Overview:  The teacher stops by the group and asks students to compare their solutions before the end of the period.  Gabby selected the point she wants to locate a new store, and then she places three points around it.  Miguel says he wanted to select an area that is growing, and Jonah says he selected a point that is right next to a Super T.  Liza challenges Jonah’s solution, saying the problem would be trivial if she could simply locate a new store next to every existing store.  Jonah rebuts by arguing that he is not locating a store next to every store, but only next to the Super T, which is a large grocery store, and customers may benefit from competition.

Prior knowledge:  Students rely primarily on their knowledge of the context of the problem to select three points to narrow down their search.  The students disagree whether they should place a new store near or far away from existing grocery stores.  Gabby uses knowledge of a mathematical practice with her logic to solve the problem.  Rather than selecting three points as givens and placing a new point in between, Gabby first selects a point for the new grocery store.  Other than Gabby, the students do not get beyond the step of selecting three points, so they do not apply any knowledge to find a point equidistant from their three selected points.

Other points of interest:  The teacher encourages the students in the group to talk to one another, because they will need to come to a consensus on their solution.  Also, although Jonah and Miguel have both begun by selecting three points, Gabby’s first step was actually to select the point of the new grocery store.  Gabby solves the problem in an opposite order from most students.  Most students select three points and place a new store between those points.  Gabby has instead selected the location of the new store and then identified three more points around that location.