Coming next week: "Polygon" v. "A Simple, Closed, Plane Curve Composed Of Finitely Many Straight Line Segments."
And for the record, the differences here are real. Not real to 8th graders, but mathematically real. And actually some mathematically honest version of these differences is usually interesting to a class full of eighth graders …
Dan Meyer (yeah that's allowed):
There is a difference. The difference is important. Precision is important. Precision, for some students, is perplexing. No denying any of that. However, the attention paid that particular issue in that last thread was a dramatic instance of tree-noticing and forest-missing.
It’s interesting that everybody seems to assume that NCTM overlooks this issue…. The companion sheet [pdf] could do with some improvements, but at least it looks at the catenary question.