Monday, March 14, 2016

Happy Pi Day - Dominos, Measurement, and Differentiation


So today is Pi Day, as in 3.14.  My math students think about pie, and an infinitely long decimal, and sometimes stories of a classmate long ago who could reel off the first 25 digits, or the first 100 digits.  However, I want the students to come away with an understanding that Pi is actually the ratio of every (yes, every) circle's circumference to its diagonal. Pi is an irrational number, meaning it cannot be written as a fraction with integer numerator and non-zero integer denominator.  We didn't have a chance to organize a pie-a-palooza for today, so I brought in round cookies (okay, a stretch to think of them as mini-pies, but they certainly are desserts and they are mostly round). 
 I intended to have my students watch my favorite Pi Day video  (you've got to check this out!!), especially because after its mesmerizing 3 minute 14 seconds (hey, wait a minute....) it explains the math in a very accessible way.  Then they would measure the cookies, measuring circumference with a string, and diameter and finding the ratio, and going from there.  Thanks to my colleague for sharing her idea, which was a table for measuring lots of round objects.  I borrowed it, wrote "cookie" in the first row, stacked a variety of round objects on the table,  and added some differentiation for my different classes as follows:  

My seventh graders watched the video and measured, calculating ratios.  We will discuss their results tomorrow.
One eighth grade class watched the video, measured, then built a scatter plot of their results with the data and drew a line of fit. I will show them how to find the line's equation tomorrow.
The other eighth grade class did all of the above and generated equations for the line of fit, which we wrote on the board.  Tomorrow we will compare equations, thinking the slope of each should be near 3.14.  Hmmmm. 

So, I spent Pi Day without eating a bite of pie, which is fine with me.  My students came away from Pi Day having eaten a well-measured cookie, understanding that Pi is irrational, and that it is the ratio of circumference to diameter of each and every circle.  Everyone was engaged! It was a very good day.


No comments:

Post a Comment