Overview:  In this Summary, the teacher compares two similar solutions from two different groups.  Each of the groups used circles to solve the grocery store problem (like in Explore 1).  They constructed circles of a fixed radius around existing grocery stores to locate an area for a new store.  However, the two groups made different assumptions based on the contextual information in the problem.  The first group to present their solution made circles of radius 2 miles.  They put a new store in the southwest corner of the map, which is a less populated area and is not covered by any circle.  The second group says they used a radius of 1 mile to construct their circles.  Also, they decided to locate the new grocery store on Oakmeade in Chesterton.  The two groups start a debate the factors contributing to their respective solutions, including the populations of the different regions and how far people can walk to the store.  The teacher emphasizes that, geometrically speaking, the two groups have very similar solutions.  However, because the groups made different assumptions to work on the problem, they came up with two different ideas about where to locate the new store.

Prior knowledge:  The teacher establishes a connection with students’ knowledge of the context of the problem.  Because the teacher highlights two solutions that are geometrically equivalent, the differences in students’ decisions about the contextual factors contributing to the problem become much more salient.

Other points of interest:  In the class discussion in this summary, students engage in a debate in which many people contribute ideas, students talk and ask questions directly to one another.  It is not clear whether the teacher has planned for this level of engagement between students.  However, it seems that the discussion about the community factors involved in selecting a new grocery store provokes conversation between students.  The conversation in this summary is a departure from the IRE (Mehan, 1979) pattern of interactions that are more common in mathematics classrooms.  In this episode we see students and teacher sharing control of the direction of the dialogue (Lemke, 1990), a type of conversation that is relatively rare in classroom exchanges.