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Last year I was doing super short warm ups. We gave the students 3-5 problems that were specifically designed to be easy. The routine was as soon as students came into the class, they’d go to their VNPS and work out the problems, where I would immediately let them know if they were correct or not. The whole thing typically took 5 minutes. The idea was to give the students a quick victory to start the class off with the idea that they can be good at math. After the warm-up they were given a challenge problem. The main purpose of the challenge problem was to give the students something to do after they finished their warm-ups. These were harder problems that required more thinking. I had a tendancy to make these too hard and would often lose about 20 minutes walking the students through these. In addition I had a hard time getting the kids to even try the challenge problem. The above routine was established before I had learned as much as I know now about inquiry based classrooms
Reflecting back, I like warm-ups at the boards being super fast and giving the students something to do as soon as they walk in, but I’m thinking I’ll replace the challenge problem with something like a would you rather, estimation 180 or open middle problem. Something that is more open and has a low floor. My periods are blocked so I’ve got about 100 minutes typically, so I’m okay with the total warm up routine taking 15 or so minutes.