One of my favorite problems (and the one I presented at TMC this year) is What it’s Worth? from Nrich. To say I “like” this problem would be like saying Sarah Hagan “likes” interactive notebooks. Clearly an understatement.
Anyway, here’s the prompt:
What I like most about this problem is that there are so many, OH so many, methods to solving it. It is a FANTASTIC way to get students to focus on the pathways to the solution rather than the solution itself. After the students figure out the value of the question mark, they go about discussing the numerous methods they used in order to arrive at their answer. Furthermore, the problem includes 6 “beginnings” of solutions and learners then need to make sense of those as well as determine how a solution was reached along that path.
To my surprise, along with Nrich’s site updates, this problem has improved as well. Rather than showing a written start to the problem, provided are 6 visual introductions.