By Teachers, For Teachers
Today we celebrate one of the most famous ratios in the world—certainly the most famous irrational ratio. Pi is the ratio between a circle’s diameter (the distance across the circle) and its circumference (the distance around the circle). Some of the greatest minds in history, including Archimedes, Liu Hiu, Newton, Euler, and Gauss have worked on better and better ways to calculate this incalculable number. Your students don’t need to tackle that problem today, but if you’re looking for a way to get them thinking a little bit about the mysteries of geometry, we’ve got some ideas for you.
Pi isn’t just a mathematical concept, it’s been vital to history and culture since ancient times. Have students select one of the following historical figures or settings and do a little research to see how they contributed to the world’s knowledge of Pi, and how being able to use Pi helped them advance culturally or scientifically.
To understand why Pi is so important, students have to understand some mathematical concepts first. On the board, draw a three-column K-W-L chart. Down the left side, write the following vocabulary terms:
Have volunteers tell what they know about the terms. Write the main points in the “K” column. Then, have volunteers ask questions about the terms. Write these in the “W” column. Finally, have students research the answers to these questions using their textbooks, the internet, or the school library. Finally, have them share their answers with the class and write them in the “L” column.
Younger students may have trouble understanding the mathematical language surrounding Pi. But that doesn’t mean they can’t get a grasp on the idea. All you need to teach elementary students about Pi is a long piece of string, a ruler, and a few common classroom objects.
Gather a few tubular objects, such as mugs, cans, water bottles, even thick markers. Break the class into small groups and distribute the objects to the groups, along with string and rulers. Demonstrate to students how to wrap the string around the objects, mark the string, and then measure the length of string they used to figure out the distance around the object. Then have them use the ruler to measure the distance across the objects. Have the groups work together to measure each object in these two ways and record their results.
Finally, have students use calculators or computers to divide each distance around an object by the distance across the same object. Have them share their calculations. Note the pattern that emerges—all the calculations should be about 3, or a little bit more. This is because Pi is a constant. No matter how big the circle, dividing the distance around the circle by the distance across the circle always gets you the same result.
The current world-record holder for learning the digits of pi is Akira Haraguchi, who recited 100,000 digits of Pi over the course of 16 hours. Memorizing digits of Pi doesn't make you a math genius, but it is a way to learn some good memory techniques. Here are a couple of good ones:
Sentence Mnemonics: Create a memorable sentence where the length of each word corresponds to a digit of Pi. For example, the sentence "How(3) I(1) wish(4) I(1) could(5) calculate(9) Pi(2)" can help you remember that the first seven digits of Pi are 3.141592. Longer sentences can help you remember more digits.
Major Mnemonics: A little more ambitious? You can try the Major memory system, which helps you remember numbers as sounds. You can learn about the full technique on the web, or even with an iPad app.
Singing Mnemonics: One of the best guides to memory is song--it's how we remember the alphabet, after all. Breaking the digits of pi into groups and learning to sing them can help you learn more digits than you'd believe. And if all else fails, there's always the Pi Song.
Finally, be sure to check out our Pi Day video. And let us know what you plan to do today in the comments!