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# Defining Pi Project Revisions and Circles Review

Lesson 16 of 17

## Objective: Students will be able to use today's class to finish up work as needed.

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.

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#### Work Period

*60 min*

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.

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#### Closing: Circle Up

*5 min*

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.

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- UNIT 1: Statistics: Data in One Variable
- UNIT 2: Statistics: Bivariate Data
- UNIT 3: Statistics: Modeling With Exponential Functions
- UNIT 4: Statistics: Using Probability to Make Decisions
- UNIT 5: Trigonometry: Triangles
- UNIT 6: Trigonometry: Circles
- UNIT 7: Trigonometry: The Unit Circle
- UNIT 8: Trigonometry: Periodic Functions

- LESSON 1: Circles on the Coordinate Plane
- LESSON 2: Manipulating Circles on Geogebra
- LESSON 3: Old and New Knowledge of Circles
- LESSON 4: Problem Solving with Isosceles Triangles and Circles
- LESSON 5: The Defining Pi Project, Day 1
- LESSON 6: The Defining Pi Project, Day 2
- LESSON 7: The Defining Pi Project, Day 3
- LESSON 8: The Defining Pi Project, Day 4
- LESSON 9: The Defining Pi Project, Day 5
- LESSON 10: The Defining Pi Project, Day 6
- LESSON 11: The Defining Pi Project, Day 7
- LESSON 12: The Defining Pi Project, Day 8 (Wrapping Up)
- LESSON 13: Arc Length and Sector Area
- LESSON 14: Radian Measure
- LESSON 15: Review of Circles Learning Targets
- LESSON 16: Defining Pi Project Revisions and Circles Review
- LESSON 17: Circles Review: Open Spaces