Every year on 14 March, written 3/14 in the American style, maths classrooms around the world celebrate Pi Day. It began in 1988 at the Exploratorium, a science museum in San Francisco, where the physicist Larry Shaw marched staff around a circle and handed out fruit pies. Since 2020, 14 March has also been UNESCO's International Day of Mathematics.
Here are five activities that work with mixed ages, need almost no preparation and keep nobody's personal details. At the bottom of the page there is a worksheet: print this page and the chalkboard disappears, leaving plain ink on paper.
1. Measure a circle (any age)
Hand out string, rulers and a pile of round things: paper plates, tins, rolls of tape, a bike wheel if someone has one. For each object, pupils wrap the string around the edge to measure the circumference, then measure straight across the middle for the diameter. Then they divide the first by the second.
Collect everyone's answers on the board. They won't be exactly 3.14159, because string stretches and rulers wobble, but they will crowd around 3.1. That is the big idea of π: for every circle, big or small, the distance around is a little more than three times the distance across.
Talking point: which objects gave the best answers? Usually the biggest ones, because a small measuring mistake matters less on a big circle.
2. Find your birthday (ages 8 and up)
Everyone looks up their birthday on the home page. Pupils don't need to type anything private: a birthday, a favourite number or their first name works just as well.
Then plot the class on a long strip of paper, roughly by how deep each birthday hides. Rounding is plenty: "about 300,000 digits in" is fine. Who is deepest? Then ask the key question: why do birthdays written with eight digits (14031999) hide so much deeper than ones written with six (140399)?
The answer: each extra digit makes a number about ten times harder to find, so two extra digits push it about a hundred times deeper.
3. Name fight (ages 7 and up)
Two pupils each put their first name into a Name Fight. Every letter becomes a digit on a phone keypad, and whichever name turns up first in π wins.
Run a tournament, then ask: is it pure luck? Pupils usually notice that short names win a lot. That is not unfair, it is maths: a three-letter name is a three-digit number, which is far easier to find than a seven-digit one. Older pupils can read the maths of how far apart we are.
4. Dial a digit (any age)
Choose a position, say decimal 100, and ask everyone to guess the digit there. Then dial it and reveal the answer. Repeat ten times and count the class's correct guesses. Since there are ten possible digits, each guess has one chance in ten of being right, so a class of thirty should get roughly three right each round.
Good positions to try: decimal 10 (it's a 5), decimal 100 (a 9) and decimal 762, where six 9s in a row begin. Read about that last one in the Feynman point.
5. Memory relay (older pupils)
Teams learn ten new decimals a day with the Memory Trainer in the weeks before Pi Day, then recite them in turn on 14 March, one digit per pupil, round and round. The team that gets furthest without a mistake wins a pie (or, more realistically, a round of applause).
Questions for discussion
- Is every number in π? How could you ever be sure? (Our honest answer.)
- Why is 22/7 a good guess for π, and when does it go wrong? (22 ÷ 7 = 3.142857…, which is right for two decimals.)
- Why do we celebrate on 14 March in some countries but write the date as 14/3?
Worksheet: my Pi Day
Name: ____________________ Class: __________
Part A: measure three circles. For each one, write down what it is, then measure.
- Object: __________ Around (circumference): _____ cm. Across (diameter): _____ cm. Around ÷ across = _____
- Object: __________ Around (circumference): _____ cm. Across (diameter): _____ cm. Around ÷ across = _____
- Object: __________ Around (circumference): _____ cm. Across (diameter): _____ cm. Around ÷ across = _____
Which answer was closest to 3.14? __________
Part B: digits.
- Write the first six digits of π: ___ . __________
- Guess the digit at decimal 100: _____ Now check it on the dial. Was I right? _____
- Work out 22 ÷ 7 to four decimals: __________ How many decimals match π? _____
- Work out 355 ÷ 113 to seven decimals: __________ How many decimals match π? _____
Part C: think.
- A name with 4 letters and a name with 6 letters have a Name Fight. Which one do you think usually wins, and why?
- Do you think every number is in π? Explain your answer.
Answers for the teacher: 4. 3.14159. 5. A 9. 6. 3.1429, two decimals match. 7. 3.1415929, six decimals match. 8. Usually the 4-letter name, because a 4-digit number is about a hundred times easier to find than a 6-digit one. 9. Nobody knows for sure! Any well-argued answer is a good one.
Sources
- Wikipedia: Pi Day
- International Day of Mathematics, UNESCO's 14 March celebration.
- US Congress: H.Res. 224 (2009), supporting National Pi Day
- Wikipedia: Approximations of π, for 22/7 and 355/113.