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PUP Math Romina's proof to Ankur's challenge
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PUP Math Romina's proof to Ankur's challenge [video]. Retrieved from https://doi.org/doi:10.7282/T30P0Z85

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TitlePUP Math Romina's proof to Ankur's challenge
PublisherCambridge, MA: Annenberg Learner, 1998-01-09, c1998-01-09
Persistent URLhttps://doi.org/doi:10.7282/T30P0Z85
DescriptionIn this edited and narrated episode from the Private Universe Project in Mathematics, five tenth-grade students consider two different problems. FIRST PROBLEM STATEMENT: “Choosing from two colors of Unifix® cubes, red and yellow, how many total combinations exist for towers 5 tall, that each contains two red? Convince us that you have found them all.” SECOND PROBLEM STATEMENT (Ankur’s Challenge): “How many towers can you build four tall, selecting from cubes available in three different colors of Unifix® cubes, so that the resulting towers contain at least one of each color?” During the session Ankur and Michael work together at one end of the table and Jeff, Romina, and Brian work at the other end. Ankur and Michael use binary notation to solve the first problem. While waiting for Jeff, Romina, and Brian to complete the first tower problem of five-tall with a choice of two colors, Ankur poses a new question about towers four tall with a selection of three colors: “How many with at least one of each color?” Romina develops a notation that she calls “ones, zeroes, and Xs” to represent the three colors in the problem. First at the table and then at the chalkboard, Romina presents her reasoning to the others as she works to convince them that there thirty-six total towers that meet Ankur’s criteria. She shows them her representation to justify the six possible arrangements for two “1s” in the four positions of the tower. She fills the blank positions with “X0” or “0X” for the other two colors. She then explains that the resulting twelve towers would be multipied by three to account for the three different colors of cubes available.
Math ToolUnifix cubes
Math StrandCounting, Combinatorics
Math ProblemAnkur's challenge
NCTM Grade Range9-12
NCTM Content StandardNumber and operations
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Reasoning by cases, Controlling for variables, Recognizing a pattern
Grade Level10
Student ParticipantsBrian (Kenilworth, student), Romina (student), Jeff (student), Michael A. (Kenilworth, student), Ankur (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateDavid Brearley High School (Kenilworth, N.J.)
SettingInformal learning
Student GenderMixed
Student EthnicityMixed
Camera ViewsStudent view
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.
Date Captured1998-01-09
Local IdentifierPM4_RominasProof
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes PUP Math Romina's proof to Ankur's challenge
   Date: 2010
   Detail: Available in electronic form in RUcore, the Rutgers Community Repository.
   Author: Steffero, Maria. (Rutgers Graduate School of Education)

   Name: Tracing beliefs and behaviors of a participant in a longitudinal study for the development of mathematical ideas and reasoning: a case study.
   Reference: http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052894
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes PUP Math Romina's proof to Ankur's challenge
   Date: 1999
   Author: Muter, Ethel M. (Rutgers Graduate School of Education)

   Name: The development of student ideas in combinatorics and proof : a six year study
Related Publication
   Type: Related publication
   Label: Workshops (web-based) utilize the video PUP Math Romina's proof to Ankur's challenge
   Publisher: Annenberg Learner
   Creator: Harvard-Smithsonian Center for Astrophysics
Source
   Title: Private Universe Project in Mathematics Workshops. Cambridge, MA: Annenberg Learner.
   Identifier: http://www.learner.org/workshops/pupmath/index.html
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