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Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle
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Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle [video]. Retrieved from https://doi.org/doi:10.7282/T3GH9HT0

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TitleNight Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle
PublisherNew Brunswick, NJ: Robert B. Davis Institute for learning, , c1999-05-12
Persistent URLhttps://doi.org/doi:10.7282/T3GH9HT0
DescriptionThis is the fifth of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) have been discussing Pascal’s Triangle. The researcher rewrites row 3 of Pascal’s Triangle in what the students call “choose” notation (1 3 3 1 becomes “3 choose 0, “3 choose 1,” “3 choose 2,” and “3 choose 3”). The researcher then asks the students to write more rows of Pascal’s Triangle in this notation, including a general row (row n). As the students work on this task, they describe connections between Pascal’s Triangle and the binomial expansion and between the n-th row of Pascal’s Triangle and the answer to the n-tall towers problem.
Notes:
The n-tall towers problem is: How many towers n cubes tall is it possible to make when there are two colors of cubes to choose from?
“Choose” notation is the notation for counting the number of combinations; “n choose r” gives the number of ways of selecting subsets containing r objects from a set containing n objects. When counting combinations, the order of selection is irrelevant. “n choose r” is equal to n!/[(n – r)!r!].
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, Referencing a previous problem, Recognizing a pattern
Grade Level11
Student ParticipantsJeff (student), Romina (student), Michael A. (Kenilworth, student), Ankur (student)
MediatorsMaher, Carolyn Alexander (Researcher), Kiczek, Regina D. (Researcher), Steencken, Elena Perrone (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-CLIP005
Related Publication
   Type: Dissertation
   Label: Ed.D. dissertation references the video footage that includes Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle
   Detail: Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
   Author: Uptegrove, Elizabeth B. (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: A28-19990512-KNWH-PV-CLASS-GR11-CMB-TW10T-RAW
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