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Night session, Pascal's identity, clip 1 of 7: thinking about the meaning of combinatorics notation
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Night session, Pascal's identity, clip 1 of 7: thinking about the meaning of combinatorics notation [video]. Retrieved from https://doi.org/doi:10.7282/T3ZK5GH2

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TitleNight session, Pascal's identity, clip 1 of 7: thinking about the meaning of combinatorics notation
PublisherNew Brunswick, NJ: Robert B. Davis Institute for learning, , c1999-05-12
Persistent URLhttps://doi.org/doi:10.7282/T3ZK5GH2
DescriptionThis is the first of seven clips from the night session. In it, Jeff, Michael, and Romina discuss the coefficients of the binomial expansion, specifically (a+b) to the 10th power. In attempting to explain why 45 is the coefficient of the third term in this expansion, the students refer to counting how many 10-tall towers have exactly two cubes of a specific color.
Note: The 10-tall towers problem is an instance of the n-tall towers problem: How many towers n cubes tall is it possible to make when there are two colors of cubes to choose from?
Math ToolCalculator
Math StrandCounting, Combinatorics
Math ProblemPascal's identity, Towers
NCTM Grade Range9-12
NCTM Content StandardNumber and operations, Algebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Inductive reasoning, Recognizing a pattern, Recursive reasoning, Referencing a previous problem
Grade Level11
Student ParticipantsJeff (student), Romina (student), Michael A. (Kenilworth, student)
MediatorsMaher, Carolyn Alexander (Researcher), Pantozzi, Ralph S. (Researcher)
CorporateDavid Brearley High School (Kenilworth, N.J.)
SettingInformal learning
Student GenderMixed
Student EthnicityMixed
Camera ViewsClassroom 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 Captured1999-05-12
Local IdentifierA28-CMB-TW10T-CLIP001
Related Publication
   Type: Dissertation
   Label: Ed.D. dissertation references the video footage that includes Night session, Pascal's Identity, clip 1 of 7.
   Detail: Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
   Author: Uptegrove, Elizabeth (Rutgers Graduate School of Education)

   Name: To symbols from meaning: students' investigations in counting.
Source
   Title: A28, Night session, Pascal's identity, grade 11, May 12 1999, raw footage
   Identifier: 28-19990512-KNWH-PV-CLASS-GR11-CMB-TW10T-RAW
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