InterMath | Workshop Support | Write Up Template
Title:
Changes in the Circumference
Problem Statement:
Explore how changing the diameter of a circle affects its circumference. 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?
Problem setup:
I am trying to explore the affects of the circumference of a circle when I increase and/or decrease its’ diameter
by doubling, tripling, and halving it. I will also examine the relationship between the two.
Plans to Solve/Investigate the Problem :
First, I will construct a circle in GSP. I will measure the radius, diameter, and circumference. Then I will
construct circles that have a diameter that is doubled, tripled, and halve the size of the original. Finally, I will
compare all of the diameters and circumferences of the circles that have been increased and decreased and
determine why the changes happen.
Investigation/Exploration of the Problem :
First, using the tool bar, I constructed a circle in GSP. I constructed a segment between the center of the circle
(point A) and a point on the circle (point B), which created the radius. Next, I doubled the radius to give me the
diameter – because d = 2r. Finally I highlighted the circle and measured the circumference. I further
investigated the relationship between the circumference and diameter. I divided the circumference by the
diameter which calculated to be the approximate of  , which is true because circumference is found by
multiplying radius by 2 and by  . (As illustrated below, this also took place after I doubled, tripled, and
halved the diameter, circumference, and radius.)
Circumference
AB = 25.46 cm
m AB = 4.05 cm = radius
C
A
B
m CB = 8.10 cm = diameter
Circumference
AB
= 3.14
m CB
To double the diameter, I highlighted the original diameter of the circle and point c and constructed a circle by
center and radius, now the new circle is double the size of the original circle. It has a doubled radius, diameter,
and circumference.
Circumference c 1 = 50.91 cm
m CB = 8.10 cm = radius
C
A
B
D
m DC = 16.21 cm = diameter
Circumference c 1 
= 3.14
m DC
c1
To triple the diameter, I constructed the midpoint of line segment DC, which was point A of the original circle
(the center) – because I need it to be tripled not quadrupled. If I had highlighted the diameter of the doubled
circle and a point on that circle, as I had done previously, then the diameter, circumference, and radius of the
original circle would have quadrupled.
Circumference c 2 = 76.37 cm
m AD = 12.15 cm = radius
m ED = 24.31 cm = diameter
Circumference c 2 
= 3.14
m ED
E
C
A
B
D
c1
c2
To halve the diameter of the original circle I went back to only looking at the original circle. I constructed the
midpoint of the radius AB. By constructing the midpoint of AB I was able to find halve of the diameter,
circumference, and radius of the original circle.
Circumference c 3 = 12.73 cm
m FB = 2.03 cm = radius
C
A
F
B
m GF = 4.05 cm = diameter
G
Circumference c 3 
= 3.14
c3
m GF
All of these changes occur because diameter, circumference, and radius are all interrelate due to their
measurement formulas. One cannot change without simultaneously changing the others. This could have easily
been determined by simple multiplication, but it was much easier to visualize with the pictures.
Original:
Circumference
Doubled:
AB = 25.46 cm
Circumference
Tripled:
AB2 = 50.91 cm
Circumference
Halved:
AB3 = 76.37 cm
m AB2 = 8.10 cm = radius
m AB3 = 12.15 cm = radius
m CB = 8.10 cm = diameter
m CB2 = 16.21 cm = diameter
m CB3 = 24.31 cm = diameter
Circumference
AB
= 3.14
m CB
Circumference
AB2
m CB2
AB
= 12.73 cm
2
m AB = 4.05 cm = radius
Circumference
Circumference
= 3.14
m CB3
AB3
m AB
2
= 2.03 cm
m CB
= 3.14
2
= 4.05 cm
Circumference
AB
2
= 3.14
m CB
2
Extensions of the Problem:
If this were done in the classroom, I would allow the students to find all different size circle and have them find
the radius, diameter, and circumference and have them explore the relationship between them and further relate
and connect them to these GSP findings.
Georgia Performance Standards:
Geometry
Students will further develop their understanding of plane and solid geometric figures, incorporating the use of
appropriate technology and using this knowledge to solve authentic problems.
M6G1. Students will further develop their understanding of plane figures.
 Determine and use lines of symmetry.
 Investigate rotational symmetry, including degree of rotation.
 Use the concepts of ratio, proportion and scale factor to demonstrate the relationships between similar
plane figures.


Interpret and sketch simple scale drawings.
Solve problems involving scale drawings.
Measurement
Students will understand the systems of units for measuring perimeter, area, and volume. They will also
understand how to measure the volume and surface area of solid figures. Students will understand the systems
of units of measuring (customary and metric) and measure quantities efficiently.
M6M1. Students will convert from one unit to another within one system of measurement (customary or
metric) by using proportional relationships.
M6M2. Students will use appropriate units of measure for finding the perimeter, area, and volume and express
the answer using the appropriate unit.



Measure length to the nearest half, fourth, eighth and sixteenth of an inch.
Select and use units of appropriate size and type to measure length, perimeter, area and volume.
Compare and contrast units of measure for perimeter, area, and volume.
Author & Contact:
Mandie Pulley
mandie_pulley@yahoo.com

Important Note: You should compose your write-up targeting an audience in mind rather than just the
instructor for the course. You are creating a page to publish it on the web.