Middle school is the best time to celebrate pi because middle school students are learning about formulas for finding area and circumference, exploring ratio and proportion, and investigating irrational numbers. Pi is all of those! The Apple Pi unit from Illuminations is full of investigations and interactives that students can use to understand pi as a ratio; to understand how pi relates to the area of a circle as well as its circumference; and to understand what area, circumference, radius, and diameter each tell us about circles (check out the “Problems” tab on the Circle Tool interactive and get your students talking about grazing goats).

As your middle school students explore pi, the question of what pi is really equal to might come up. Is pi 3.14? 3 and 14/100? 3 1/7? 22/7? Read Dr. Math’s FAQ about pi, to see the great ways to explore what it means for pi to be an irrational. To help students visualize what it means that the decimal representation of pi is non-terminating and non-repeating, you can also celebrate pi day with a pi necklace. Discuss with students (or have students make) necklaces for 3.17 and 22/7. How do they look different from a pi necklace?

Do your algebra 1 students know that pi, because it is a ratio, is also a slope? In the Pi Line investigation from Illuminations, students “unwrap” circles of diameter x and place those unwrapped circles  perpendicular to the x-axis. Before you have students explore these unwrapped circles, have them predict what the graph of the unwrapped circles will look like. Will it be linear? Or will it be curved like a circle? Either before or after students construct their graph, they can grapple with what slope and rate of change would mean in this context. How would your students finish this sentence: “Increasing the diameter of a circle by one unit ______________ the circumference by __________________.”? Does their answer change after this investigation?