Overview:  Liza, Jonah, Miguel, and Gabby are all working on slightly different solutions to the problem.  Miguel and Gabby have each selected a pair of points and are measuring to find the midpoint of those segments.  Jonah draws two diagonals across the designated region and decides to locate a new grocery store at the intersection of those diagonals.  Liza has the idea to place the new store in the southeast corner of the map, near the interstate.  The students decide that it is okay that they do not all have the same solution, because each of them can justify their respective solution.

Prior knowledge:  Students combine prior knowledge of school mathematics with knowledge of the context of the problem.  Both Miguel and Gabby draw line segments and use measuring to find the midpoint of those segments.  However, Miguel and Gabby use different line segments based on different assumptions about the best area to locate a new store.  Jonah uses a fairly basic mathematical solution, finding the intersection of two diagonals for the new grocery store.  Miguel challenges Jonah’s solution based on the contextual information, namely that Jonah’s grocery store is directly on top of a park.  Liza relies entirely on contextual information to locate a new grocery store.

Other points of interest:  Although students all have different solutions for solving the problem, they provoke one another to make comparisons between their solutions by asking questions and by challenging one another’s ideas (DeJarnette, Dao, & González, 2013).  Students take turns asking questions to each other, which helps them to elaborate upon their different strategies.  However, at the end of the vignette, students’ discussion do not seem to lead them towards establishing a more sophisticated geometric solution to the problem.  Students seem satisfied that they all have different solutions to the problem.