## 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

# Circumference-Diameter Ratio and Arc Length

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

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

Print Lesson
11 teachers like this lesson
Standards:
Subject(s):
Math, Geometry, circles, properties of circles, circle constructions
65 minutes

### Jessica Uy

##### Similar Lessons

###### Riding a Ferris Wheel - Day 2 of 2
12th Grade Math » Trigonometric Functions
Big Idea: Make the transition from the Ferris wheel problem to the unit circle.
Favorites(6)
Resources(10)
Troy, MI
Environment: Suburban

###### Arc Length and Sector Area
12th Grade Math » Trigonometry: Circles
Big Idea: Students find their friend similarity lurking in a table of repeated calculations. A firm concept of radian measure follows close behind.
Favorites(12)
Resources(14)
Worcester, MA
Environment: Urban

###### Is John Guilty
12th Grade Math » Trigonometry as a Real-Valued Functions
Big Idea: By analyzing data from an accident students will determine whether a driver was speeding when he wrecked his vehicle.
Favorites(0)
Resources(19)
Independence, MO
Environment: Suburban