Reflection: Developing a Conceptual Understanding Circumference-Diameter Ratio and Arc Length - Section 2: What is Pi?


Very few of my students have done a pi investigation in the past (in either middle or elementary school) and most of my students struggle to grasp the notion that pi is not simply “3.14” but rather a ratio between the circumference of a circle and its own diameter.  The “What is Pi?” investigation certainly helps to develop students’ conceptual understanding of what pi represents because it engages students in a hands on way.  What I’ve seen this year, in particular, is that asking them why we always get approximately 3.14 when we divide the circumference of a circle by its own diameter forces them to make the connection back to the idea that all circles are similar.  This whole-class discussion helps me to see how weaving in transformations throughout the year has supported my students’ understanding and sense making.    

  Make Sense of Pi through the Idea that All Circles are Similar
  Developing a Conceptual Understanding: Make Sense of Pi through the Idea that All Circles are Similar
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Circumference-Diameter Ratio and Arc Length

Unit 9: Discovering and Proving Circles Properties
Lesson 5 of 8

Objective: Students will be able to explain pi as the ratio of a circle's circumference to its diameter.

Big Idea: Through a hands-on task involving circular objects, string, and measuring tools, students will make sense of pi!

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11 teachers like this lesson
Math, Geometry, circles, properties of circles, circle constructions
  65 minutes
pi eye
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