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Grades 6-8 Lessons: So Much Pi!
Three hands-on lessons to help kids understand and celebrate pi.
Standard Met: CCSS.MathContent .8.NS.A.2
Objective: Translate pi’s digits into a work of art
What You Need: Strips of paper or building printouts (equal in size), tape, colored construction paper, beads
What to Do: Scotland’s 2018 Teacher of the Year Chris Smith, who teaches students ages 11–18, is passionate about pi. He has shown his students that the possibilities for celebrating this infinitely long number are, well, limitless!
Start by discussing the value of pi. “Pi is not very big. It’s a wee bit more than 3, though less than 4,” says Smith. “But it’s infinitely long. It just keeps going and going and going, and there’s not a point at which a nice pattern develops.” To demonstrate pi’s infinite quality, have students visit this site, where they can search for a string of numbers, such as their birthdate, in the first 200 million digits of pi.
Then, invite students to work together to translate pi’s digits into a work of art. Smith has a couple of favorites.
On the walls of the school gym, Smith’s students pasted dozens of paper skyscrapers, or “pi-scrapers,” with heights corresponding to the digits of pi. For the first four digits—which are 3.141—start with a three-story building, followed by a one-story building, a four-story building, and another one-story building. How long can your students make their “pi-line”? Smith’s classes reached 150 digits of pi!
For a project he calls the Colors of Pi, Smith assigns a different color to each digit, 0 through 9. Then, he distributes colored construction paper or beads, and challenges students to make paper chains or beaded necklaces with colors corresponding to the digits of pi. They can make short or long necklaces, as long as the correspondence is correct. (See page 55 for pi trinkets you can make!)
Finally, challenge students to write and perform a song or spoken-word poem about pi. They can set it to the tune of a well-known song or make up their own melody and lyrics. Encourage them to weave in as much information about pi as they can. Have them visit this web page to check out Smith’s “Pi Maths Class Anthem,” otherwise known as “Pi.M.C.A.”
Standard Met: CCSS.MathContent.7.G.B.4
Objective: Find that pi is the ratio of any circle’s circumference to its diameter
What You Need: Circular household objects (plates, lids, etc.), masking tape, rulers, whiteboard, Twizzlers (optional)
What to Do: Mitchell Daar, who teaches middle school math in New York City, facilitates a lesson in which students discover pi on their own.
He starts by handing out a variety of circular objects and asks students how they would go about measuring the distance around a circle. “I give them a ruler partly as a joke but also to help them realize they can’t measure the circumference with it,” says Daar.
Next, he gives them masking tape to wrap around their circular objects. (He has also used Twizzlers—“when they use candy, they remember it for the rest of time!”) Students tear off two pieces of tape—one that is the length around the circle (the circumference) and one that is the length across the circle through the center (the diameter). Then, Daar has them tear off tape for two more circular objects and tells them to look for a pattern. “They start to see that there’s this relationship—that the circumference is about three times as long [as the diameter],” he explains.
Finally, they use rulers to measure the length of each piece of tape and then divide circumference by diameter. Daar records the data on the board, and together they calculate the average of all the ratios. “It’ll pop up as 3.1-something [every time],” says Daar. “It’s pretty powerful for them to see that!”
Standards Met: CCSS.Math.Content .7.G.B.4; 8.G.C.9
Objective: Apply the formulas for area of a circle and volume of a cylinder
to real-life situations
What You Need: Pizza shop menus and cardboard circles, dessert pies, rulers
What to Do: Amy Limke, a seventh-grade math teacher in Rockton, Illinois, has her students apply formulas involving pi to two real-life situations: pizza and pie (the other one)!
Activity #1: Pick up menus from a local pizza shop so students can see sizes and prices. Ask: “How can we determine which pizza size represents the best deal?” Explain that students can find out the cost per square inch of each size pie by determining the unit rate. First, challenge them to find the area using the formula A = πr2, or area equals pi (3.14) times the radius squared. Then, they should divide the price of the pizza by the area. The result will be the price per square inch. Once students know the price per square inch for each size, they will also know which pie is the better deal!
Activity #2: Have student volunteers bring in store-bought dessert pies. Ask: “How can we determine how many bites are in a pie?” Assuming one inch cubed is about the size of a bite, find out how many bites are in a pie to determine the volume. Measure the radius and height of the pie, and then use the formula for volume of a cylinder (V = πr2h, or volume equals pi times radius squared times height) to determine how many inches cubed—or bites—are in the pie. Once they have the answer, students eat their pie!
Photo: Courtesy of Chris Smith
A collection of activities from the pages of Scholastic Teacher magazine.