Rise and Sine

Converting From Degrees to Radians (and How to Teach it!)

converting degrees to radians title

Converting from degrees to radians is a key part of a student’s success in precalculus (and some units in geometry and algebra 2, too!) When I taught pre-calc, I was surprised at some of the pushback I would receive from students after introducing what a radian is. 

Over the years I learned getting comfortable converting from degrees to radians can require some practice and patience. A radian may be a brand new term to many students. Once I began breaking it down and really making sure students could master converting angle measures, I began to see students have more success in future units. 

So, What is a Radian?

It’s a unit of measure based on the radius of the circle (see where the name came from?) One radian is equal to approximately 57.3˚.

degree vs. radians

How to Convert from Degrees to Radians

For the first lesson, after defining a radian, I like to show what 1 degree looks like vs. what 1 radian looks like. I also point out that there’s many unit conversions that we already do. Feet to inches, minutes to hours, and yards to feet, to name a few. Converting degrees to radians is the newest conversion to add to their math toolbox. 

Then, we convert. Multiply by π/180 or 180/π .. but take a moment to explain why! Each of those expressions are equal to one, so when you multiply by either one it doesn’t change the measure of the angle, just the unit it is expressed in. Just like all the conversions they learned in the lower grades. 

converting angles from degrees to radians guided notes

Here’s a ready to go lesson if you’re looking for one! It includes examples, notes, classwork, and homework. No prep for you! 

Converting Angle Measures Hands-On Activity

After getting the necessary stuff out of the way, I try to make follow-up activities a little more interesting. A cut and paste activity like this one is great to throw in the mix.

converting from radians to degrees cut and paste activity

Teaching tips: Pair or group students and have them cut out the angles. They will sort and match each angle with their equal measure in degrees or radians. Have them check their work with one another before they glue them down!

I like when students have the opportunity to work together so they can help one another and the teacher (you!) can work with struggling students, kids who were absent, etc. When students have the opportunity to talk through their questions with classmates I feel they really begin to become more confident in math and that just warms my little math teacher’s heart! 

Converting from Degrees to Radians Digital Self-Checking Worksheet

I think self-checking digital worksheets are the perfect resource to always have on hand! Here’s why I love them:

  • They are easy to assign if you regularly use google (they do require a free google account)
  • Students love the immediate feedback! 
  • You can assign them for homework so students can come to class ready with questions (if they have any)
  • You can keep some in your back pocket to assign when there is a substitute
  • They make good end of chapter/semester reviews
  • Way more engaging than a paper worksheet

This converting angle measures self-checking worksheet bundle has three assignments:

  1. convert from degrees to radians
  2. covert from radians to degrees
  3. converting angle measures

Each assignment has 12 questions. There are directions included to help students input π no matter the device they are using to make it as user-friendly as possible!

I hope you found something you can implement in your classroom!

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