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.
Weekly Online Homework is a strategy aimed at building up the expectations in class by infusing them into my students' home lives. On Monday, my students are assigned homework that is due on Friday of that week. I use the class website to drive this communication with my students and their parents. The homework that is assigned is differentiated because the assignments are from adaptive online content providers. In addition, my students learn to be responsible for themselves, leading to huge growth in their self-advocacy and learning. On Friday, rewards and consequences are tied to the Dojo Dollars class economy. Because of the online nature of the homework, it can be instantly graded.
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 Vocab Blitz is a visual strategy used to teach concepts through the use of math vocabulary. Students answer deep questions about the relationship between words and math and earn tickets. They place these in the Raffle Jar, which we pick from on Fridays for a small prize. Math vocabulary just for the sake of knowing academic language is good, but the Vocab Blitz explicitly asks students to apply the terms, which allows me to build more rigorous questions and connect ideas (i.e. how volume connects to science). For example, by knowing what the dividend actually is, we have a shared language that we can use when trying to figure out if a problem is asking us to multiply or divide, and to connect to improper fractions' numerator when converting them.