ProRadian Story

The Problem: Students Don’t Understand Radian Measure     Our Solution: ProRadian Protractors

Jennifer SilvermanHi, I’m Jen Silverman – welcome to my protractor site. I created ProRadian protractors after teaching high school math in public and independent schools for 14 years. I am now doing various consulting projects around math curriculum, managing this growing business, and buying and selling vintage glass and pottery.

Here’s how ProRadian Protractors were born: in the spring of 2011, while teaching a Precalculus class at a public high school, I realized (again) that most students have a hard time understanding radian measure. Kids have been using degree measure for years, but they don’t see radians until they begin to study trigonometry. Then they are expected to memorize the complicated “Unit Circle.”

One Radian I decided that we should back-up, and explain radian angle measure in a simple, fundamental way. By definition, 1 radian is the measure of a central angle formed when the intercepted arc is equal in length to the radius. So, one radian is as big as the angle marked ϴ in this diagram. But what does a radian measure of 2.1 look like? or a radian measure of 0.7? The students did not conceptualize radians as units of angle measure.

I thought that kids should practice measuring angles using radians as units. I searched for a radian-scaled protractor online and in every catalog I could find, but I had no luck! So, I made one. I field-tested the first protractor and got a very good response from the kids. They could see that half a circle had a radian measure a bit more than 3. At this point, however, they still didn’t have a good idea about how or why these units were connected to π.  I realized that I needed another protractor, scaled in fractional parts of π.

I wrote a series of lessons in which students used the new protractors, which I named ProRadian1 and ProRadian2. (The kids wanted to call them “The Silverman”, as in “Take out your Silverman and measure this angle.”) The lessons were review topics from Geometry, familiar tasks with an unfamiliar unit. These proved to be very effective for my students, and there were many enthusiastic comments about how now it made sense.


Since that spring, I have been working to produce and market ProRadian protractors. I have filed a Design Patent application and have a Registered Trademark for the name ProRadian. I found a local manufacturer and began with a shipment of 400 sets, delivered just in time to present to a group of 96 educators at the NCTM Eastern Regional Conference in October, 2012. I got my big shipment of newly-refined, laser-cut, silk-screened protractors, my pre-printed bags, and my red inserts with a mini-lesson and began selling the new ones in early 2013. At the request of an engineer, I designed ProRadian Pro, scaled in 0.01 radians. This is a precise measurement tool, suitable for high school, university, or professional use.

You can purchase ProRadian Protractors here in the Pro Shop (that’s the best way) or check my Vendors page for other options. I hope you give them a try – they changed the way my students learned about radians – from memorization to understanding.


I have presented ProRadian Protractors to enthusiastic reviews at many conferences, including NCTM’s Annual Meeting and Conference in Boston, April, 2015. The lessons, tied to the CCSS, including appropriate standards from fourth, seventh, and eighth grade, were very well received.

I am nearly done with my original shipment of 20,000 protractors, and I am looking for the best deal to order a new shipment and not raise my prices.

Check out our spread in the Nasco Catalog:


Thanks for reading!

Jen Silverman