Reflection: High Quality Task Circles Unit Assessment - Section 2: Circles Unit Assessment


This problem is rich with opportunities for students to do a lot of sense making.  Students have to make sense of what it means to have an arc that is 1/9 of a circle, 12 meters long, and can fit eight desks.  Students need to be able to interpret the question “how far are the desks from the center of the circle?” and to understand that the distance at hand is represented by the radius, not diameter, of the circle containing the arc.  Students’ work on part (a) of this problem often reveals the strengths of their thinking and the possible breakdowns in their understanding.


What I love about part (b) is that most students can successfully work their way through the problem if they really make sense of what it means to have an arc with the same central angle but half the distance from the center.  My favorite approach is not the one that requires students to calculate that each desk takes up 1.5 meters of an arc, but rather, the one that leads students to simply conclude that the arc length is directly proportional to the radius and will therefore hold half the number of desks.

  Proportional Reasoning and Sense Making
  High Quality Task: Proportional Reasoning and Sense Making
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Circles Unit Assessment

Unit 9: Discovering and Proving Circles Properties
Lesson 8 of 8

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

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

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1 teacher likes this lesson
Math, Geometry, circles, properties of circles, circle constructions
  90 minutes
circles sample test
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