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What does probability mean to you? The chance of snow tomorrow is 20%. The probability of winning the lottery is 1 in 4 million. These statements are common examples:
"which reflect the expression of people's assessment of the possibility of uncertain events which might occur. Such assessments influence the decision making process of people in business and government. The mathematical development of the theory of probability provides the logical foundation for such and other probabilistic statements, decision making processes and appropriate actions.... The concept of probability is simply a numerical assessment of the likelihood of the occurrence of some uncertain event.
from Probability and Statistics:
A No Nonsense Approach
by Alexander and Phadia, p.67
Assignment Exercises
Readings Bello & Britton, Sections 10.1-10.3 Wanda Weideman's article:
Problem Solving Math Class:
"Word Problems
Were Never Like This"http://www.enc.org/professional
/research/journal/math/documents
/0,1944,ACQ-107228-7228,00.shtm
Web Resources These web resources have links to probability sites.
1) The dice database:Experimental probability often differs from theoretical probability, and we need to understand that empirical probability will match theoretical probability - BUT maybe only in the long-run with lots of data gathered from many, many experiments.So, we are going to gather data on rolling two dice. Please roll two dice at least 100 times and record the sum of each roll. Enter your results in the dice database (http://www.enjoy.org:591/dice/). Then we will calculate to see how close we are to theoretical probability.
You may do this experiment with your own students, by yourself, or you can use the Dice Probability applet
(http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/intro_prob_models.html)2) Complete the following exercises.
Exercises
1) pp. 648-649, Ex. 2, 3, 5, 6, 7, 8, 9, 10, 14, 15, 26, 27, 28, 29
2) pp. 658-661, Ex. 1, 2, 4, 9, 16, 18, 22, 36
3) pp. 666-667, Ex. 5, 6, 7, 9, 10, 14, 26, 27, 28
4) To show how probability is used to make predictions about unknown populations ( fish in a pond, etc.) solve the Yellow Chips Game
http://www.learningwave.com/chapters/probability/zmachines/chips.html5) Complete the Fair Games Worksheet, an activity from Probability of the Middle School Mathematics Project (see bibliography). After deciding what would make a "fair" spinner or dart board, students can then create their own two-person game board.
6) What is wrong with each of these statements:
a) Since there are 50 states, the probability of being born in Alaska is 1/50.
b) The probability that a person smokes is 0.45 and that he drinks is 0.50. Therefore, the probability that her smokes or drinks is 0.95.
c) The probability that a certain candidate for congress will win is 0.60 and that she will lose is 0.25.
Buffon's Needle applet - interactive geometric probability
http://www.mste.uiuc.edu/reese/buffon/buffon.htmlThe Classic M&M Graphing and Probability Lesson Plan for grades 1-5
http://ericir.syr.edu/Virtual/Lessons/Mathematics/Probability/PRB0005.htmlComplete unit on probability
http://www.mathgoodies.com/lessons/toc_vol6.shtmwhere you can find great interactive probability spinner
http://www.mathgoodies.com/lessons/vol6/intro_probability.htmlGeometric Probability on the TI-82
http://www.ti.com/calc/docs/act/garvey4.htmIntroduction to Probability - the Math Forum's probability information
http://forum.swarthmore.edu/dr.math/faq/faq.prob.intro.htmlKen White's Coin Flipping Page- interactive coin flipping site
http://shazam.econ.ubc.ca/flip/Numbers, Please! The Telephone Directory and Probability - a site by Regina Brunner that shows how to use the telephone directory to generate random numbers.
http://www.nctm.org/mt/1997/12/90.09.numbers.htmProbability applet - has a 1/3 - 2/3 probability of falling off the cliff. Young people may? like this, but I had problems with the concept.
http://www.mste.uiuc.edu/activity/cliff/Probability Worksheets - for Neufeld Learning systems- the first page is matched with their program ( which you can download) but it is the other pages with the worksheets that might be helpful.
http://www.neufeldmath.com/worksheets/probability/Six lesson plans on probability - ranging for all grades from the ERIC Database.
http://ericir.syr.edu/Virtual/Lessons/Mathematics/Probability/Spreadsheets to estimate for probability simulations - all the formulas are listed at the site
http://users.interact.net.au/~phob/spreadsh.htmVisual Laboratories in Probability and Statistics - need to have more memory
http://www.math.uah.edu/stat/
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