DescriptionIn the fourth of five clips, the four twelfth grade students explain their conjecture that Pascal's Triangle can be used to predict the number of paths to any point in the Taxicab grid to Carolyn Maher, the researcher. Romina relates the building of Unifix Towers, when selecting from two colors, to the moves on the Taxi grid, which can be in either a horizontal or a vertical direction, and demonstrates that in each case there is a correspondence to the addition rule 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 4 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 inscriptions 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-GMYTAXI-RAW