I planned to allow 10 minutes for students to ask questions & make progress on the triangle pile up. They make everything into such a big deal. After a reassuring talk about how I am confident that they have a lot of tools in their math bag of tricks, students did realize they could do this. I pointed out and we discussed Standards of Math Practice 1, 5 & 6. I’m excited to learn that “tools” refers to math skills in addition to physical and virtual items (trig & Pythagorean theorem, for examples).
I had a student ask me why we were doing this and that this is not something that would occur in “real life.” I responded that the task itself is not the goal, but persistence, precision & practice using tools were the real objectives. Their reply was “Oh, that makes sense” and they got to work!
Once they were sold and digging in, they really got on a roll. I couldn’t stop them to move on to another activity, it was just so beautiful to see them patiently working.
[update 4/24: It appears that folks are coming to this site to find the solution to the trig pile up. I want to make sure you know that the colorful work of the student above has some errors and is not a correct solution. I would never post the real solution here, silly!]