Activity Overview
The Discovery of Pi
With Cabri Jr., and hands on materials
Students will measure the diameter and circumference of various round objects and compare them to determine pi. They will then perform this acivity again utilizing the Cabri Jr. App on the TI 84 Calculator.
Before the Activity
Be sure to review cabri Jr. instructions with students. This activity can be done as a whole group activity or in smaller groups in the classroom. Students will need to know how to perform a linear regression. You may want to have additional circumference and diameter data on hand to utilize with the student data, for a more accurate depiction of pi.
Students will also need prior knowledge of lists.
Texas Essential Knowledge and Skills Addressed: G2B, G5B, G7B, G7C
During the Activity
The Discovery of Pi
With Cabri Jr., and hands on materials
Teacher Instructions
The students will measure the diameter and circumference of various round objects. They will report their measurements to the scribe and discover the relationship between the circumference and diameter. They will then enter their data into list and then plot their data. The students will then perform a linear regression on the data to determine the line of best fit for their data. Students will pay close attention as to why all of the points do not lie exactly on the line y=Pix.
Then students will then use Cabri Jr. to construct a circle and measure the diameter and circumference. The students will record their data in L1 and L2 and then plot their data, then they will perform a linear regression on the data and pay close attention to the equation that is found and then explain why all the points from this set of data lie on the line y=Pix . The students will record all data on the handout below. Have students complete the handout. The name of the activity is "Let's Gather Round the Circle". Once students have measured their objects, have them enter data for 2 lists (L1 should be the diameter, and L2 should be the circumference). Point out to students that some data will lie on the line, but not all of it will. When measuring by hand there is a margin of error. In the next section of the activity, students will measure the circumference and diameter of a circle constructed in Cabri Jr. Since time is always a factor in the classroom, I have the students find the radius and then multiply to find the diameter. Once students have created a circle on their screen they should press to grab the point and make their circle smaller or larger with the arrow keys and record the radius and diameter in the table. The students will then record their new data in Ω and and then plot their data.
After the Activity
Follow up with a study of Eratosthenes and how he determined the circumference of the earth or how Archimedes determined pi.