Pi Day (Grades 6-12)

Graphic: Brian Deep

Because pi (the ratio of the circumference of a circle to its diameter) is an important concept in mathematics and science, March 14--3/14--has been proclaimed as a special "pi day." Scientists have explored the concept of pi, an irrational number, beginning perhaps as far back as 4000 years ago and continuing right up to the present. Early evidence of the use of pi can be found in civilizations ranging from Ancient Babylon to Greece, Egypt, and China. In fact, some time between A.D. 430 and 501, a Chinese astronomer estimated pi to a value that was so accurate that it took a thousand years before its accuracy was matched in Europe. In 1596, a Dutch mathematician helped to expand the calculation of pi to 35 places by figuring out three more digits. It is said that he had those three digits, 388, inscribed on his tombstone. With the advent of the computer, pi has been calculated to over 51 billion decimal places!

Connections

Here are just a few suggestions for making the day special:

• Celebrate pi day by having students create and display pi day cards, pi day poems, or pi day posters.
• Celebrate with food. The food connection is punningly obvious--students can share a pizza pie or apple pie but first must figure out the circumference and the diameter.
• Celebrate with this problem: Some people celebrate pi approximation day on July 22, sometimes written as 22/7. Why? (As you probably already know, in fraction form, pi is approximately 22/7.)
• Play the What's Pi Anyway? game. Put a number of research questions in a bowl, and have students, working in small teams, pick a question. Questions should ask about the development of pi. For example, who were the key groups or people involved in determining its existence and usefulness? When did people begin to use pi in their calculations? Do mathematicians continue to compute pi, and if so, why? Let the teams research their answers and report their findings to the class.

Web Resources

1. The Pi Pages
   
   http://www.cecm.sfu.ca/pi/pi.html
   A super site, good for middle school students and even better for high school students. Covers the history of pi, people who computed pi values, news about pi, pi art, and lots more.
   
   
2. A History of Pi
   
   http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html
   An interesting treatment of the history of pi, with a number of web links and a reference list.
   
   

Ready-to-Go Activities

1. Buffon's Needle: An Analysis and Simulation
   
   http://www.mste.uiuc.edu/reese/buffon/buffon.html
   (Part of ENC#002429) Grades 11-12. Suppose you drop a needle on a piece of lined paper. What are the chances that the needle will land across one of the lines? The site provides an applet for simulating the problem, plus its surprising connection to pi and an explanation of the math behind it.
   
   
2. Making a Pi Necklace
   
   http://mathforum.org/teachers/middle/activities/pi_day.html
   A seventh grade teacher uses this activity as a way to introduce irrational numbers.
   
   
3. Activities for Pi Mathematics
   
   http://archive.ncsa.uiuc.edu/edu/RSE/RSEorange/Piactivities.html
   (Part of an ENC Digital Dozen selection, ENC#004496) Middle school activities.
   
   
4. Pi Day Songs
   
   http://www.winternet.com/~mchristi/piday.html
   Appropriate for 3/14 of any year and usually sung at 1:59 p.m., of course.
   
   
5. Archimedes and the Computation of Pi
   
   http://www.math.utah.edu/~alfeld/Archimedes/Archimedes.html
   An applet for middle and high school geometry students that lets them investigate Archimedes' computation of pi graphically and interactively.
   
   
6. Graphics for the Calculus Classroom: Archimedes' Calculation of Pi
   
   http://www.ima.umn.edu/~arnold/graphics.html#archimedes
   (Part of an ENC Digital Dozen selection, ENC#004507) Grades 11-12+. Archimedes' approach is illustrated here in a sequence of slides.
   
   
7. The Pi Trivia Game
   
   http://eveander.com/trivia/
   For high school students and up. It makes you ponder questions you've probably never thought of, such as what is another name for pi in German. Using a multiple-choice format, this game is quite a challenge and also great fun!
   
   
8. Famous Problems in the History of Mathematics: Finding the Value of Pi
   
   http://mathforum.org/isaac/problems/pi1.html
   (Part of an ENC Digital Dozen selection, ENC#013284) Grades 6-12+. Besides the history of humankind's understanding of pi, this site offers a page of values of pi calculated throughout the ages.
   
   
9. Monte Carlo Estimation for Pi
   
   http://polymer.bu.edu/java/java/montepi/MontePi.html
   Grades 11-12. How closely can you estimate pi by throwing darts at a figure of a circle inscribed in a square? After you read about the problem, try the applet to find out.
   
   
10. Pi Mathematics
    
    http://archive.ncsa.uiuc.edu/edu/RSE/RSEorange/buttons.html
    (An ENC Digital Dozen selection, ENC#004496) Grades 5-8. This web site for middle school classes provides students with a variety of activities to explore the concept of pi, such as discovering the approximate value of pi.
    
    

Classroom Resources from the ENC Collection

1. The joy of pi
   Featured in ENC Focus  
   Date: 1997 Grade(s): 6 - 12 Cost: $12.00 ENC#: 018556
   This colorful little book is delightfully informative and interesting! Speckled throughout the text, you'll find sidebars (and "sidecircles") filled with pi trivia, jokes, quotes, and factoids. Running throughout the text, you'll find the first 1 million decimal digits of pi. And filling the chapters, you'll find the history of pi and more, including accounts of world record-breaking calculations of pi such as the story of the Chudnovsky brothers who calculated pi to 8 billion digits using a supercomputer they built in their Manhattan apartment! If you and your students want to challenge your memory, check out the Memorizing Pi chapter for mnemonics, poems, and other tricks for recalling numerous digits of this illustrious number.
   (For more details see ENC Record)
   
   
   
2. The story of pi
   Date: 1989 Grade(s): 9 - Post-Sec. Cost: $29.95 ENC#: 000894
   This animated videotape and accompanying workbook, a supplement for high school and community college courses, defines pi and tells about its early history, uses similarity to explain why the ratio of the circumference to the diameter is the same for all circles, gives animated proofs of the perimeter and formulas of a circle, and shows Archimedes' method for estimating pi.
   (For more details see ENC Record)
   
   
   
3. Sir Cumference and the dragon of Pi: a math adventure
   Featured in ENC Focus  
   Date: 1999 Grade(s): 4 - 7 Cost: $6.95 ENC#: 014832
   This is a fun book for students just learning about pi and also for those who are pi "experts"--they all will appreciate the cleverness of the story. You might want to make sure that students note the last page of the book, where it explains that pi is usually written in decimal form and that numbers to the right of the decimal are about equal to a seventh.
   (For more details see ENC Record)
   
   
   

Search Strategies

Find more materials by searching Curriculum Resources on ENC Online using these terms: Archimedes (287-212 B.C.), Circles, Euler, Leonhard (), Irrational numbers, or Pi.

Connections to Standards

Realizing that there are many ways to use this Classroom Calendar entry, we chose these standards because they relate to the entry, in full or in part. If you want to explore the standards further, please use the link(s) provided.

Connections to NCTM Standards
Connections: Recognize and apply mathematics in contexts outside of mathematics
Geometry: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Measurement: Understand measurable attributes of objects and the units, systems, and processes of measurement
Measurement: Apply appropriate techniques, tools, and formulas to determine measurements