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* *Reflection: Trust and Respect
Circles Unit Assessment - Section 1: Look at Student Work Samples from Arcs and Angles Menu

While it takes time to go through students’ work on the Circles Menu to select student work and justification samples, I have found that this is one of the most authentic ways to get students to tangibly identify for themselves what goes into a high quality justification as opposed to a mediocre, sometimes lengthy, sometimes sparse, explanation. I called on Recorder/Reporters to share out on behalf of their group, asking them to provide evidence in the student work. Students were able to say “this work seems well justified because they were able to clearly name the relationship they used” or “this doesn’t seem like a justification at all...it kind of feels like the student just explained what they did, step-by-step, without taking about how they knew they could do that.” I felt that it was so powerful for students to describe their peers’ work so clearly and articulately.

*Looking at Others’ Work to Get Better at Justification*

*Trust and Respect: Looking at Others’ Work to Get Better at Justification*

# Circles Unit Assessment

Lesson 8 of 8

## Objective: Students will be able to solve problems by identifying relationships among radii, chords, tangents, angles and arcs.

Before we start this activity, I tell students that they will be taking a critical look at student work, which means they most be especially respectful when voicing their critique. I pass out an 11"x17" paper to each group, which has samples of student work from the Arcs and Angles menu photocopied onto it. My expectations are that each student in the group will write in their own color, recording the elements of the justifications they thought were effective (or ineffective). I also remind groups that Recorder/Reporters should be prepared to share on the group's behalf.

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#### Circles Unit Assessment

*65 min*

This test features a variety of test questions: true/false, fill in the blank, and vocabulary matching, to assess students’ foundational knowledge of circles properties—these are the kinds of questions that requires students to attend to precision (**MP6**). Problems #4-7 give students the opportunity to apply their understanding of chord, tangent, and angles/arcs properties while solving problems.

I include Problem #8 because it requires students to use higher order thinking skills; students must integrate several different concepts to solve the problem (any parallelogram inscribed in a circle must be a rectangle, properties of rectangle diagonals and equilateral triangles, arc length) while looking for and making use of structure—this problem definitely asks students to make sense of the problem and persevere while solving it (**MP1**, **MP7**). The two proofs on the test require students to thoughtfully justify their reasoning while writing the proof; the second proof, in particular, encourages a variety of strategies to think through the proof.

#### Resources

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Foundational Circles Vocabulary and Chord Properties
- LESSON 2: Tangent Properties
- LESSON 3: Chord and Tangent Group Challenge
- LESSON 4: Arcs and Angles: Central and Inscribed Angles
- LESSON 5: Circumference-Diameter Ratio and Arc Length
- LESSON 6: Review: Arcs, Angles, Chords, Tangents, and Proof
- LESSON 7: Prove Circles Conjectures
- LESSON 8: Circles Unit Assessment