Overview:  The teacher has three different solution strategies presented on the board, but the teacher draws students’ attention to a solution based on finding a center of a triangle.  The teacher illustrates the one group made a triangle, and the class needs a formal way to discuss what the “center” of a triangle is.  The teacher tells students that there are actually multiple centers to a triangle, but they are most interested in this lesson in the circumcenter.  The teacher writes a definition for students that the circumcenter of a triangle is the intersection of the perpendicular bisectors of the respective sides.  The teacher then moves away from the triangle solution to establish the definition of “perpendicular bisector” with students.  One student, Conrad, asks the teacher what the perpendicular bisector has to do with the triangle solution for the grocery store problem.  The teacher illustrates with the diagram that the three perpendicular bisectors of the triangle intersect in a single point, which is equidistant from the other points on the triangle.  In the teacher’s diagram, the circumcenter of the triangle is actually outside the triangle.

Prior knowledge:  The teachers establishes a connection with students’ knowledge of school mathematics.  The teacher attempts to use a group’s solution to establish the definition of perpendicular bisector, and to show students how perpendicular bisectors can be used to find a center of a triangle.  The teacher introduces formal mathematical vocabulary for “circumcenter” and “perpendicular bisector”, and the teacher illustrates these concepts with diagrams.

Other points of interest:  It is not clear in this summary that students recognize the connection between the perpendicular bisector and the solution to the grocery store problem.  The teacher makes a connection with students who used a triangle to solve the problem, but this decision by the teacher may disengage students who used other methods to solve the problem.  Also, when the teacher draws the circumcenter of a triangle on the board, the circumcenter is actually outside the triangle.  This atypical example may require some discussion of how the “center” of the triangle can be outside the triangle.  Also, it may be important to discuss what this diagram would be in terms of locating a new grocery store.