“Let’s Find Pi with Calculators” – A Pi Day Activity
- Bruce Hartman
- 42 minutes ago
- 4 min read
As a math teacher, Pi Day’s one of my favorite holidays of the school year. I love to hype up the day and celebrate in my classes. Personally, I look forward to the latest Pi Day challenge, figuring out the math and logic riddles to eventually join the Genius Board. We analyze the lyrics of one of my favorite mathematical parodies, “Pi Rap Battle - Lose Yourself (in the Digits)” on YouTube. Another way we have celebrated is by writing a “Pi-Ku” which takes a pi-inspired spin on the traditional Haiku poetry format. Pi-Ku’s have stanzas with lines of 3, 1, and 4 syllables instead of 5, 7, and 5. An example of a Pi-Ku would be “Let’s find π, with, calculators!” which leads us to today’s blog focus: using calculators to experimentally determine the value of π by measuring the circumference and diameter of everyday circular objects.
This activity itself may have the world record for longevity! The first attempts to calculate π in this way date back to the Babylonians and Egyptians nearly 4000 years ago. Using ropes to measure the diameters and circumferences of massive circles, the value of π then was found to be slightly greater than 3, with an estimate of around 3 1/8. In this modern classroom activity, students can use calculators to find a closer approximation of π in multiple ways.In these activities, our circles will be much smaller in diameter than the ones used in ancient times. Either pieces of string or a soft tape measure can be used to find the circumference, with solid rulers better suited for measuring diameters. For ease and accuracy of measurements, rulers and tapes with centimeter scales are recommended. Depending on the time and availability of classroom resources, values for some circular objects can be prepopulated in their tables, whether measured beforehand or found online, such as the dimensions of US coins. A large roll of tape can be cut to the length of one circumference with little error in diameter. After obtaining a few measurements, this activity can be varied across different grade levels: early middle school, late middle school, and high school. A surprise gift can be given to the group with the closest value to π! In the attached video, I will demonstrate each middle school variation of this activity using the Casio fx-300ES Plus 2nd edition scientific calculator and the high school activity using the Casio fx-9750GIII graphing calculator. In each video, I will use the values in the following table to demonstrate.
Early middle school students can create a table of their measurements and use the calculator to determine the value of each circumference divided by its diameter. I find it is best to have the calculators set to Line Output to show decimal results automatically. After finding the ratio for each item, they can then average their results to find their best estimate of π.
In late middle school, students will study proportional relationships, leading to their first encounter with linear equations. To analyze their values, they can create a data plot to draw in their line of best fit. Using points on their line, they can calculate the slope. Since this linear relationship is proportional, the slope is the proportionality constant between circumference and diameter. Going further, they can compare their slope by hand to the slope calculated using a linear regression. Their data can be entered into the statistics app of a scientific calculator to determine the equation of the “perfect” line of best fit. This regression model will determine the y-intercept and slope of the line of best. The slope should be close to π, as the formula for the circumference of a circle is C=πd. The y-intercept should be near zero, as it is a proportional relationship.
Note: If you are using the fx-991CW or fx-9910CW Classwiz 2nd Edition calculators, check out the Casio Curriculum Alignment page for detailed instructions from a similar activity involving circumference and diameter from IMv360 – Gr 7 Unit 3:Lesson 3 which shows two other methods of analyzing the data. One set of instructions uses the Spreadsheet App while the other uses the Statistics App to create a QR Code, which can be scanned to view a Scatter Plot of the data in www.ClassPad.net.
For high school, this same activity can be extended to allow students to analyze their own measured data versus practice data from textbooks or prior exams. I feel that when student-created data is incorporated into an activity, greater engagement and discussions happen. Currently, my Algebra 1 students are working on analyzing 2-variable statistics by creating x-y scatter plots, finding the linear regression equation, and using the correlation coefficient to determine the fit of their data. In my state, graphing calculators are required for high school exams. I stress to my students to view the data as a scatter plot before completing the regression for two reasons. At this level, I want them to double-check for any ‘visual’ typos in their entered data and verify the ‘shape’ of the data to choose the best regression model. Once they have the linear regression equation calculated, they can draw it in the data plot and copy the equation to a function variable to further analyze in the graph or table apps. The attached video will show you the process using the free fx-9750GIII graphing calculator emulator embedded within www.ClassPad.net.
Remember, if your high school does not use graphing calculators, the linear regression equation and r-value can also be found using scientific calculators, as shown in the last middle school example.