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Night Session, Pascal’s Identity, Clip 6 of 7: Examples of Pascal’s Identity in the notation for combinations
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Night Session, Pascal’s Identity, Clip 6 of 7: Examples of Pascal’s Identity in the notation for combinations [video]. Retrieved from https://doi.org/doi:10.7282/T3M908HT

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TitleNight Session, Pascal’s Identity, Clip 6 of 7: Examples of Pascal’s Identity in the notation for combinations
PublisherNew Brunswick, NJ: Robert B. Davis Institute for learning, , c1999-05-12
Persistent URLhttps://doi.org/doi:10.7282/T3M908HT
DescriptionThis is the sixth of seven clips from the night session. After Jeff draws Pascal’s Triangle in what the students call “choose” notation, the researcher asks the students to express an instance of the addition rule using that “choose” notation (the notation for selecting combinations). Michael gives an example, and then he and the other students discuss the meaning of other specific instances of Pascal’s Identity in “choose” notation, in terms of specific instances of the pizza problem.
Notes:
The n-topping pizza problem is: How many pizzas can be made when there are n different pizza toppings 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, Pizza
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, Referencing a previous problem, Recognizing a pattern, Proportional reasoning
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-CLIP006
Related Publication
   Type: Dissertation
   Label: Ed.D. dissertation references the video footage that includes Night session, Pascal's Identity, clip 6 of 7
   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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