March 13, 2022
Recently I have been thinking about the importance and power of … storytelling in teaching and learning mathematics. Through … storytelling, students can engage in ways that develop a positive mathematical identity in which they see themselves as thinkers and doers of mathematics and as a mathematician. – Trena Wilkerson – President NCTM
A couple of Saturdays ago I went on a picnic with my wife and 3 friends. Among my contributions was a small apple pie which I bought at a local grocery store specifically because the price of the pie was $3.14 given that it was the day before π day – March 14th.
I shared the photo (above) with my college educated friends and asked them what was interesting about it. What came up for them was whether the price of the pie was reasonable. After a few minutes of discussion, I asked them why do you think the manager of the store picked such an unusual price. Normally, if you add the savings, it would be $3.99. Again, more conversation without any significant insights. So I threw out another bit of information. Tomorrow – Sunday – is π Day. “Really?” was the response, “I guess the bakery industry wants to promote the eating of pies tomorrow.” Of course, I couldn’t leave it at that. It was a perfect opportunity for me to see if I could jog their memory by giving them the definition of π. “π is a symbol used to identify the circumference of a circle divided by the diameter. And it doesn’t matter what the size of the circle is.” My audience was not impressed. One of them blurted out that he remembers that π was whole bunch of numbers. Now we were making some progress, I thought. So I continued, “π is a symbol that identifies the relationship of the circumference with the diameter. In fact, if the diameter were a string, we could wrap the diameter three and a little more times around the circle. That little more is about 1/7th of the diameter. So π is approximately 3 1/7 or 3.14 which is rather inconvenient. At least it was in 1897 when the Indiana House of Representatives tried to pass a bill initiated by Edward J. Goodwin, who wanted to make the number π more “convenient” such as 3.2. Watch the video below for the story line.
This story is great way to start a discussion of π with students or anyone else for that matter. What kind of number is it? It’s not rational for one thing. That is, it can’t be written as a ratio of two natural numbers. Another good way to prepare elementary students for a discussion of irrational numbers is to show them the video The Weird Number. The ending has students wonder about the existence of such non-rational numbers.
Here’s my π page. Link. For upper elementary and high school kids do the the Buffon Needle Surprise.
Here’s an interesting story about π called Homeless Pi.