Taxicab problem, clip 5 of 5: extending the taxicab correspondence to pizza with toppings and binary notation
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Taxicab problem, clip 5 of 5: extending the taxicab correspondence to pizza with toppings and binary notation
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A02A26-GMY-TAXI-CLIP005
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http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054874
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English
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Research data
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Action research
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Educational interventions (small group)
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David Brearley High School (Kenilworth, N.J.)
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Brian (Kenilworth, student)
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Romina (student)
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Michael A. (Kenilworth, student)
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Mathematics education
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Number and operations
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Reasoning and proof
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Critical thinking in children--New Jersey--Case studies
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Kenilworth Public Schools
Abstract
(type = summary)
In 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.
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1
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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 5 of 5: extending the taxicab correspondence to pizza with toppings and binary notation. [video]. Retrieved from http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054874
Note
(type = available formats)
Available in QuickTime streaming and downloadable Flash digital video files.
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Maher
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Carolyn Alexander
Role
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Rutgers, the State University of New Jersey
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Powell
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Arthur B.
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Rutgers, the State University of New Jersey
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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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TitleInfo
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 5 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.P882 2003
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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
Detail
Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
Identifier
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doi:10.7282/T3TT4QSB
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