were greater than 2pi!

Warning: the rest of the post is less essential than those radian cut-outs. 🙂

The next day was the big intro to the unit circle. I’ve moved away from “these are the coordinates, let’s memorize the unit circle and draw it on everything really quickly” because I realized when I started teaching precal we need to know sin 5pi/6 *without* having to draw the whole thing. So instead we talked about short/medium/tall triangles and just remembering 3 numbers: 1, 2, 3 and which one is short/medium/tall (or skinny/wide). I have them draw the triangle for each question. I think maybe I should also have them highlight the part we care about? Or now I’m thinking (and I’m going to try this tomorrow with reciprocal functions) of sacrificing one of our wedges and making it a triangle we can label and move around. I’ll report back.

Doc file and extra practice file

We spent the next day practicing and me stamping off correct answers, which I need to find an equitable way to do. I normally go around the room and stamp, but I always seem to miss tables. I need one of those numbered ticket things like at the butcher or Joann’s. Anyone have any great ideas on that?

They are definitely not where I want them to be after 5 days of this, but I think they are getting there. We shall see. Maybe I’ll just throw in the towel and start doing timed unit circle quizzes again.

## Trig Addendum: Modified Radian Fraction Cutouts | Insert Clever Math Pun Here

September 10, 2015 at 7:44 pm

[…] about the awesomeness that is Radian Fraction Cutouts in Shireen’s original post (and my implementation). After using them in Algebra II last year, I made one little modification that made them even […]

## One reason I’ll still use pi - Making Your Own Sense

August 24, 2016 at 4:36 pm

[…] it’s better for teaching radian measure of angles and also trigonometry. Meh. A good dose of cutting slices of circles is really a much better innovation than rewriting the books to use a different constant. Plus I […]

## Lg

August 25, 2017 at 9:30 pm

Did you teach reference angles? It’s much easier to think that any angle in radians that has a divisor of 6 is 30 degrees away from the x axis. The sign and cosine are the same value, then they just figure out the quadrant to know if the value is positive or negative. Then you don’t have to draw the unit circle. No one should ever memorize, but reference angles make life easier.

## Meg Craig

August 27, 2017 at 11:38 am

Yes, I use reference angles/triangles. I don’t have my students memorize/draw the unit circle, but I find it still helps to know where things are in the unit circle, especially when finding inverse values.