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## Media Clips: Boulder Lottery; The Probability of Slot Machines

Students analyze items from the media to answer mathematical questions related to the article. The clips this month, from the Colorado State lottery and a Marilyn vos Savant column on probability, involve probability and counting problems.

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## Farkle Fundamentals and Fun

The dice game Farkle provides an excellent basis for four activities that reinforce probability and expected value concepts for students in an introductory statistics class. These concepts appear in the increasingly popular AP statistics course (Peck 2011) and are used in analyzing ethical issues from insurance and gambling (COMAP 2009; Woodward and Woodward 1994). In addition to investigating these four fun activities, we also investigate a strategy to optimize a player's score on a turn in Farkle and indicate possible additional explorations.

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## The Back Page: My Favorite Lesson: The Bulldog Lottery

Several years ago I became the lead teacher for a newly created statistics course. I wanted the course to emphasize projects that would allow students to apply statistical knowledge to real-world situations. My Bulldog Lottery lesson allows students to apply the concepts of probability and expected value to a real-world phenomenon.

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## Probability and Commutativity: A Possible Misconception

Ann stated, “If you roll two dice (number cubes) and the numbers are 1 and 2, saying that 1 and 2 and 2 and 1 are different things, that is not true. It is like saying 8 + 9 and 9 + 8 have different outcomes.”

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## Reader Reflections – September 2013

Readers comment on published articles or offer their own ideas.

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## Using Data to Motivate the Use of Empirical Sampling Distributions

Research shows that students often struggle with understanding empirical sampling distributions. Using hands-on and technology models and simulations of problems generated by real data help students begin to make connections between repeated sampling, sample size, distribution, variation, and center. A task to assist teachers in implementing research-based strategies is included.

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## Calendar and Solutions – January 2013 and February 2013

A set of problems of many types.

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## Reader Reflections – April 2012

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## Reader Reflections – April 2012

Readers react to published articles or submit their own mathematical explorations.

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## August 2016

A set of problems of many types