In order to keep the group of students working independently, we have a class tutor who helps with both behavior management and helping students problem solve through their math practice. I select students who demonstrate mastery of the content and also responsibility to manage a class, allowing different students to try during different rotations/classes. The student walks around, helping students troubleshoot through technical issues and math questions as well. Additionally, they have control over the ClassDojo system, awarding students postive points and giving "needs work" points as well.
The basketball problem is a built in way to teach the students about rigor. At the beginning of the year, we discussed how math is like an onion. There are many layers and each one is more complex than the last. The "shot" is an opportunity to reward risk-taking and get the students really thinking about the most high-complexity questions that I can ask. For this reason, students are doubly invested in this part of class. One because they want to challenge themselves, and two because they want to get up there and take the shot.
Through peer learning, students work together to practice skills and complete their independent practice. Through constant positive narration and coaching over best practices in peer learning, students are developing the skills needed to successfully collaborate and learn from other students.
CSI Time is an inquiry based strategy where students must solve a "math mystery" that introduces a concept that we will learn. They have until the end of the week to collaboratively (with their detective partner) discover the clues and work their way to the "criminall". In just 10 minutes, students have worked themselves into a frenzy to grapple with content they may not already know what to do with. This desire to problem solve pushes students during the lesson that follows to learn the skills they need to solve the mystery.