These questions are jam. They’re hard. They require some serious divergent thinking. But most of all, they do an excellent job of what Ben Blum-Smith calls jamming a concept — students who can factor polynomials will be forced to apply the concept but unable rely on a familiar procedure.
Most of all, the steps (at least the steps I used, assuming my solutions are correct) are all algebraically simple, relative to the rigor of the question.
I love these questions, and Five Triangles’ stuff in general — I use it all the time as extension or group work. That said, while I enjoy these questions and think they do an excellent job of assessing higher-order conceptual understanding, I worry that they are inauthentic in that 1) I have no idea how to teach kids to be able to access questions like these and 2) many students who have strong skills could in good faith get these questions wrong.
I worry that assigning too many questions like these without more scaffolding creates a haves and have-nots environment in my classroom– some kids get it and excel, but more don’t and become frustrated. I want to find more questions at that level of rigor but with lower-level entrance points so all of my students can learn from them.
Finally, a tougher (I think) question — I’m still working on part b.