March/April 2000 Copyright © Information Today, Inc. |
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Let’s Make a Deal Math: The Study of Probability | ||
by Linda C. Joseph, Columbus (Ohio) Public Schools, Library of Congress |
[Editor's note: URLs mentioned in this article appear in the chart that follows.]
"Heads,
you go first; tails, I do.” “I need to roll a seven to win.” “If I can
spin and land on a green space the jackpot is mine.” How many times have
you played a game and hoped to win? What is the probability of winning?
Games can be fair or unfair, depending on the rules. Why are some choices
better than other choices? Introduce your students to some fascinating
problems and learn about probable outcomes.
Probability Introduction
Begin your study of probability
by having students flip a coin 50 times. Have them keep a record so they
can compare their results using a tally sheet. M&M activities are another
engaging way to introduce fractions, percents, and probability.
Ken White’s Coin Flipping
Page
Choose a penny or a dime
to flip. Input the number of times to flip the coin and click to start
flipping. A page will display the coins as heads and tails with the totals
at the bottom. In addition, results are given for the entire number of
coins flipped.
Coin Flipping
In this simulation you
flip a quarter and a statistical record is kept for heads and the probability
of getting a head—P(Head). Questions are posed regarding the expected probability
and their comparison to the found probability. Answers are linked on a
separate page.
m&m Candy Comparison
Making a Pie Graph with
ClarisWorks
Customizing Colors and
Text
Repeat steps 3 and 4 for the remainder of the legend. |
Mighty M&M Math
Another great place to
visit is the Mighty M&M Math Project, a self-sustaining Web site that
eliminates the need for registrations or deadlines. Here, students can
upload their M&M color data and compare their results with other classes
around the world. Great instructions for completing the activity are provided,
along with a link to the M&Ms network.
Probability Investigations
After establishing the
concept of probability, challenge students to tackle more complex problems
that involve more imagination and reason. What may or may not seem obvious
at first glance could lead to intriguing investigations and solutions.
The Birthday Problem
How likely is it that two
people in your class have the same birthday? How likely is it in other
classes? A concise explanation is provided with a formula for calculating
the probability of a match with N birthdays. If you want something a bit
easier, run 10 trials and observe what happens. The material at this site
is geared for middle and high school students.
The Cereal Box problem
“Hey kids,” the announcer
barks, “collect all eight of these great prizes in specially marked boxes
of cereal.” How many boxes would you have to purchase to get all of the
advertised prizes? Use this lesson as a springboard to explore experimental
and theoretical values. Run the cereal box simulation program that allows
you to select the number of prizes and log the trials. Trial statistics
include the number of trials, average, maximum, minimum, and range. After
several trials, collect the data and begin to draw conclusions.
The Cliff Hanger
Homer Simpson stands at
the precipice of a cliff. One wrong step will spell disaster. What advice
might you be able to provide Homer about his chances of escaping?
Monty Hall Problem
“Would you make a deal
to trade up to $500 in cash for one of these three doors, knowing behind
one of them is $3,254 in cash or valuable merchandise? Several people may
have to make that decision during the next few minutes as we bring you
the Marketplace of America—Let’s Make a Deal! And now, here’s America’s
top trader, TV’s Big Dealer, Monty Hall!”
The well-known Monty Hall Problem is based on the Let’s Make a Deal television show of the 1960s and 1970s. Show host Monty Hall would ask a contestant to pick one of three doors. Behind one of these doors was a large prize. Behind the other two doors were lesser prizes or a booby prize like a group of goats. Once the contestant picked a door, Monty would open one of the remaining two doors that did not have a good prize. Then, he would offer the contestant a chance to switch doors.
Take a box and cut three slots for doors. Put cardboard dividers in the back. Label the doors, Door #1, Door #2, and Door #3. Find two plastic toy goats. Use these for the booby prizes. Find candy money for the good prize. Pick one of your students to play the part of the host. Then choose contestants from the class. Before playing, have them predict whether or not it is better to switch doors after one is revealed. Tally the results on the Monty Hall Tally Table. Next, jump on the Web and have your students try one of the Monty Hall simulation games. What happened? Compare the results in your classroom.
Monty Hall, Three Doors
Monty Hall, Three Doors
is a fast-paced simulation game that records the number of times you keep
or switch your door and the experimental probability to win. A treasure-trove
of information regarding many aspects of probability is one click away.
Included are a variety of simulations that will stretch the minds of young
mathematicians.
Monty Hall
In this rendition of the
Monty Hall Problem, you select one of three boxes, then keep or trade your
box. A summary of wins and losses along with percentages is displayed after
each game. One additional choice is available for those who must know the
answer before making a decision. By clicking on the cheat button the winning
box will be revealed.
The Monty Hall Problem
High school students will
be challenged to think about solutions to various scenarios associated
with the Monty Hall Problem. Several formulas are suggested for calculating
the best strategies to use when keeping or switching doors. Experiment
with these strategies while playing the simulation game. Keep a journal
of the results and compare with others in the class.
Now Playing: Let’s Make
a Deal
Read the story behind the
Monty Hall controversy that began with a reader’s question to Marilyn Vos
Savant’s Sunday Parade column. View photographs of the famous game show
host and columnist. Then, play yet another version of the game, this time,
with photographs of goats, and a bright red car as the prizes behind the
doors.
Lessons
AITLC Teacher Lesson
Plan: Flipping Coins
This lesson is designed
for grades 3-6 and focuses on fractions using the Ken White Coin Flipping
site.
Bumped Again! Why Does
Delta Overbook?
The setup for this problem
states that 90 percent of the customers that have purchased a ticket check
in for a flight with 113 seats. If they sell 120 tickets, what is the probability
that at most 113 customers will check in? In this lesson a TI-83 calculator
is used for random-number generation and finding theoretical solutions.
Lessons on Probability
from Math Goodies
Many facets of probability
are presented and explained utilizing illustrations and a few interactive
examples. At the end of each lesson is a quiz covering the material for
each topic. Students will need lots of guidance from teachers in order
to understand and take advantage of this site.
Be sure to visit the MultiMedia Schools Home Page (http://www.infotoday.com/MMSchools) with active links to all of the Web sites mentioned in this article. Then fly over to CyberBee (http://www.cyberbee.com) for the Let’s Make a Deal WebQuest, more curriculum ideas, treasure hunts, research tools, and activities to use with your students and staff. |
Linda Joseph is the author
of Net Curriculum: An Educator’s
Guide to Using the Internet, published by CyberAge Books. The recipient
of numerous awards, in addition to her work in the Columbus Public Schools
and the Library of Congress, Linda is a part-time instructor for Ohio State
University. Communications to the author may be addressed to her at Columbus
Public Schools, 737 East Hudson Street, Columbus, OH 43211; 614/365-5277;
ljoseph@iwaynet.net.
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