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.
I use Daily Exit Tickets to assess mastery of the day's objectives and to make sure students have a clear understanding of how they're doing. Students answer a few targeted questions on a Daily Exit Ticket, and the following day we review mastery shown by each student and celebrate their achievement (please see the "Data Review" strategy video). I read out each student's name who achieved mastery, and we quickly celebrate to recognize their hard work. For the students who have not reached mastery yet, this motivates them to keep striving to get that checkmark on the board. Rather than just using outdated student data from summative assessments, Daily Exit Tickets give me and my students a quick read on how they're growing throughout the week. Though these mini-assessments do not connect to my grading system, they allow me to track my students' daily progress throughout each week.
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.
Stamina captains track stamina among students at their table throughout independent work. Especially while working on differentiated or individualized practice, students may feel "alone" in their work and thus easily get distracted (whereas they might feel more pressure if all students are working on the same exact practice). Thus, through emphasizing the skill of stamina, students constantly think about their level of focus and ability to avoid distractions. When students begin discussing something that is off-topic, the stamina captain will write down their name on a post-it. After that, those students get a chance to "fix" their behavior by getting back on task. If their stamina is not fixed, they then get a phone call home as a consequence for their lack of focus. Through this closed loop, parents and students understand their focus and work at school.