
(Click on image above to run simulation.)

WhatŐs needed...
Resources: Shoe box tops;
toothpicks; computer applet and Geometer's
Sketchpad
Classroom Environment: Students in
groups with access to computers; teacher
demonstration station.
Strategy: Groups work together to
come up with a group prediction through
experimentation.

Introduction
One of the reasons
probability is one of my favorite topics to teach is
that it can lead to many surprises along with some
useful math done in interesting ways. The challenge
in this activity is to see if students can make a
prediction about the likelihood of toothpicks
landing on lines when dropped randomly using
experimental and theoretical data.
Preliminaries
 Make a set of shoebox top
toothpick tossing ŇarenasÓ.
 Draw equidistant, parallel
lines inside the shoebox top. The distance between
the lines should be the same as the length of the
toothpicks. Make one of these for each of your
groups.
 If you don't have the
boxes, you can demonstrate the experiment by
dropping the toothpicks on a tiled floor. Here I
dropped a bunch on a hardwood floor. (See photo
below. I highlighted the toothpicks and lines on the
floor. An adjustment will need to be made since the
toothpicks will not be the same as the perpendicular
distance between lines.)

Setting the Stage
 Have your students sit in
groups or teams. You are facing them standing next
to your one computer station. (Maybe even projecting
on a digital white board.) Show them an arena for
the experiment.
 Tell your class that they
will be answering a question that was originally
posed by a man named GeorgesLouis Leclerc, Comte de
Buffon about 250 years ago. "Suppose we have a floor
made of parallel strips of wood, each the same
width, and we drop a needle onto the floor. What is
the probability that the needle will lie across a
line between two strips?" (source: Wikipedia)
 Take guesses from your
class. Then ask them to explain their guess.
 Ask them: How might we
proceed to find out which student or group made the
best guess? LetŐs do the experiment to help us find
out.
Doing the Activity
 Hand out the activity sheet. Make
sure the students understand the instructions.
 Each group will drop 50
toothpicks 10 at a time on their parallel lined
arena.
 Students toss the
toothpicks and make their predictions about what the
class crossing average will be.
The teacher can do the
experiment with a student and show the results on a spreadsheet.
 By Group  Worksheet 1
 By Class  Worksheet 2
 Complete worksheet 2 with
the class. Who had the best guess? (Compare the
group results with individual group guesses.)
 After finishing, ask the
students how they might come up with even a better
or best "guess"? (Theoretical probability is 2/Pi or
approximately .6366197. See part
2 for more detail.)
Debriefing the activity and what about the
surprise?
 Go to this website: http://www.metablake.com/pi.swf
 Can you explain what is
happening?
 How did Pi get into the
act? Hint: Double
your number of your individual throws and divide it
by the number of crosses. What do you get? Check
with other groups. What can you conclude? (Your
answer is an approximation for Pi.)
 Why does this happen? (See
George Reese's explanation.)
Additional Resources
Updated:
3.19.13
