Pass the Pigs

Group: Van Campbell, Columbus Middle School, Columbus, IN.

Thomas Keys, Kenwood Academy High School, Chicago, IL.

Charles Loeffler, Jones Middle School, Marion, IN.

Class: Any math class 7th grade and up.

Materials: Pass the PigsJ 8 game, rules of the game, record sheets, and calculators.

Goal: Develop a winning strategy for Pass the Pigs.

Time Required: 5 class periods

Background: Collect, record and find the mean value of a set of data.

Setting: Day 1 - After learning the rules for Pass the Pigs, the class will be broken into small groups of 2-3 students each. Four teams will be assigned to a table where they will play the game, and keep track of their respective plays and scores on Record Sheet 1. For this activity, the oinker rule on touching pigs (setting total score to zero) will not be enforced. If this situation occurs, it will be considered a "pig out."

Days 2-3 -Winning the game requires a team to end a turn with a positive number of points before pigging out (and lose the points accumulated in that turn). The winning strategy then, will be to decide when to end a given turn. Groups will develop a working strategy based on the previous day's data. The students should understand clearly that this working strategy may be modified during their data collection. Teams will use Record Sheet 2 to gather data to support or modify their strategy.

Day 4 - Four groups at each table will play the game Pass the Pigs, strictly using their adopted strategies. Each group will keep track of their plays and scores on Record Sheet 1.

Day 5 - Class discussion based on which strategies worked, why they worked, and which strategies need be modified. An additional game using the modified strategies can be played if time permits.

Problem: Each group will develop a strategy that they think will be successful in playing the game Pass the Pigs.

Evaluations: (1): A group write-up detailing the strategy created and the mathematics that support it; this includes all Record Sheets and a clear statement of their strategy.

(2): Groups will play against each other strictly using their group's strategy.

(3): Individual write-up detailing their group's performance on day 4 task and any modification they would have made.

Extensions: (1) Determine the experimental probability of each outcome of a single pig toss.

(2) Use the results from extension 1, to complete an experimental probability table for tossing two pigs.

(3) Compare and contrast the sample space and probability table for tossing two pigs with the sample space and probability table for tossing a pair of dice and getting the sum.

(4) Re-define the point value for two pig tosses possibly using multiplication, division and subtraction.

(5) Does having the rule that touching pigs sets you back to zero change your strategy?

Teacher Notes: "Pass the Pigs" is a Milton Bradley produced game available locally. The cost is approximately \$7.00.

When playing the game Pass the Pigs, the rules have been relaxed. In particular, if the pigs touch each other, the group "pigs out" but does not lose all of their total points. Extensions (2-4) should not take place until topics on probability have been covered and the students have had a chance to practice playing a modified game.

Name of Group:

RECORD SHEET 1

 TURN TOSSES POINTS TOTAL TOSSES TOTAL POINTS

Name of Group:

RECORD SHEET 2

 Tosses Points Total Tosses Total Points Average Tosses Average Points

SAMPLE

RECORD SHEET 1

 TURN TOSSES POINTS TOTAL TOSSES TOTAL POINTS 1 //// 10,5,5,10 4 30 2 //// 5,5,5,' 4 0 3 //// 20,1,1,5,' 5 0 4 //// 5,5,1,' 4 0 5 /// 10,1,' 3 0 6 / ' 1 0 7 /// 5,10,' 3 0 8 / ' 1 0 9 //// 5,5,5,5,' 5 0 10 // 20,' 2 0 11 / ' 1 0 12 / ' 1 0 13 / ' 1 0 14 //// 5,5,10,1,5 5 26 15 / ' 1 0 16 / ' 1 0 17 // 5,' 2 0 18 //// 5,1,1,20 4 27 19 // 5,' 2 0 20 //// 5,10,1,1,5 5 22 21 // 5,20 2 25 22 // 5,' 2 0 23 /// 5,1,' 3 0 24 //// 1,1,5,5 4 12 25 /// 5,5,' 3 0 26 // 5,5 2 10 27 // 15,' 2 0 28 / ' 1 0 29 / ' 1 0 30 // 5,10 2 15 31 /// 1,1,20 3 22 32 / ' 1 0 33 /// 5,1,20 3 26

' MEANS YOU PIGGED OUT

Funded in part by the National Science Foundation and Indiana University 1995