Intermath | Workshop Support
Lesson Plan

Changes in the Circumference

Circumference in the circles

What happens to the circumference of a circle if you double the
diameter? If you triple the diameter? If you halve the diameter? As the
diameter increases (or decreases) in measure, how does the
circumference change? Why does this change occur? 

Grade levels
Grades 6 to 8


We decided to solve this problem by using Geosketchpad.  We constructed a line segment and then drew three circles:  one doubled, one tripled and one halved.  We came to the conclusion that when the diameter is doubled, the circumference is doubled, when the diameter is tripled, the circumference in tripled.  We also found when the diameter is halved, the circumference is halved.  As an extension, we decided to find the relationship of the area to the diameter

After exploring with the Geosketchpad, we decided to explore with Excel.  We found the relationship was confirmed that we found with Geosketchpad..

The results are shown here:

Lesson Type (lab, demo, worksheet, hands-on, other)
Hands-on, computer

Estimated time
Approximately one hour

Resources & Materials
Geosketchpad file

Excel Spreadsheet

NCTM Process Standard(s)
(may be more than one. Standard(s) need to appear here, not just reference number)

Author & Contact
Peggy Reigle

Link(s) to lesson plan and other materials
Link to Lesson Plan 1
Link to Lesson Plan 2