Intent

In this activity, students see that the analysis of data can help inform decision making.

Mathematics

In The Game of Pig, students saw that averages, particularly in the context of expected value, could be used to develop an optimal strategy for a game. Now they apply their ideas about decision making and strategy based on measures of central tendency of data, especially medianand mean.

with a focus on the limitations of each measure.

Progression

Students work on the activity individually and then talk about and justify their reasoning in a class discussion.

Approximate Time

5 minutes for introduction

20 minutes for activity (at home or in class)

15 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Doing the Activity

Introduce this activity by stating that just as settlers did 150 years ago, students will have to make many decisions based on the information available to them. Sometimes settlers had to work with little or no information, or misinformation, or speculation, or even superstition.

In this activity, students will be asked to make decisions based on data about rainfall along various trails.

Discussing and Debriefing the Activity

Have students share their reasoning for Question 1, either in small groups or as a class. There are good reasons for choosing each of the three trails. Here are a few.

Ask volunteers to comment on Addison’s and Lydia’s methods in Questions 2 and 3. Students might note that Addison’s method tends to overemphasize Enoch’s experience (42 rainy days), while Lydia’s method underemphasizes this case. You might use the term outlier.

to describe a case that is substantially outside the range of the majority of values.

When appropriate, ask, What is the mathematical name for Addison’s method? For Lydia’s method? Students should be able to identify the mean and the median. (Note that neither method is necessarily the best tool for decision making in this context, even though the average was crucial in analysis of The Game of Pig. If students make the connection, you might confirm that expected value is essentially an average.)

Be sure students understand the definition of each method and how each computation is done. In particular, discuss how to find the median of a data set with an even number of items. You can use the third set of data in the table, for the Oregon Trail, to illustrate that in such a case, the median is defined as the average of the two values that “share the middle” once the items are listed in numeric order.

You might also identify mean and medianas “measures of the center” for a set of data (or, more formally, “measures of central tendency”). That is, they are methods of choosing a single number to represent some type of “middle” of a data set.

Key Questions

Which trail did you choose? Why?

What is the mathematical name for Addison’s method? For Lydia’s method?