I notice that I’ve seen this gif on social media a few times recently.
I notice that the exterior angles seem to add up to 360 degrees.
I notice that I’m drawing on a lot of prior knowledge to make that conclusion. There are lots of angles one could highlight in the original polygons; I understand which ones are exterior. I understand the idea of angles greater than 180 degrees, so that a full rotation makes sense as 360 degrees. There are probably other things I don’t realize I know because I’ve spent lots of time solving angle problems with polygons.
I wonder if this would make any sense to a typical 8th grader.
I wonder when in an instructional sequence this gif would make the most sense.
I wonder if this gif makes a substantive mathematical idea seem like “magic.” I wonder what message that sends about the nature of mathematics.
I wonder how often I explain an idea in a way that connects with students who already understand an idea, but not with students who feel confused.