I post an opening problem asking students to convert both 3 radians and 3π radians to degrees. I circulate throughout the room and look to see what students understand. How this problem goes depends mostly on how far students have gotten on their practice; the second module of the current Delta Math assignment helps specifically with converting radian measures that are not given in terms of π.
This problem helps students attend to precision because it provides a very simply illumination of what a difference π makes when included in an expression. Students can be slow to get used to writing and saying out-loud the "pi" part of radian measures, but usually by talking through this problem that distinction becomes clear.
Wherever the conversation goes, there are two ideas I make sure to touch on: the necessary calculation for 3π radians is actually much easier that the one for 3 radians. Also, the degree measure for 3 radians (~171.9 degrees) is nearly, but not quite 180 degrees, and I encourage students to think about how this relates to 3 being not quite as much as π.
A note to teachers: ok, I recognize that all of these narratives are "notes to teachers," but this one is less about today's lesson and more about my curriculum in general. I am including this lesson as a way of sharing what really happens in my classroom. Today is just an open-ended work period, and I really try to stay out of the way as students decide what they're going to work on. There is plenty to do: revisions to the Defining Pi Project, last minute finishing up on the project, the current Delta Math assignment on radians and arc length, the Unit 2 review, the construction of a perfect "Cheat Sheet" for the upcoming Unit 2 exam.
Days like this are very important. To me, for my students, for our relationship, and for their self-efficacy.
We circle up to check in at the end of class. I ask everyone to share a just a few words about what they did today.