Intent

Beyond creating a more personalized experience of the mathematics in the unit, this activity engages students in the mathematical task of meeting conditions in order to determine possible solutions for a problem situation.

Mathematics

Students assemble groups of people that match a set of constraints derived from possible scenarios of westward migration. Although the methods used are informal, this serves as an initial experience in interpreting mathematically imprecise language. When combined with its companion activity, Hats for the Family, the activity gives students experience in the mathematical task of finding minimum and maximum numbers based on their interpretation of the set of constraints.

Progression

Students work in groups to create four hypothetical family units, information that will be referred to throughout the unit.

Approximate Time

45 minutes

Classroom Organization

Groups

Materials

Folders (1 per group)

Posters, markers, and tape

Doing the Activity

The activity describes four types of family units that might have been part of a wagon train. Each group of students will create one family of each type. During the course of the unit, groups will follow the planning and movement of these families along the trail. Keeping track of these families helps to make the unit’s context more real for students. “Supporting Families Throughout the Overland Trail” offers suggestions for helping groups create and keep track of families. [link to supporting families in the 1.3 unit overview.]

Groups will name their family members by drawing from the list of settlers’ names in Overland Trail Names. Some of these names will appear in later activities. Seeing “their” family members in these situations will enhance students’ engagement in the unit.

Emphasize that each group as a whole is responsible for creating the families and meeting the given constraints, even though each student will have final responsibility for one particular family.

Adjust accordingly for groups with other than four members. It is essential that each group create one of each type of family and keep track of them. You might have some students keep track of more than one family or have the entire group monitor an unassigned family.

While students work, observe and support group interaction and careful record keeping. You or groups must decide how to record the information about each group’s four families. Groups might keep their information in a folder while the class creates a chart summarizing the information about all families the class has created.

As you observe groups working, you may find it useful to have a sense of the size and structure of each family type. Here is a summary of some of the limitations that result from specific interpretations of the descriptions. For instance, “between one and six hired hands” is interpreted to mean “at least one and at most six.” Students might reach slightly different conclusions, based on different interpretations. Students will determine maximum and minimum family sizes in Hats for Families.

Altogether, a wagon train consisting of one family of each type will have from 21 to 56 people.

It can be useful to bring the class together about one third of the way through the activity to check in. Ask what has been challenging. Replies may include monitoring group processes, record keeping, and meeting the demands of the family conditions. [link to math maps]

There are some ambiguities in the wording of the constraints, such as use of the word between in the description of the large family. If students raise this issue, urge them to make decisions as a group about how to interpret these ambiguities.

Confirm the manner in which students are expected to record final decisions about the families: first and last name, age, and sex. Each student must have access to her or his own data, and each group member’s data, at all times.

As groups near the finish of their work, ensure that they have met the requirements for recording the information about each group member’s family. Depending on how you have decided to support student record keeping (perhaps using individual file folders or charts), remind students to complete that task as well.

Discussing and Debriefing the Activity

When all groups are done creating their families, compile a class chart summarizing information about all of the families created. Have presenters talk about any assumptions they made. Organize the information in a chart like the one below or in another way that students suggest.

Post this chart for reference throughout the unit. Point out that some families may require more than one wagon; students will use this fact in later activities. Also for use later, ask students to find the total number of adults and the total number of children in their entire class wagon train.

Make sure students monitor the progress of their Overland Trail families throughout the unit. To do so, they will need to keep track of certain information. Specifically, each student will need to know:

Reading this list aloud can give students one last opportunity to double check that they have each of these pieces of information recorded.

Key Questions

What has been challenging for your group in this activity?

How did your group decide to interpret that constraint?

What assumptions did you make?

How many men, women, and children are in each of your families?