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

Through a variety of assessment items, students will demonstrate their understanding of circles properties by using precise academic vocabulary, solving problems, and writing proofs.

25 minutes

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.

65 minutes

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.

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