Polar graphs can be tricky. Though most students can plot polar points given a radius and an angle, it’s a very different proposition for students to really picture how the radius of a polar function varies as the angle increases. Essentially, the students can create a table of values and plot those ordered pairs, but connecting the dots…that’s another story (it’s just not intuitive for most students).

This year, however, I think I taught it more effectively and assessed the students more effectively, so I’d like to share.

Here’s the activity that I have my students do. It connects to prior knowledge (graphs of sinusoidal functions): Graphing a Rose Curve – WHY?

I ask them to focus on specific critical points (mins, maxes, and zeros) that they can gather from a rectangular equation of the same form as the polar equation. that’s nothing new.

**The new thing is this desmos graph** (CHECK IT OUT!!) that helps them make sense of how to connect the dots, and how the sinusoidal function is connected to the polar graph.

On their quiz, I asked the students to explain to me how the radius changed over particular intervals of angle measures, and overall I was very impressed with the students’ ability to put their thinking into words.

Here’s a video that shows the full functionality of the desmos graph. It’s one of my favorite demos that I’ve ever created.