Intent

In this activity, students focus on the need for clarity when communicating a strategy[link to Glossary]—that is, a complete plan of action.

Mathematics

In this unit, the “best” strategy is the one that produces the highest average score per turn in the long run. Later in the unit, students will learn the formal name for this concept, expected value [link to Glossary]. For now, you can begin to focus their attention on the idea of an average score per turn.

Progression

Through their work in groups and with the whole class, students will come to understand the need to articulate strategies clearly and completely.

Approximate Time

10 minutes for small-group discussion

20 minutes for whole-class discussion

Classroom Organization

Small groups, followed by whole-class discussion

Materials

Sentence strips

Doing the Activity

Ask all students to report their homework results from Pig at Home to their groups. This is an opportunity to reinforce a productive group dynamic and to emphasize the importance of all students doing their homework.

Focus students’ constructive critiques on the clarity and completeness of each strategy. For example, a student might say, “Your strategy doesn’t tell me what to do if . . . .”

Ask each group to decide which of the strategies reported is the best one the group has discovered so far. Have each group write this strategy on a sentence strip and post it for reference during the class discussion.

Discussing and Debriefing the Activity

When all the strategies are posted, ask groups to test some of them. For example, groups could compare the total scores after ten turns using each of several strategies.

You might also ask students to imagine two players using two different strategies. One player has taken 500 turns and scored 1185 points; the other has taken 600 turns and scored 1342 points. Ask each group to try to come to a consensus about which player seems to have used the better strategy. Let some volunteers present their groups’ decisions and reasoning.

As needed, bring out the idea that at the rates the players are going, when each player has taken 1000 turns (or any other particular number), the first player will have more points than the second because the first player has a higher average score per turn.

In this context, “best” means “the most points per turn in the long run.” You may want to point out explicitly that the best strategy might not necessarily give the highest score in a particular game. The best strategy is the one that is most likely to help a player win in the long run.

Students’ central task in this unit will be to find the best strategy for playing Pig. Post this goal for reference during the rest of the unit:

Key Questions

Can you define a “best” strategy?

How can we describe the highest average score per turn in the long run?

Does this group’s strategy seem complete and clear?

What do we mean by the “best” strategy?

Which of these two players seems to have used the better strategy?