Magazine article Teaching Children Mathematics

Gummy Bears in the White House

Magazine article Teaching Children Mathematics

Gummy Bears in the White House

Article excerpt

Representation is an essential issue in statistical sampling. Policy in educational, scientific, and political arenas is driven by results based on samples that ideally reflect the characteristics of the larger group from which they are drawn. Biased samples can lead to unfortunate situations when they are used as a basis for reporting results or making decisions. The central question is this: Do the characteristics of a sample occur in approximately the same proportion as in the general population from which the sample was taken? Obtaining a representational sample for a diverse population can be a difficult task.

This article describes a one-week lesson in which gummy-bears candy was used to illustrate sampling procedures and to generate discussion and questions. The lesson models the "exploration of statistics in real-world situations" essential for the development of "an appreciation for statistical methods as powerful means for decision making," as recommended in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 105). The lesson is described, the data results are reported, and the students' reactions to problems of representation after holding an election are discussed. The data reported were taken from a lesson done with a class of fifth- and sixth-grade students at a large, diverse public elementary school. The lesson was based on "Gummy Bear Graphs" in Book 2 of the Santa Ana-Fullerton Elementary Mathematics Project (SAFEMAP 1991).

Gummy-Bear Graphs

To investigate the idea of sampling, the class looked at the distribution of gummy bears of different colors in packages from the same manufacturer. The class was divided into eight four-student teams. Each team was given a bag of gummy bears and was told to treat its bag of bears with care. After opening the bag, the team counted the bears and sorted them by color: red, yellow, green, white, orange, and purple.

Each team constructed a bar graph using the actual gummy bears as counting units. Then each team made a frequency table and colored a bar graph to display their data [ILLUSTRATION FOR FIGURE 1 OMITTED]. One member of each team then colored the team's results on the whole-class gummy-bear chart [ILLUSTRATION FOR FIGURE 2 OMITTED].

The data for the individual bags and for the whole class are summarized in table 1. No two bags had the same color distribution, but some similarities among the distributions could be seen. For example, six of the eight bags had at least seven bears of one color, although not necessarily of the same color. Similarly, all but one bag had at least one bear of each color. Several students observed that when the data from all the teams were combined, each color appeared about the same number of times.

Interdisciplinary Connections: Gummy-Bear Government

To foster a connection between mathematics and social studies, the students next applied their data to elections in the gummy bears' world. Quantitative methods and proportional reasoning were applied in a social-sciences context. This part of the activity required the students to analyze and describe both the mathematical and social aspects of the lesson.

TABLE 1

Distribution of gummy bears by color

            Red   Yellow   Green   White   Orange   Purple    Total

Team A       2        4       7       3       4        3        23
Team B       3        4       5       8       3        8        31
Team C       4        4       4       1       2        6        21
Team D       8        4       5       3       3        2        25
Team E       5        3       6       3       5        3        25
Team F       5        7       2       5       4        0        23
Team G       2        2       1       8       5        5        23
Team H       5        1       3       4       5        7        25

Total       34      29       33      35      31       34       196

Voting for group interests

The students entered the world of gummy-bear government. …

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