One of the reasons
probability is a favorite attraction 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 data.
- Make a set of shoebox
top toothpick tossing ŇarenasÓ.
Note: 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.
- 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
Setting the Stage
Doing the Activity
- 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 Georges-Louis
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:
- 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
- Hand out the activity sheet. Make
sure the students understand the instructions.
- Each group will drop a
total of 100 toothpicks 10 at a time on their
parallel lined arena.
- Students toss the
toothpicks and record them on the student sheet.
When finished each group will share their results
via a spreadsheet projected
onto the white board by the teacher.
Debriefing the activity and what about the
- Students help the teacher
to complete the summary spreadsheet.
- After finishing, ask the
students how they might come up with even a better
or best "guess"? (Theoretical probability is 2/Pi or
approximately .6366.) Who had the best estimate in
the class? Compare the group results with the
individual group guesses to determine who had the
closest estimate. (That is, the group that came
closest to .6366)
- Go to this website: http://www.metablake.com/pi.swf
- Can you explain what is
happening? Note the number that is constantly
changing. Does it seem to be getting closer to a
well known constant? It's Pi - approximately
- How did Pi get into the
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.)
- Watch this simulation.
1:17 min video.
Pi 2:07 min video. Teacher TV. Buffon's needle
experiment done using french bread and taped lines!
- Imagine throwing a green
dart onto an xy plane (dartboard) when a toothpick
crosses a line and a red dart when the toothpick
lands between the lines. After over 56,000 throws
here's what the dartboard looks like.
- To see the actual simulation done in Scratch go to here.