A couple years ago, Kate Nowak asked us to ask our kids:

What is 1 Radian?” Try it. Dare ya. They’ll do a little better with: “What is 1 Degree?”

I really loved the question, and I did it last year with my precalculus kids, and then again this year. In fact, today I had a mini-assessment in precalculus which had the question:

What, conceptually, is 3 radians? Don’t convert to degrees — rather, I want you to explain radians on their own terms as if you don’t know about degrees. You may (and are encouraged to) draw pictures to help your explanation.

My kids did pretty well. They still were struggling with a bit of the writing aspect, but for the most part, they had the concept down. Why? It’s because my colleague and geogebra-amaze-face math teacher friend made this applet which I used in my class. Since this blog can’t embed geogebra fiels, I entreat you to go to the geogebratube page to check it out.

Although very simple, I dare anyone to leave the applet not understanding: “a radian is the angle subtended by the bit of a circumference of ~~the circle~~ ~~that has 1 radius~~ a circle that has a length of a single radius.” What makes it so powerful is that it *shows *radii being pulled out of the center of the circle, like a clown pulls colorful a neverending set of handkerchiefs out of his pocket.

If you want to see the applet work but are too lazy to go to the page, I have made a short video showing it work.

PS. Again, I did not make this applet. My awesome colleague did. And although there are other radian applets out there, there is something that is just *perfect** *about this one.

### Like this:

Like Loading...

*Related*

Nice catch, Michael – I think your wording probably does clear it up a bit.

Sam – what a lovely applet your colleague created. I LOVE the colors, they definitely make the idea pop. I’ve linked to the applet on my own virtual filing cabinet. Thanks!

Love this applet. Just asked my precal kids on a quiz the other day: If a bug on this particular circle traveled one radian, how far in linear measurement did it travel? They all knew what the radius was, they had told me a hundred times what the definition of a radian was (in their own words), but only 2 of 23 could tell me how far that bug traveled!

That kind of thing is maddening, isn’t it? Feynmann tells a lovely story like this about a particular law of optic where students recite a law to him, he asks them to look at a lake and talk about refraction and they stare blankly at him. Understanding a fact and applying it in context are SO different. Maybe it is another ‘cognitive load’ issue?

Awesome demonstration of what exactly 1 radian is. I had never really taken time to think about this. Math is great.

Sam, I ordered Radian protractors from Jen Silverman. They absolutely had results in class. I think connecting radians to degrees and circles with real objects like a protractor made a huge difference in understanding.

@Glenn, thanks! @Tina, did you have them roll the protractors? @Sam, I have similar applets at proradian.net.

Pingback: What is a radian? | Reflections on Holes in Graphs and Reasoning

I love reading your blog because you are always asking, “Why are we teaching this?” and working to build conceptual understanding. I have been teaching Precalculus for 17 years, but with changing state standards and Common Core it is a bit confusing to know exactly what topics are considered “Precalculus” these days. If you have time, I’d love to have a list of your units (the topics you teach) to compare to mine. I am looking forward to using some of the ideas you have posted in your Precalc blogs. It is fun to see that you do some of the same things I do.

I just wanted to chime in my “Thanks for sharing!” I love this. Thank you also for the video as I initially fell into the “too lazy” category.

Awesome!

Pingback: Introducing and Understanding Radian Measure | Mr. Siderer's Weblog