Engaging students: Using radians to measure angles instead of degrees

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Cody Jacobs. His topic, from Precalculus: using radians to measure angles instead of degrees

green lineHow could you as a teacher create an activity or project that involves your topic?

I believe the best way to get students to start using radians, or know how to convert from degrees to radians. Is giving students a lot of problems where they go back and forth between radians and degrees. It is a fairly simple task but you want all of your students to be able to easily recall how to do this. Another activity could be going over the unit circle with your students. Using the unit circle occurs frequently from pre calculus going forward, just be sure to express that the radian measure is the arc-length divided by the radius of the unit circle to the following point. I also know that my high school teacher always made us fill out the unit circle on every test giving us the degree measurement and making us fill out the radians. This really helped us concrete radian measurements in our head, just for those 5 points it would provide us.

green lineHow can this topic be used in your students’ future courses in mathematics or science?

I would say after radians and the unit circle is introduced, just about every math class after that has something to do with the two. Even if it is just looking for multiple solutions to a problem, where you just add two radians to the solution you already found. But why do we use radians instead of degrees in high math classes? This is because radians are a unitless measurement. Radians are defined as arc-length divided by radius, so the units cancel. This is helpful in higher level math classes because radians are easy to use in derivative and limit formulas. This is the main reason we use radians instead of degrees in higher level classes, the convenience.

green line

How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

Desmos.com is yet again another great technological resource to use when introducing radians to the classroom. There is a great activity call “What is a Radian?” That introduces an activity student can do using a plate and folding it into different sections. I actually believe this is how I was introduced to radians in high school. The second part of the activity on desmos after you finish with the plate introduction, is asking students key questions. How many radians are in a certain degree measurements? How many degrees are in a certain radian measurement? As always desmos is still great at introducing radians and lets you easily monitor your students progress.

 

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