As students enter the room, I check in with them briefly and hand them the Piecewise Functions Practice packet. They may comment that it is really thick and I tell them that we won't be doing all of it... Once all students have entered, I ask them to flip through the packet to see if they can figure out what is going on. Then I tell them that there are 4 sections and that they need to do at least one level out of each section. I tell them that the idea is that they need to show me that they learned each of the 4 key skills of the learning target, and that their job is to challenge themselves to show their learning at the most challenging possible level.
I ask them to flip through the packet before getting started to think about which level they want to choose. Once they have some ideas, I ask them to get started.
The purpose of the closing is to reflect on the main idea of the lesson, and today, along with the content, the big idea was really to think about which level of challenge was appropriate. Because this is a structure that I will be using frequently, I really want to set up a classroom culture in which students are the agents of their learning process and in which they make thoughtful decisions about how to learn. Asking them to reflect on their learning at the end of class helps build their awareness of how they are doing and also helps them hold themselves accountable for their use of time.
This is also a time that it is great for you to give them feedback on their answers. If I find that I don't agree with a students' self-assessment, I tell them, "I actually don't think you did a great job today," or "I feel like you could have chosen more of a challenge," or "I think you might have learned more if you started with an easier level and then worked up to that one." I really want to initiate an on-going dialogue with students about their choices in class each day and to show them that I will critically assess their self-assessments. In other words, this self-assessment is not just a time-filler, but is really important to the work of the class.