The week before I was asking students in Pre-Calculus 12 to sort trig functions, I was asking students in Grade 6 to sort triangles.

I adapted a textbook task. One of these days, I’m going to finish my post “In Defence of Textbooks. Kinda.”

To get ready, I gave each pair of students a handful of SET cards to sort. Students shared their sorting rules. “There are many ways to sort” was the message. Did this in Pre-Calculus 12, too, by the way.

Next, I gave each pair of students this blackline master:

I asked students to sort the eight triangles into groups. That’s it. About two minutes later some asked, “Can we have rulers?” I gave some rulers.

I called on students to share their sorting rules. (The textbook just tells students to sort the triangles by the number of equal sides.) Order matters. The first pair of students classifed the triangles as small, medium, or large. This closely matched the groups made by the second pair who measured the perimeter of each triangle: something like, “shorter than x centimetres, between x and y centimetres, and longer than y centimetres.” The third pair sorted the triangles based on the length of the longest side. This set up the fourth pair who noticed that, for some triangles, the lengths of two or three sides were equal.

Then, and only then, I defined the terms *scalene*, *isosceles*, and *equilateral*.

In this post, Patrick Vennebush has his sons define *arithmetic progression* by giving them examples and non-examples.

Compare either approach with this. (Read the comments: Bowman nails it.)

After, students were sent to the hallways, library, gym, and playground with their iPads to take/make a photo of a each type of triangle. Students returned to share their favourite scalene, isosceles, and equilateral triangles through the Apple TV. This led to some fun conversations.

I didn’t collect students’ photos. My photos at DEC reception instead: