Applying Mathematical Concepts in IB Geometry to… Oreos!
How are formulas discovered? Where does pi come from? These are the questions that students explored this week in geometry. Leading up to this week, students discussed in general terms the ideas of order and chaos, and how we can make sense of the world by noticing patterns.
To continue this conversation, but now applying it directly to a mathematical context, students took a day to explore one of the most famous mathematical constants, pi. Before doing the exploration, students were asked to offer ideas on how they thought formulas were discovered. A number of students responded that it must have something to do with testing different math problems, and one student made the connection that in doing these problems, you would look for certain patterns, and then you would test your findings to see if the patterns are consistent. These were some great insights that lead directly into our activity for the day, which focused on discovering where pi comes from. To understand the origins of pi, students measured the circumference and diameter of various objects, including wood blocks, candles, cups, and even an Oreo cookie that they got to eat!
After taking these measurements, the class discussed their observations, and came to the conclusion that no matter how big or small an object is, if you take the ratio of the circumference and diameter, you always get pi. This information was then used to make sense of certain formulas involving circles, but even more so, it was used to understand that formulas are developed from concreate experiences that we can replicate ourselves. Examining and applying real world examples is only one of the many ways our IB learners are expanding their mathematical knowledge!