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.
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.
Before my students begin our system of rotations at the beginning of the year, I take time to make it very clear where they will go, what they will do, and what materials they will need. I also make sure to do frequent checks for understanding. Dedicating extra time to review Rotation Expectations at the beginning of the year helps to ensure that rotations will run smoothly throughout the year. Class tutors are also selected for each rotation. They walk around to support their peers who need help and even help to manage class behavior. Class tutors are given an iPad with access to our ClassDojo site, where they award "positive points" to students following expectations and "needs improvement points" to those who are not following expectations. Through explaining my expectations and leveraging the class tutor to reinforce these expectations, I ensure that my students are giving their best efforts during our rotations.
Plickers are an online check for understanding procedure where students can answer multiple choice questions. Students are each assigned a "plicker" or paper clicker that enables them to respond based on how they are holding it. The training for it's use is quick, and we can use a tablet to instantly record the results. The results can be uploaded and tracked for even more data! This ability to stop instruction to see how students are doing is essential to having a flexible and student-need based classroom. Plickers allows me to get real time data and make decisions that make me a better time manager and allows me to potentially see misconceptions.