Overview:  In this explore, the students first select three points on the map to narrow down their search.  Although three of the students want to place the three points in heavily populated areas, Aaliyah prefers to place one point in the area where she lives.  Once the students select three points, Lee suggests marking a midpoint of two of the selected points.  Although he says he wants to select the midpoint, the point Lee marks is not actually the midpoint of the segment.  It seems that Lee marks a point on the segment that is in an open region, rather than the midpoint. The teacher stops by the group and emphasizes to students that they should establish a geometric solution to the problem.  The teacher folds Lee’s paper to show him that the point Lee marked is not the midpoint.  The actual midpoint of the segment is fairly close to an existing grocery store, a Union Fresh.  Aaliyah thinks such competition would not be fair for Union Fresh, but the other members of the group seem to think the competition will be good for the stores.

Prior knowledge:  Students use prior knowledge of the context of the problem.  The knowledge of the context is what guides students to select their three points, and students’ use of the context provokes a conflict between Aaliyah and the other members of the group.  Lee uses his knowledge of the school mathematics concept of midpoint to label what he calls the midpoint of a line segment in his triangle.  Although Lee uses the term “midpoint”, the point he marks on the map is not actually the midpoint of the segment.  The teacher introduces a mathematical practice of paper folding to show Lee a strategy for identifying the midpoint of a segment.  The teacher also encourages students to use their knowledge of school mathematics when he reminds them to come up with a geometric solution to the problem.

Other points of interest:  During the first part of the explore, students’ main concern is to use the context of the problem to identify three points on the map.  Aaliyah disagrees with the rest of her group members.  When the teacher approaches the group, Aaliyah appeals to the teacher regarding the choice of the three points.  Rather than responding to Aaliyah’s concern about how to select the three points, the teacher focuses on whether or not students have a mathematical solution to the problem.