Overview:  The teacher launches the problem by discussing how students can locate points on a map in geometry.  The teacher makes a distinction between how students might describe a point when using a road map (e.g., giving an address) versus how they would describe the location of a point in geometry.  The teacher elicits examples from students, including the examples that multiple points could lie on a single circle, or two points could be connected by a line segment.  The teacher tells students that, in today’s lesson, they will have many points on a map, and they will need to use geometry to describe the location of a new point relative to the other points.

Prior knowledge:  The teacher performs a review of students’ prior knowledge of school mathematics, specifically how to locate points in geometry.  The teacher asks students to consider how they can describe the location of a point, and students offer multiple examples of strategies that they have likely studied in this or another mathematics class (using a coordinate system, measuring distance, making a circle).  The teacher also attempts to highlight how students will use their knowledge of school mathematics on the grocery store problem, especially with his final comments.  The teacher tells students to “think about different ways you can relate points to one another.  Think about using different geometric relationships, like circles, or line segments, or triangles, and things like that.”  With this comment, the teacher encourages students to use their prior knowledge of geometric relationships to solve the problem.

Other points of interest:  When the teacher asks students how they could describe the location of a point in the plane, students first offer ideas that require a metric.  Describing the coordinates of a point requires assigning a coordinate system to the plane, and finding the distance between two points requires either measuring with some unit or applying a distance formula according to a coordinate system.  For the purpose of the grocery store problem, the teacher seems to want students to think about how to relate points without attaching any metric, numbers, or units to them.  Mariana’s suggestion, that you could use three points to make a circle, would only be viable if the three given points happened to share a center, which is not very likely.  However, the teacher uses this suggestion as a starting point for students to consider spatial relationships between points rather than numerical relationships.