In this lesson students approximate using the perimeter of regular polygons inscribed in a circle. Students wrote a general formula for the perimeter of a polygon in a previous lesson, which they will extend to approximate the circumference of a circle. The relatively unstructured presentation of this activity is purposeful so students can build their perseverance and sense-making (MP1). Students will work with their groups to determine what information they need, how they calculate this information in the specific cases, and how they can express those repeated procedures in a generalized formula (MP8).

Once students build a generalized formula, they apply the formula to approximate the value of . During the Lesson Synthesis students learn methods that ancient mathematicians used to generate both upper and lower bounds of . This lesson presents an opportunity for seeing how mathematics has changed over history and how ancient techniques from around the world are still in use but with the added power of computers.