A B C D

Solutions for Session 10, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7

Problem C1

Here are some possible answers:

 a. Ms. L'Esperance encourages students to make inferences and predictions by focusing their attention on the problem context and asking them to make suggestions regarding what she should tell her friend about how big to build his homes. b. Many of the children concluded that Ms. L'Esperance should tell her friend to build homes for four people. However, other children took into account the variance in the data and concluded that, while he should build some homes for two people, he should build the most homes for three or four people. c. When the teacher asks the students to consider the number of data points collected (the sample size), she implicitly encouraged them to consider ideas of sampling and population.

 Problem C2 The data make a strong case that homes should be built for families of size two, three, four, and five. You may agree with the students that four is an appropriate conclusion, but you probably also realize that this sample is very small and that more data should be gathered.

Problem C3

 a. This response makes sense in that it is based on the mode; the limitation is that it does not take into account the variation in the data. b. This response takes into account the variation in the data. c. This response is based on the two values with the greatest number of responses, so the student does consider variation in a narrow sense but does not take into account the limited sample. d. In this context, this response doesn't make sense; the student has gone beyond the actual data involved and is considering issues of sampling and population.

 Problem C4 The sample is biased in that, as children, they all live in households that contain at least two people; thus, households in which one person lives are not considered. Some questions a teacher might pose include, "Why doesn't our line plot show any families of size one?" and "Does anyone in your neighborhood live in a household with only one person?"

 Problem C5 The students are likely to wonder why the average size of households is so much smaller than what their data indicated. You would want students to think about how their sample was collected and the bias or limitations inherent in their sample.

Problem C6

Here are some questions you might ask:

 • What should we tell my friend about where this information came from and the part of our city in which he should build homes of this size? • If my friend decides to build houses in another city, should they be the same size as the houses we think he should build here?

 Problem C7 Two conjectures that might result are, "The typical family size in our area is four people" and "You will not find families in our area that have 10 people." These could be formulated as new questions to be investigated: "What is the typical family size in our area?" and "What is the range of family size in our area?" The students could investigate this question in several ways. They might want to survey students in other classes and grade levels in their school on family size, they might want to have each student survey 10 neighbors, or they might want to locate census data for their community.

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