DescriptionIn the second of five clips, the four twelfth grade students employ various strategies to determine the number of shortest paths to the remaining two points, B and C, on the problem grid. Various patterns, invented notations, and color-coded diagrams are shared in an attempt to find a solution for the problem. As they calculate total numbers of routes for successively larger areas of the grid, the students conjecture about a possible relationship to the Towers Problem . When Romina calculates the numbers of shortest routes for the points where each shortest route has length 5, she makes the conjecture that the problem follows the pattern of Pascal's Triangle.
PROBLEM STATEMENT: The problem was presented to the students with an accompanying representation on a single (fourth) quadrant of a coordinate grid of squares with the “taxi stand” located at (0,0) and the three “pick-up” points A (blue), B(red) and C(green) at (1,-4), (4,-3) and (5,-5) respectively, implying that movement could only occur horizontally or vertically toward a point. The problem states that: A taxi driver is given a specific territory of a town, as represented by the grid. All trips originate at the taxi stand. One very slow night, the driver is dispatched only three times; each time, she picks up passengers at one of the intersections indicated on the map. To pass the time, she considers all the possible routes she could have taken to each pick-up point and wonders if she could have chosen a shorter route. What is the shortest route from the taxi stand to each point? How do you know it is the shortest? Is there more than one shortest route to each point? If not, why not? If so, how many? Justify your answers.
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Related Publication Type: Dissertation Label: Ph.D. dissertation references the video footage that includes Taxicab problem, clip 2 of 5. Detail: Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection. Author: Powell, Arthur B. (Rutgers Graduate School of Education)
Name: So let's prove it!: emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptons of learners engaged in a combinatorial task .
Source Title: A02, Taxicab problem, full session, grade 12, May 5, 2000, raw footage Identifier: A02-20000505-KNWH-SV-AFTRS-GR12-GMY-TAXI-RAW
Source Title: A26,Taxicab problem: full session, grade 12, May 5, 2000, raw footage Identifier: A26-20000505-KNWH-WV-AFTRS-GR12-GMY-TAXI-RAW