A B C D 

a. 

The question is, "How many people are in a family?"

b. 

Each child was told to use connecting cubes to show the number of people that live in his or her house.

c. 

One might expect that the issue of "center" (median) would arise when determining the typical size of families, as well as the issue of variation in the data.

d. 

Some statistical ideas are the nature of data, quantitative variables, variation, range, measures of center, sampling, making a line plot, and interpreting a line plot.

Problem A2

It is likely that this rich context more fully engages children because there is a clear purpose for investigating family size. The context also increases the authenticity of the task. There is a real-world rationale for why a person in a specific profession would need to know the size of families or households in a particular area. While children might also be curious about the number of people in each of their families, they do not have a reason -- other than their interest -- to extend the investigation beyond their classroom.

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Problem A3

The rich context grounds students more firmly in the situation. With the clear purpose of examining family size and the fact that the data are about them, they more readily analyze the data with the real-world situation in mind than they would if they were just thinking about numbers out of context.

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Problem A4

Again, the rich context grounds students in the situation. They are invested in helping the teacher's friend and have a clear purpose for interpreting the data so that they can make an appropriate recommendation. The students are also able to draw on their own knowledge about the neighborhood and about family size. Thus, as they interpret the results, they are more likely to raise issues, think beyond their own classroom sample, and become curious about the larger population.

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Problem A5

The teacher's phrase resembles the definition of a "household" as set by the 2000 United States census. Answers to the second question will vary, but might include "all the people you spend holidays with," "the people you're related to," and "your mother, father, sisters, and brothers."

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Problem A6

Sensitive issues might involve brothers and sisters who no longer live in the same household, parents or siblings who have died, single- and dual-parent households, same-sex and different-sex guardians, or joint-custody situations. These are all aspects of people's lives, and are good examples of the importance of definitions when collecting data.

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