Overview:  Elijah, Jeff, Leah, and Taylor decide that they should make circles of a fixed radius around the existing stores so that they can determine which region on the map is farthest from a store.  Leah gets compasses for the group, and they decide to make circles of radius 2-miles, because 2 miles seems a reasonable walking distance.  After making the circles, the students debate between putting a new store on Old Country Road or putting a new store on Calumet and Oakmeade.  They decide to put the store on Old Country Road because, although it’s a less populated area, many people are moving out to that area.

Prior knowledge:  The students combing their knowledge of the context of the problem with their knowledge of school mathematics.  The students use their knowledge of school mathematics when they construct circles of a fixed radius.  By seeing where there the least overlap between circles, the students identify the regions that are farthest from the grocery stores.  The students use their knowledge of the local community to make the final decision about where to put a new store.

Other points of interest:  It seems that students are unsure of whether they are fulfilling the didactical contract (Brousseau, 1997) of the class by finding a geometric solution.  When students come up with a solution to the problem, Jeff’s question, “Is that all we have to figure out?” indicates that he is not certain whether they have finished solving the problem.  Students seem satisfied that they have established a geometric solution, perhaps because they used a geometric tool (the compass), and they constructed circles as part of their solution.