SWBAT determine which skills and ideas related to circles they need to practice and understand better. SWBAT develop a portfolio to showcase their learning during this unit.

When students design their own review session and their own portfolios, you have time to work with each individual student to ensure that they get the most out of this learning opportunity.

40 minutes

This class period is devoted to individual and group review. The reason behind the lack of structure is to give students the opportunity to direct their own review. Obviously, this requires me to coach students individually, in small groups or even as a class to ensure that students find ways to use this time effectively.

I start the review session by distributing the Circles Practice Quiz and asking students not to start the quiz but rather to identify their strengths and weaknesses using the problems provided as examples. I ask them to list 3 problems they really need to focus on (on a whiteboard) and I circulate briefly to check that students are making reasonable choices. There are always students who tend to work on the problems they already understand well, so I explicitly discourage this.

Students can then get started working immediately, with some coaching about how to find or choose resources to help them. If I feel more structure is needed, it can be helpful to ask some students to volunteer to be experts. I try to choose students who have a particularly deep understanding of each problem, and I list their names on the board next to the problems they understand well, so struggling students can get help from them. Another option is to ask students not to erase their work when they do problems on whiteboards, so that if a student does a problem particularly well, you can grab that whiteboard and let other students use it as a reference. My goal is to provide as many resources as possible for students so that they are able to facilitate their own review session.

I like to take several minutes at the end of the review session to ask students to reflect on how effectively they used their time and on any other topics they need to review in greater depth before tomorrow's quiz. I circulate and have this conversation with each group or pair of students. Alternatively, I mayask students to write down their answers to some reflection questions:

(1) How well did you use your time today? Explain.

(2) What did you do that you think helped you be prepared for this quiz?

(3) What could you still do tonight to be prepared for the quiz tomorrow? Which topics in particular do you need to review? What resources can you use to help you?

I like to create a culture of reflection in my class, which happens only if I constantly ask students to reflect. Even though their answers to these particular questions might not be especially revealing, the more often that you ask these types of questions, the more comfortable students will become thinking this way.

30 minutes

Throughout the unit, I used colored paper (non-white paper) when I copy anything that could be later used in a students’ portfolio. This way, throughout the unit, students know which assessments and tasks can be part of their portfolio. It also makes the portfolio organization much easier because students can literally sort through a pile of work and pull out the possibly portfolio components easily.

The idea behind the portfolio is for students to create their own summative assessment of the unit. The big questions I ask students as they work on their portfolio are:

- How can you show your mastery of the skills and ideas of this unit?
- Which work represents your best effort and understanding?

Additionally, I ask students to think meta-cognitively about their use of the mathematical practice standards during the unit. I have narrowed the list down from all 8 in the beginning, while students familiarize themselves with these.