DescriptionIn the fifth of five clips, Romina, Brian and Michael, describe patterns and relationships identified in their solution to the Taxicab problem to Arthur Powell, a second researcher. The students justify their claim that the number of shortest routes to any point on the Taxicab grid, based on the number of horizontal and vertical moves in each case, corresponds to the addition rule for Pascal's Triangle. Romina explains the correspondence between horizontal and vertical moves on the grid to the possibility of selecting from two colors when building Towers of Unifix cubes. Michael describes a correspondence to the presence or absence of toppings for the Pizza problem and also conjectures that these relationships can be described using binary notation.
PROBEM 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 5 of 5. Date: 2003-05-01 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