Here’s another way to build intuition for Polar Coordinates. Great of lower-level students. Brief explanation: one student calls out a polar coordinate (e.g. “five comma fifty four degrees!”) and other students flick a “ball” to try to get as close as possible to that point.
Students break into groups of 4 or 5. Each group gets a big (2′ x 3′) whiteboard. They sketch an x-axis and y-axis, and can sketch more if they want to (they know a little about polar coordinates at this point).
One student is designated the “Caller/Referee” and all the others in the group are players. The players set up whatever they are going to “kick” (flick) on the corners of the board–we used small wooden blocks. The Caller says a polar coordinate (e.g. “five comma fifty four degrees!”), and then starts counting down from 10. (10… 9… 8…)
The players have until the caller reaches “0” to flick their object to that point. From here you can make up whatever scoring system feels fair. I told them “2 points for the closest person and 1 point for the next closest”. If you want them to be more accurate, you could make it more like golf: lower score is better and you get a point for every cm away from the point your block is. This would take longer to figure out, but would require students to be much more precise with their measurements. Since my goal was building intuition, I passed on this approach.
Here are a few videos of the students having fun with the game:
Students had a blast and learned a little. We spent only part of a period on it, so that’s reassuring, but it’s just not conceptually difficult. I didn’t do this for my advanced class, because though they would have fun, they’d probably get very little out of it.
One good thing was they were required to figure out the polar coordinate often and quickly. A few times I yelled “only negative r’s for a round!” so students had to quickly figure out what that meant. I suppose we could bring in functions and other things into the game, but the students need to learn about those first.
Oh yeah, and the next day they came into class asking “can we play Polar Coordinate Kickball?”. I said no and instaed we played the Polar Coordinate Battleship, after which they asked “can we play Polar Coordinate Battleship tomorrow?” Wow, I found something that HS Seniors want to do.