## Wednesday, April 6, 2011

### What are the chances of a “Pig Out”? Part I

Several years ago, I wrote the following article with my colleague, Dr. Mary Richardson, for MCTM's Mathematics in Michigan (Volume 43, Number 1). Given that the issue is no longer available, I thought it would be appropriate to share it here. Because of the article's length it has been edited and will be split between two posts.
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Introduction

Middle grades learners should be provided ample opportunities to explore probability and statistics topics.  In particular, learners should be encouraged to collect, organize, and describe data, summarize the data, make predictions and conclusions based on the data, and test these predictions and conclusions (NCTM 2000).  [Update: this connects to CCSS 7.SP.C.6.] In the following activity, learners use the Pass the Pigs dice game to design a simulation experiment in order to estimate a probability.

The Game
Pass the Pigs involves two tiny rubber pigs that players throw like dice (rules). Each pig can land in six different ways resulting in various point values.  A turn consists of a player taking as many rolls as he or she dares until: (1) deciding to stop and recording the total score for that turn, (2) a “Pig Out” is rolled and the player records a score of zero for that turn, or (3) an “Oinker” is thrown and all points accumulated in the game thus far by the player are lost.

The Activity
In this activity, learners explore the experimental probability of obtaining a “Pig Out” in the Pass the Pigs dice game.  The activity works best if learners have experience calculating measures of center, including mean, median, and mode.  Learners work in groups of two.  Each pair has one Pass the Pigs dice game and a flat table or desktop on which to work.  Each learner has a sticky note and a copy of the Activity Worksheet.

To begin the lesson, each pair of learners examines their pig dice.  We discuss the possible outcomes if the pig dice are simultaneously tossed.  Each learner is then asked to estimate the probability that a “Pig Out” will occur when playing Pass the Pigs.  Learners should write down and share their estimates and the reasoning behind them.  This leads into a discussion about different types of probability.  In addition to the two types of probability traditionally targeted in middle school (theoretical and experimental), this activity provides the opportunity to introduce learners to subjective probability.  Learners recognize that this is a situation for which there is no easy way to determine a theoretical probability and no data on hand for them to use to calculate an experimental probability.  Therefore, they must assign probabilities based upon what they think will happen (subjective probability).
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To be continued... In the meantime, please estimate what you think is the probability that a "Pig Out" will occur and share it in the comments. Thank you.