Grocery Store Launch 5
Overview: Before students work on the problem, the teacher projects the map of the community on the board at the front of the room for the class to look at together. With the map, the teacher tries to make a distinction between measuring distances between two places on a typical roadmap versus finding distances between two points on a plane in geometry. By using an example of going from his house the mall, the teacher discusses with students the different information they would need to find the distance—knowledge of the roads, travelling times, different potential routes between two places. The teacher then points out that another way to think about distances is “as the crow flies,” meaning the direct distance from one point to another. The teacher tells students that, in geometry, distances are usually considered “as the crow flies.” The teacher encourages students to think about this strategy for finding distances between points as they work on the problem.
Prior knowledge: The teacher establishes a connection with students prior knowledge of the mathematical practices of reading maps and measuring distances between points in different contexts. The teacher may expect that, while working on a problem using a familiar map, students will be inclined to use their knowledge of the distances and travel factors in the community. However, the teacher also wants students to remember another way of connecting points on a map, that is by connecting two points with a straight line. The teacher points out to students that they may rely on different practices for getting around town than they would use in a geometry class, but students should use both of those practices for their work on the grocery store problem.
Other points of interest: Similarly to what the teacher did in Launch 3, the teacher here appeals to students’ knowledge of the difference between what they may do in real life versus what they may do in a geometry class. By emphasizing students’ experiences with geometry, the teacher prioritizes what he describes as the “geometric” way of thinking about distances between points. Although the teacher does not explicitly tell students how to solve the problem, he seems to urge students to prioritize a geometric way of solving the problem over the knowledge they may have from outside of geometry.