Summary
This activity explains the difference between experimental and theoretical probability.
Materials
Additional Resources
Books
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Everyday Mathematics, University of Chicago; ISBN 1-57039-510-1
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Elementary and Middle School Mathematics, by John A. Van De Walle
Background for Teachers
Probability is experimental and theoretical (anticipated).
Experimental probability describes the actual event, "Will you
absolutely roll a 5 in 6 rolls?" You may or may not, etc. When we
are determining the probability of something we are figuring out the
theoretical (anticipated) probability. e.g., "I have a 1 in 6 chances
of rolling a 5 on a dice. If possible students should have the chance
to experiment with probability, then move into the theoretical
(anticipated). They need to know and understand the concepts of,
experimental and theoretical (anticipated) probability.
Instructional Procedures
Invitation to Learn
With a partner, flip a coin 20 times and make a tally chart of the
number of heads and tails. Record this in your math journal or on a
piece of paper and be ready to share your findings.
Instructional Procedures
- Discuss the results from the Coin Flip activity. (Similarities
and differences) Discuss what the chances (head or tail) are for
each flip.
- Talk about experimental probability (which is what they
just did). Discuss what the students think they should have
flipped if they flipped 20 times. (10:10) Show on the board
the theoretical probability of flipping a coin (tree diagram).
-
Show the diagram of Pigs in a Pipe on the overhead. Explain
that there will be 80 balls going into this machine. They will
go different directions and we will need to find out how many
(of the 80) end up in each dumpster. They will split evenly,
with the same amount going down each pipe. Work this
through together, students on their paper and you using the
overhead. Suggestion for teachers: use 2 different colors of
overhead markers on this activity, one color for the fractions
and one color for the numbers going into the pipe. The goal
is to find out what percent of the balls end up in each of the
dumpsters.
- Play The Stick Game. Pass out three sticks per small group.
The students can get the sticks ready for the game by coloring
them. Two of the sticks should be red on one side and plain on
the other. One stick should be blue on one side and plain on
the other. Use the backline for the instructions on coloring the
sticks and for playing and scoring the game.
- Record then discuss what happens during the game in student's
math journals or on a piece of paper.
- After the majority have finished, discuss what happened and
then as a class write the theoretical (anticipated) probability
on the board, the answer. Discuss how the experimental and
theoretical can be similar. When doing the tree diagram on
the board, use 3 different colors of markers (chalk), one color
to represent each stick.
Strategies for Diverse Learners
- Advanced learners could be given a tree diagram and have
to come up with the situation, numbers and provide the tree
showing who or what ended where. e.g., similar to Secret
Rooms, Family Reunion, etc.
- ELL and others will work with a partner.
Extensions
- http://www.rainforestmaths.com Site where students can work
together on chance and probability.
Family Connections
- Have the students take the worksheet The Game Show home to
do with their family.
- If they have Internet available go to http://www.rainforestmaths.
com/ and then into 6th grade, then into chances and probability.
Assessment Plan
- Students will be given another situation, Secret Rooms, in
which people will be going into a pyramid (You can decide the
number of people). Then in their journals they write about the
situation, how they figured it out, and draw their tree diagram.
- Given a word situation, such as, Family Reunion, the students
will be able to draw a probability tree diagram to show their
answer.
Bibliography
Bright, G.W., Frierson, Jr., D., Tarr, J.E., & Thomas, C. (2003). Navigating
through Probability in Grades 6-8. Reston: The National Council of Teachers of
Mathematics, Inc.
This book addresses many aspects of probability.
It mentions that learning how to use, and using tree
diagrams helps in understanding probability. Tree
diagrams also help build conceptual understanding. Many
ideas and ways to teach probability and applications are
provided.
James, Alisa, (2005), Journaling as an Assessment Option, ERIC Source,
November 25, 2006, from http://www.eric.ed.gov
This research states that journaling is a tool that
can assess student learning in affective and cognitive
domains. It allows students a nonthreatening
environment to communicate their knowledge.
Created: 07/06/2007
Updated: 02/04/2018
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