It’s the day for PI! This has to be one of my favorite days, it doesn’t matter where I am in my curriculum, Pi Day always is a day of fun. There have been many different activities I have shared with my students this day, but this activity has been my go-to lesson lately.
Even though students know (well, most know) that Pi is an Irrational Number, students still do not have a clear concept of a decimal that never ends or repeats. My activity for the day consists of 3 major components, Division, Coloring and… M&Ms! Since I have 8th graders for math all day, the first activity is a whole grade one. On the SmartBoard I simply state the question- What is Pi? Students will put a variety of answers and as a class we talk about each one and evaluate whether or not it is a valid answer. Sometimes we have to take a few student responses and combine them into a new one, but in the end the only answers on the board are ones that students decide best answer the question. Most classes will state that Pi is Irrational, but then the concept of what that really means gets a little fuzzy.
So to start investigating what it means to be an irrational number, my students each get their own party pack of M&Ms! They open the pack and create their circle from the M&Ms inside. They then represent how many M&Ms are in their bag with graph strips (I use graph units that are scaled the same size as an actual M&M). They then are asked to estimate the diameter of their M&M circle. At this point most students create a strip that represents a whole number, say 5 unit boxes (this year there were a few students who surprised me by estimating 1/2, 1/4 and 1/8 of a unit box). At this point I ask students what Pi is. The overwhelming answer is 3.14, as this is what students are asked to use on standardized tests. I then ask if that is Irrational. This usually catches students off guard, they do not link the definition of an Irrational number to the number they know as Pi yet know Pi is irrational. So I ask them what Pi actually is. I can count on students to quickly flip to the glossary and find the formal definition, and we have a short discussion on what it means. Students then ask if they can find Pi for their circle, and of course I encourage it. Since we as educated teachers know that you can’t represent Pi as a ratio of two natural numbers, students once again question if their work is correct when they find an answer that is not 3.14 first, and one that ends or repeats after 5-6 decimal places. This again leads to a good class discussion on Rational and Irrational number definitions. Students then show their work on a paper plate display that they get to design themselves.
Geometer’s Sketchpad to the rescue! Using this, we construct a few circles and measure their Diameter and Circumference. Students now have a different set of numbers to use to investigate Pi. They start dividing decimals, and conversations about calculator are brought into play. Students decide to use calculators to help them in their long division and we start getting into longer decimal representations of Pi. I allow each hour to construct a circle and we each take turns calculating a digit of our estimated Pi. Students write their digit down on a circle and decorate it, and we see which class can get the longest decimal. Students who normally dislike long division will be creating a multitude of circles and calculations to beat other classes. I normally close the lesson at this point, and we reflect on the work we have done, why we did it and what it means.
The next day I ask for a volunteer to find Pi. I get some students who will show me a picture of an actual Pi or find the symbol somewhere in the classroom, but then one will ask if they can look it up. We display their search on the SmartBoard and as a side activity for the day, I have my classes cycle through writing down the digits of Pi and placing them in the hallway. Students see Pi accumulate throughout the day and they start asking me where they can continue posting the numbers. We start to weave throughout the building and have quite a long string by the end of the day. I get my other core teachers to allow my students to “take a tour of PI” and as they walk and realize how long it is, and there are yet more digits to find, they start to create a understanding of what an irrational number actually is.
A common theme of most of my projects is utility, and this one is no exception. I also come back to this project to talk about probability since students already have data from the M&M packets. It also refreshes the Pi experience and is a good refresher of the experiences and activities of Pi day.