11.1: Diameter and Circumference of a Circle
This activity is intended to supplement Geometry, Chapter 10, Lesson 4.
ID: 9844
Time required: 30 minutes
Topic: Circles
- Use technology to verify the circumference and area formulas for the circle.
Activity Overview
In this activity, students explore the relationship between a circle’s circumference and its diameter. This will lead students to their own discovery of a value for pi.
Teacher Preparation
This activity is designed to be used in a high school geometry clssroom.
- Students should already be familiar with circles, diameter, circumference, and pi.
Classroom Management
- This activity is designed to be student-centered with the teacher acting as a facilitator while students work cooperatively. Use the following pages as a framework as to how the activity will progress.
- To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
Associated Materials
- Student Worksheet: Diameter and Circumference of a Circle http://www.ck12.org/flexr/chapter/9695
- Cabri Jr. Application
In this activity we will
- Draw a circle
- Measure the diameter of the circle
- Measure the circumference of the circle
- Calculate the ratio of the circumference to the diameter.
Problem 1
Press APPS. Move down to the Cabri Jr. APP and press ENTER. Press ENTER, or any key, to begin using the application.
Press \begin{align*}Y=\end{align*} for the \begin{align*}F1\end{align*} menu and select New.
(If asked to Save changes? press \begin{align*}\leftarrow\end{align*} ENTER to choose “No.”)
Press WINDOW for the \begin{align*}F2\end{align*} menu, move down to Circle, and press ENTER. Press ENTER to mark the center of the circle, then move the pencil to indicate the length of the radius, and press ENTER to complete the circle.
Draw a line through the two points which determined the circle. To do this, press WINDOW for the \begin{align*}F2\end{align*} menu, move to Line, then press ENTER. Move the pencil until the point on the circle is flashing, and press ENTER. Now move the pencil until the center of the circle is flashing, and press ENTER. Press CLEAR to exit the line drawing tool.
Press WINDOW for \begin{align*}F2\end{align*} and move to Point. Move to the right and down to select Intersection. Press ENTER. Move the pencil until both the line and the circle are flashing. Press ENTER to mark the point which is the intersection of the circle and the line. Now we have two points on the circle which are the endpoints of a diameter
To measure the circle’s diameter, press GRAPH for \begin{align*}F5\end{align*} and move down and right to select Measure, D. & Length. Press ENTER.
Move the pencil until one endpoint of the diameter is flashing then press ENTER. Move to the other endpoint of the diameter and when it is flashing, press ENTER. Press + to see the measurement rounded to hundredths. The hand is active so you can move the measurement to a convenient location then press ENTER.
The Measurement tool is still active so now you can find the circumference of the circle. Move the pencil until the circle is flashing. Press ENTER then + to see the circumference rounded to hundredths. Move the hand until the measurement is in a convenient location. Press ENTER. Press CLEAR to turn off the measurement tool.
Press GRAPH for \begin{align*}F5\end{align*} and move down to Calculate. Press ENTER. Move the arrow until the circumference measurement shows a flashing underline and press ENTER then \begin{align*}\div\end{align*}. Move the arrow until the diameter measurement has a flashing underline and press ENTER again. The number displayed is the ratio of the circle’s circumference to its diameter.
To explore this relationship with other circles, press CLEAR to turn off the Calculate tool. Move the arrow until the point which defined the circle’s radius or its center is flashing. Press ALPHA to activate the hand. Grab the point and move it to change the size of the circle.
To confirm that the ratio is still 3.14, repeat the Calculate procedure. (It is actually being recalculated each time the circle changes, but it is impossible to tell this since the number is unchanging.)
To exit the APP, press \begin{align*}Y=\end{align*} for the \begin{align*}F1\end{align*} menu. Move to Quit, then press ENTER.
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