Taxicab problem, clip 2 of 5: investigating the number of shortest paths.
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Taxicab problem, clip 2 of 5: investigating the number of shortest paths.
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A02A26-GMY-TAXI-CLIP002
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http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054818
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English
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Action research
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Brian (Kenilworth, student)
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Romina (student)
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Jeff (student)
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Michael A. (Kenilworth, student)
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David Brearley High School (Kenilworth, N.J.)
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Mathematics education
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Critical thinking in children--New Jersey--Case studies
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Data analysis and probability
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Number and operations
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Reasoning and proof
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Considering a simpler problem
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Kenilworth Public Schools
Abstract
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In 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.
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Education
Note
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Transcript is also available.
Note
(type = APA citation)
Robert B. Davis Institute for Learning. (2000). Taxicab problem, clip 2 of 5: investigating the number of shortest paths. [video]. Retrieved from http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054818
Note
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Available in QuickTime streaming and downloadable Flash digital video files.
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Kiczek
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Regina
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New Brunswick, NJ
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Robert B. Davis Institute for learning
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A02, Taxicab problem, full session, grade 12, May 5, 2000, raw footage
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A02-20000505-KNWH-SV-AFTRS-GR12-GMY-TAXI-RAW
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A26,Taxicab problem: full session, grade 12, May 5, 2000, raw footage
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A26-20000505-KNWH-WV-AFTRS-GR12-GMY-TAXI-RAW
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Title
So let's prove it!: emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task / by Arthur B. Powell.
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000054821
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Robert B. Davis Institute for Learning Mathematics Education Collection
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rucore00000001201
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Ph.D. dissertation references the video footage that includes Taxicab problem, clip 2 of 5.
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Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
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QA 22 2009
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Rutgers Graduate School of Education
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So let's prove it!: emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptons of learners engaged in a combinatorial task .
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000054821
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Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
Identifier
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doi:10.7282/T3FJ2GNQ
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