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.