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.
This collaborative strategy is simple but effective. Students roam the room finding new questions to answer together, and scan the code with an iPad to check their work. Then, they put all the answers together to unlock a secret code. The use of QR codes in class has greatly improved the effectiveness of student work because of their ability to stop and check their answers. Their enthusiasm for this activity is clear, and making it into a competition of sorts makes it all the more fun. I utilize the QR codes in everything from directions to links to activities. Still, my favorite use is monitoring groups during QR code breakers.
I encourage my students to evaluate their peers whenever they are involved in discourse--both in side conversations as well as in class discussions. I implemented a system of Peer Evaluations, a process that involves students using silent hand signals, in order to give my students more voice in class. Some of my students want to say what they think and exert their opinions, but there isn't enough time for every student to share. Other students easily get distracted and need physical engagement to stay focused. Through Peer Evaluations, my students can share their thoughts and are pushed to stay focused throughout student discourse.
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.