Intent

Examining this simplified game will support students in their analysis of the best strategies for playing “Big” Pig.

Mathematics

If students were to attempt to use area models and the concept of expected value to compare strategies for the game of Pig, they would find that the analysis gets complicated very quickly. Instead, they will now examine a game called Little Pig. This new game is simple enough that students can construct area models for many common strategies, but similar enough to Pig that it can suggest other ways to think about the best strategy for playing that more complicated game.

Progression

Work with Little Pig is exploratory. After analyzing many individual strategies for this game, students will consider how to find the best possible strategy. They will apply these insights later to find the best strategy for Pig itself without having to draw the complicated diagrams that quickly occur in an analysis of that game.

Approximate Time

35 minutes

Classroom Organization

Groups of 4, followed by whole-class discussion

Materials

Red, blue, and yellow cubes

Small paper bags

Sentence strips

Doing the Activity

As a class, read the rules of Little Pig. Give each group of students a bag containing one red, one yellow, and one blue cube. Just as students played Pig for the first time without much direction, have groups play this game, keeping track of their draws and scores for each turn. To help them analyze the game, ask them to keep track of both their own draws and scores and those of their partners.

Playing at least 10 rounds will be helpful. Students within each group should talk about the strategies they are using and be prepared to share one of those strategies with the class. Provide each group with a sentence strip for posting a strategy after playing the game.

Discussing and Debriefing the Activity

Be sure the strategies that students present are clear. If time allows, groups can play the game again to try out other groups’ strategies.

Have students find the expected value for the strategy of stopping after the first cube is drawn no matter what the result. Working through this simple example may help with the next activity, Pig Tails.

Key Question

How is Little Pig like “Big” Pig? How is it different?