The primary mathematical goal of the lesson is for students to be engaged in analyzing data within the context of purchasing a pair of sneakers by generating ranked data and then compiling one class list of ranked data from the group lists of ranked data. This lesson sequence is part of a unit on data analysis. The primary focus is on ranking data and aggregating ranked data with attention being given to weighted ranks. Students' understandings of average are typically grounded in an algorithmic approach which does not highlight the importance of average in terms of what it tells you about a data set. In addition, the relation of the sum to the average is not understood.
Most students think that the sum is more accurate and that an average is an approximation.
These mathematical issues can be teased out in the first problem by having students compare the results of aggregating ranked lists by both summing and averaging. While it is not expected that this comparison will clarify students' understandings, it should provide an initial activity to raise the issue which can then be revisited in the subsequent problems in this lesson sequence and later in this unit.