I'm going to be starting teaching a course called algebra COE, which is for students who didn't pass the required state algebra exam to graduate and are now seniors, to do spaced-out exam-like extended problems after extensive support.
I don't want to start the class out with "getting down to business" because I want the students to feel comfortable in the class, with me and with each other. The "getting down to business" will happen during the second week of class. Therefore, I'd like to start out with a class collaboration to solve a "fun" problem. (There are 5 students in the class)
At the same time, I don't want to start out with a problem that feels too contrived, or too much like "school math" problems. They have clearly been turned off from "school math." I want one or some that feel more like they are doing a puzzle, yet still engage algebra-related skills and open up a discussion about problem-solving as a process and skill that can be honed.
Some problems I have considered, yet I believe are too "math-feeling":
- The exponential chessboard and rice problem
- How many squares are there on the chessboard? (note: more than 64)
- The "lockers" problem
- The ooops game