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Facing the Odds: The Mathematics of Gambling and Other Risks


The purpose of this curriculum is to enhance students' interest in mathematics and provide the knowledge and skills that can help students to think more critically. This curriculum aims to make mathematics more meaningful to students and more relevant to their daily lives by introducing concepts of probability and statistics through the use of gambling- and media-related topics. With the proliferation of gambling opportunities throughout America, young people have exposure to, and inherent curiosity in gambling-related matters; this curriculum uses this curiosity to present important mathematical concepts. For example, students will learn about randomness and chance as these concepts relate to probability and gambling, the probability of winning the lottery, and the use of statistics in the media and everyday life. This curriculum also will help students to develop critical thinking and number sense skills and to apply these skills to media, advertising, and gambling issues. In particular, students will learn to make decisions and choices about gambling activities based on mathematical reasoning. Contemporary research shows that gambling behavior is prevalent among youth and that a proportion of young people are experiencing problems related to gambling. This curriculum provides an opportunity for students to learn about mathematics through relevant contemporary social issues has the potential to increase student interest in mathematics and concurrently to diminish the likelihood of the development of addictive behaviors.

How To Use This Curriculum


Due to its size, the curriculum has been divided into separate sections that can be downloaded to your hard drive. Once downloaded, you need to decompress the files with an utility like WinZip. This will allow you to view and print the different sections for personal or classroom use. You will need Adobe® Acrobat® Reader® to view and print the files. Some sections also include supplemental files as teaching resources for teachers. The supplemental files are overhead slides intended for classroom use. These files have been saved as Microsoft PowerPoint®. If you don't have Microsoft PowerPoint® installed in your computer, you can download a free PowerPoint® viewer from the Microsoft web site.

Downloads


Section Title Description Download ZIP (file size) Download Supplemental PowerPoint Files
(file size)
Errata
Posted January 6, 2003
The curriculum was updated on January 3, 2003. The curriculum's computer files should be replaced with the updated files. For convenience, the changed pages are collectively available for downloading by clicking on the icon to the right. Printed copies of the curriculum can be updated by simply printing the errata document and replacing the pages in your version. Download File
(54.5 kb) PDF file


Updated January 2003
 
Curriculum Preface The curriculum preface includes a brief introduction for teachers interested in using this curriculum. It also includes the curriculum's background and overview. Download File
(2,410 kb)


Updated January 2003
 
Section 1: Introduction to Probability Section 1 covers concepts of probability, randomness, probability in the real world, combined probability, independent and dependent events, section exercises, worksheets and worksheet answers. Download File
(2,071 kb)


Updated January 2003
Download File
(258 kb)
Section 2: Probability and Gambling Section 2 covers concepts of probability, the probability of winning the lottery, lottery comparisons and misconceptions, section exercises, worksheets, and worksheet answers. Download File
(585 kb)


Updated January 2003
Download File
(26 kb)
Section 3: Media Literacy & Gambling Section 3 discusses tools to help the student analyze media messages, particularly in the area of substance abuse and gambling activities. It also includes activities to help students develop critical thinking skills that will allow them to objectively evaluate gambling opportunities. Also included are section exercises, worksheets, and worksheet answers. Download File
(655 kb)
Download File
(76 kb)
Section 4: Reality of Winning The Lottery Section 4 will supply students with information that will assist them in making wise decisions about whether to play the lottery in the future. After studying the material in this section, the student will be more informed about the lottery’s financial and mathematical reality. The objective of this section is to help students make the transition from magical thinking to mathematical thinking, and to know when mathematical thinking is appropriate and useful. Also included are section exercises, worksheets, and worksheet answers. Download File
(2,208 kb)

Updated January 2003

Download File
(120 kb)
Section 5: Statistics in Everyday Life Section 5 reviews the statistical concepts of averages (mean, median, and mode) and the way they are used in popular scientific media. This section also discusses the concept of sampling as part of a scientific study. It also aims to develop mathematical literacy by promoting number sense. Section exercises, worksheets, and worksheet answers are also included. Download File
(2,475 kb)

Updated January 2003

Download File
(146 kb)
References and Glossary This section includes the bibliography and a glossary of terms used in this curriculum. Download File
(51 kb)

Contact Us


We value your feedback. Please send any questions, comments or suggestions about the organization or content of this curriculum to the following address: info@divisiononaddictions.org.

Frequently Asked Questions


A reader writes:

Note: Exercise 1-10 in Section 1 illustrates the concept that with any group of 23 people, there is a 50% chance that two or more people in that group will have the same birthday (Paulos, 1988, p. 27; McGervey, 1986, p. 9).

A teacher wrote:

I taught the "Facing the Odds The Mathematics of Gambling" with my 8th grade class in St. Gabriel, LA. I found a shorter way to solve the "Shared Birthdays" activity in your curriculum. It seems that you will get the same result if you use the following formula: (Permutation of 365 items taken N at a time) divided by (365 raised to the N power). Where N is the number of people in the activity. In an abbreviated for it would look like this: P(365,n)/(365^n). If you find that this formula works, let me know if you'd like to include it in your "Facing the Odds Curriculum." The formula worked for me each time, in place of the long tedious calculation in the curriculum.

The Division Responds:

You are absolutely correct. The combined probabilities in the "Shared Birthday" activity, 364/365 * 363/365 * 362/365 ... can be simplified. The continued product of the common denominator, 365, can be expressed as a power of 365. The numerators can also be expressed as the permutation of 365 items taken N at a time.

However, the simplified expression may not carry the same meaning for the students. One goal of the exercise is to introduce the concept of combined probabilities. The concept that there are 364 days that are not the same as the first birthday, 363 days that are not the same as two non-matching days, etc. retains the idea that the number of possible non-matching days decreases and finding one is increasingly less likely. Perhaps even more powerful is the opportunity to examine the effect of combined probabilities. The last term in the continued product (for N = 23) is 343/365 = .94. In simple terms this is still a large probability and students may be amazed at how quickly the product of what seem to be large probabilities turns into a relatively small probability. Other less computationally-demanding exercises could also be used. For example, you could ask students to figure out how large a group of people would have a greater than 50% chance of having at least two people born on the same day of the week.

The simplification that you pointed out could ease computation but might obscure the "number sense" that derives from going through the longer process. Once the concept of combinatorial probabilities is learned, simplifying the computation could be a valuable opportunity to introduce or revisit concepts such as permutation that go into the simplification. I would not move too quickly to the simplification for fear that the basic goal of the exercise would not be met.

Richard A. LaBrie, Ed.D.
Associate Director of Research and Data Analysis
Harvard Medical School Division on Addictions

© Division on Addiction. All Rights Reserved. Last Updated:  January 04, 2012