## Reflection: Grappling with Complexity CORNERSTONE: Circumference Formula - Section 2: Guided Practice + Independent Practice

Problem #6 in the extension - The Yin/Yang Problem - could be a lesson unto itself.  Students are told that the shape is made up of three half circles but they have trouble seeing the three half circles.

I found myself asking the following question to students who were stuck:

1) Can you draw the diameter for each of the three semi-circles?

2) What is the diameter of each semi-circle?  How did you determine the diameter.

3) How can you use the circumference formula to find the perimeter (circumference) of a half circle?

Only the fastest and most skilled students from my class reached this problem.  I think it really deserves its own dedicated time separate from the current lesson.  It is here because I knew I did not have enough time in my scope and sequence to dedicate a day to it.  I will have to find a way to make time for this problem because it really challenges students to make sense of a problem and persevere in solving it (mathematical practice standard 1).

The Yin/Yang Problem
Grappling with Complexity: The Yin/Yang Problem

# CORNERSTONE: Circumference Formula

Unit 6: Geometry
Lesson 7 of 37

## Big Idea: Students apply the circumference formula and use fact families to see how it is derived from the ratio PI.

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Standards:
Subject(s):
Math, areas, circumference (Determining Measurements), Geometry, 7th Grade M, Circumference Formula, circles, perimeter, Diameter, pi
50 minutes

### Grant Harris

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