Lessons

Re-create the methods used by early mathematicians to approximate the value of pi.

» The most common & useful method to illustrate is the way Archimedes (and others) would estimate the area of a circle by placing a regular polygon inside (and outside) it. The best place to start is with an inscribed hexagon, first finding the shape’s area and then deriving the value of pi as if it equaled the circle (the inside hexagon makes π = 2.598). Go to the octagon (π = 2.835) , and eventually the n-gon. You’ll close in on the circle and on the actual pi very slowly, but the rate at which you do is interesting in itself.
» In a class studying Trigonometry or higher, see if students can derive a formula to produce the estimate for pi given an inscribed circle of n sides! The answer: n sin (180/n) cos (180/n). This phrase becomes pi as n approaches infinity. At an n = 1,000, we have four correct digits of the number. At n = 1,000,000, we have ten. A rather inefficient way to compute pi!

Perform the very interesting Buffon’s Needle approach to estimating pi, which uses toothpicks and a lined piece of paper. If you don’t have the supplies & patience to act it out by hand, illustrate it with one of the many online simulators. Here are the best ones we’ve found.

Find the fair-share size of each slice of pie that your students are about to eat! As a demo or as group work, take the number of pies donated, an assumed diameter per pie, and the number of students in the class, and find the area of each piece when everyone gets an equal slice.

» For a further step, calculate the slice’s volume, or its surface area (assuming the pies are short cylinders!).
» Angie Mentges’ class at Sidney M.S. in Dayton, OH divided 11 pies among 28 students.

Bring in some big-ticket circular items for students to measure & estimate area, such as a rubber tire, a hula hoop, etc.

»»»» Students at Stephen Mack M.S. in Rockford, IL computed a pi of 3.114 after measuring a Goodyear drag-racing tire in class.

Pick up a menu from a local pizzeria, and based on the prices and stated sizes (12″, 14″, etc.), have students determine which pizza is the best value.

» At Stephen Mack M.S. in Rockford, IL, students even measured the semicircle size of their bites. “The pizza cost 6 cents a bite,” the teacher concluded.

Use string, rulers and round treats to check the value of pi. Make a number line (like an oversized ruler, perhaps) on the chalkboard, and have students mark their results on it. Compare them to the actual value of pi.

» Students’ results likely won’t be too close to 3.14! 3.10 or 3.18 would be pretty darn good. Discuss what’s causing the slight error, and whether the size of the circular object affects it.
» Fifth and sixth graders at Foothill Knolls Elem. in Ontario, CA measured Cheerios, Ding Dong cupcakes, crackers, M&Ms, and cookies for this project.

Hold a Pi Trivia Game, challenging students to find answers either in handout packets or the Internet on the history and uses of pi.

» Students at Holy Angels School in Dayton, OH took part in the 3.14 Trivia Game, where students looked for answers about pi mathematicians, and uses of the number in nature, art, and architecture.

Hold a “round coin” collection drive, asking everyone to, well, toss some circles in the jar. Maybe, in the end, count up the coins (by type, of course) and add up their total surface area?

» Leon H.S. in Tallahassee, FL raised $286 this way for the March of Dimes.

Read your students a Pi story, such as “Sir Cumference and the Dragon of Pi,” by Cindy Neuschwander. Or choose a selection from a more heady work, like David Blatner’s “The Joy of Pi.”

In small groups or individually, have students give a short speech (1-5 min.) on how pi, or math in general, is involved in their favorite hobbies.

» “They’re up there talking about soccer and horseback riding and ballet, but it gets them thinking about math and talking about math,” said Corrine Biscardi, of her students at Galvin M.S. in Wakefield, MA.

In honor of Albert Einstein’s birthday, have students make a display about the scientist, his life, quotations, and discoveries. Include poems and handmade birthday cards for old Al.