THE TASK:
 
You are going to determine the probabilities of winning two lottery games and report your calculations. The California Lottery has a listing of the odds of winning each game, you are going to prove their math.
 
After you have done your calculations you are going to create a PowerPoint presentation advising an adult friend or family member about playing the lottery games based on your mathematical knowledge and calculations.

THE PROCESS:
 
* You will work in pairs, but each student will be responsible for keeping a math journal of his/her work.
 
* You will be doing calculations and keeping notes relating to your presentation in your math journal. Make sure each set of calculations is clearly labeled and neatly done.

* You will complete the PowerPoint presentation as a pair.

 
* Go to the California Lottery website and click on each Game icon in the right frame to find out how to play each game. Choose "How to Play" to learn about each game.
 
* Everyone must analyze two games. One must be the Daily Derby or Daily 3 and the other is the team's choice (Super Lotto Plus, Hot Spot or Fantasy 5). What are all of the possible ways you can win? Calculate the probability of each way to win. Apply the ideas of permutations and combinations when determining the probability of winning each of these games. Verify all of the possible outcomes. (The odds are on the lottery website) Do your calculations agree with the Lottery Commission’s? How different are the odds and probabilities in the case of a lottery? (Answer these questions in your journal) Use the "LINKS TO HELP YOU LEARN ABOUT PROBABILITY" below to help you learn about calculating probability.

* You should be forming an opinion by now about the validity of our starting quote “The lottery: a tax on people who flunked math.”  Take a minute or two now and write a response to this quote in your journal. Why do you think she calls it a “tax”? Even if a person has a complete understanding of the probabilities involved, might they still play the lottery? Why do you think they might? (Answer these questions in your journal)
 
* Reflection Questions: What do you think about the wisdom of people’s decisions to sell their home and put all the money on the lottery? Could you actually spend enough to guarantee a win in a lottery like the Superlotto or Powerball? What if you are a very wealthy person looking to make a profit, would you advise trying to win the lottery as a way to actually make money? (Answer these questions in your journal)
 
* Create a PowerPoint presentation advising an adult friend or family member about playing the lottery games based on your mathematical knowledge and calculations. Include brief overview about the games and how to calculate the odds. You may base your advice on more than just your calculations.

Extension: Calculate the probability of other unrelated events to put the probability of winning the lottery into perspective.
http://sunsite.berkeley.edu/KidsClick!/
Kid'sClick Search engine created by librarians.
http://www.bls.gov/
U.S. Department of Labor Bureau of Labor Statistics
http://www.fedstats.gov/
FEDSTATS-The gateway to statistics from over 100 U.S. Federal agencies

 

LINKS TO HELP YOU LEARN ABOUT PROBABILITY:
http://www.calottery.com/
The official California Lottery website.
http://mathforum.org/dr.math/faq/faq.comb.perm.html
A helpful web page on calculating permutations and combinations
http://mathforum.org/library/drmath/view/56117.html
A helpful discussion of odds vs. probability
http://mathforum.org/library/drmath/view/56122.html
An explanation of how probabilities for a  “powerball” type lottery can be calculated
http://mathforum.org/dr.math/faq/faq.prob.intro.html
An introduction to probability
http://mathforum.org/library/drmath/view/56495.html
An explanation of the differences between odds and probability
http://mathforum.org/dr.math/faq/faq.prob.world.html
A good overview of why we need to know probability- and how it applies in the real world

LINKS TO HELP YOU WITH YOUR POWERPOINT PRESENTATION:
http://www.bitbetter.com/powerfaq.htm#anchor1939512
Powerpoint FAQ
http://imet.csus.edu/imet4/disbell/powerpoint/powerpointtutorial.htm
A PowerPoint tutorial that was created for teachers.
http://www.microsoft.com/mac/products/office/2001/powerpoint/ppt_default.asp?navindex=s1
Mactopia Powerpoint Tutorial and FAQ
http://www.roadtools.com/tips.html
Road Tools - Great Powerpoint Tips  
http://www.accd.edu/spc/it/ttc/powerpt/
Powerpoint Tutorial
http://dgl.microsoft.com/
MS Design Gallery Live - ClipArt & More  
http://www.graphicsland.com/powerpoint-templates.htm
Graphicsland-Powerpoint Templates
http://www.websiteestates.com/education/templatesindex.html
WebSiteEstates-Powerpoint Templates

 
EVALUATION:
http://imet.csus.edu/imet4/tlburke/probability/rubric.html Online Rubric
 
 
CONCLUSION:
After a close look at the math behind the lottery games students should be able to make an informed decision regarding the profitability of playing lottery games.
 
 
 
IF YOU JUST LOVE PROBABILITY- HERE ARE SOME MORE RESOURCES
http://illuminations.nctm.org/imath/6-8/BoxModel/index.html
box model to show probability
http://www-stat.stanford.edu/~susan/surprise/
has lots of different websites
http://www.schoolnet.ca/vp-pv/amof/
the amazing mathematical object factory- combination and permutation simulations
http://www.shodor.org/interactivate/activities/dice/index.html#
the dice table activity
http://www.shodor.org/interactivate/activities/#pro
list of activities
http://www.shodor.org/interactivate/activities/marbles/index.html#
marble bag probability activity
http://cap.epsb.ca/math14_Jim/math9/strand4/4203.htm
independent events- with dice, coins, spinners and simulations
http://www.dartmouth.edu/~chance/
chance course- great- look under teaching aids for discussion about lotteries

California Algebra 2 Standards Addressed:
18.0 Students use fundamental counting principles to compute combinations and permutations.
19.0 Students use combinations and permutations to compute probabilities.

http://webquest.sdsu.edu/
A link to information about webquests. This site is hosted by the Educational Technology Department at San Diego State University and updated by Bernie Dodge.

 CREDITS:
All images are from the California Lottery website.
 

e-mail Terri Burke