Happy Pi Day! Of course, this year’s Pi Day is the “Pi Day of the Century” because in a year that ends in ’15, the date reads: 3/14/15, the first five digits of pi. I’m sure you’ve had some fun at 9:26:53 when the date and time read a total of 10 digits, instead of the typical 8 digits.
It’s important to stress, not only the numerical value of pi, but the conceptual value, as well.
Yesterday, in my classes, we discussed the true meaning of pi, which is the ratio of the circumference to the diameter of any circle. The wondrous thing about pi is that no matter how big or small a circle may be, that ratio will always remain constant.
We discussed the concept of an irrational number versus a rational number, and why pi is usually depicted by a symbol. I’m glad that elicited the question of: “is pi a variable?” because it gave us a chance to truly discuss irrational numbers, and that any symbol can represent something, whether we know the value of that symbol or not. This led to a quick introduction of e, which my students will get to know intimately in a couple of years.
Since I am currently teaching 9th grade, my students have recently studied ancient civilizations in their global history classes, particularly the Phoenicians and King Hiram. This was important because I had my students engage in a close reading exercise of an ancient, non-fictional text that discusses Hiram and the construction of a round basin.
In this particular text, the dimensions of the cross-section of the outer circumference of the basin lead to the fact that pi may have been believed to be, in that time, “3.” Furthermore, we calculated the inner dimensions of that basin to show an even closer approximation to pi, approximately 3.139… . However, the dimensions given were in ancient measurement units, such as cubits and handbreadths. Some students knew what these measurements meant, and others did not, so the students who were aware explained and demonstrated that a cubit is the distance from one’s elbow to the tip of one’s finger, and a handbreadth is the width of one’s palm. I was pleased that my students engaged themselves in a discussion of standardized versus non-standardized measurements, and that it would be reasonable to assume that not every cubit or handbreadth is congruent. We concluded that the Phoenicians, typically considered to be a “first mover” of the times with their ship-making, purple-dye using, and trading, would be intellectually inclined to derive these dimensions. Or were they? Did they simply create the basin, and then perform the calculations? We may never know, which led to an even more in-depth discussion and interpretation of the non-fictional text. The inevitable: “is this going to be on the next test?!” question arose, but I quickly explained that it’s fun and interesting to engage in knowledge simply for the sake of knowledge. Being a well-rounded, educated individual is just as important as getting good grades.
To cap off the class, my students participated in a (very heated!) hand-drawn, circle-making contest. We discussed how we would know if a circle was “perfect,” by finding the ratio of the circumference to various diameters within that circle. We used a “percent error calculator” in an Excel file to find the percent error of some of the most eye-pleasing circles, and briefly talked about what percent error means, and how we can use it to inform decisions. We crowned a winner, who is now the prized owner of the below certificate!
I’d like to give a proper shout-out to Denis Sheeran (@mathedisonhsnj), a new PLN connection, for sharing some of this materials with me for this activity (don’t worry Denis, I changed the name of the High School on the certificate!).
So, in conclusion, discussing pi day in a high school setting can exist at an appropriate grade level. It is possible to integrate mathematical reasoning, scientific reasoning and measurement, historical context, and literary elements in the classroom to engage in a concept that begs to be dissected and discussed.
All this, and we didn’t even need a plate and fork!
And, if you really wanted to know, my own percent error was around 9%. I guess pressure got the best of me on that one! We did just finish a circles unit in Geometry, and I have been known to sketch some “wow, that looks amazing!” circles!