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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 8 of 10: Rebuilding Pascal's Triangle using n choose r notation. [video] Retrieved from https://doi.org/doi:10.7282/T39022RB

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 8 of 10: Rebuilding Pascal's Triangle using n choose r notation.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-13
Persistent URLhttps://doi.org/doi:10.7282/T39022RB
DescriptionIn the eighth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Stephanie is asked by the researcher, Carolyn Maher, to recreate Pascal's Triangle with each numerical value replaced by the appropriate combinatorics term. She examines how the entries in each row can be generated from the row before and begins to develop a general rule for representing the additive property for any value of n with two consecutive values of r..
The problems as presented to Stephanie:
Record each value in Pascal's Triangle using n choose r notation. Is there a general notation that can describe the additive property of the triangle?
Math ToolColor markers
Math StrandAlgebra
Math ProblemBinomial expansion, Explore Pascal's triangle
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Constructing a pictorial model, Referencing a previous problem, Recognizing a pattern, Making conjectures
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student 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 Captured1996-03-13
Local IdentifierA68A69-ALG-BIEX-CLIP008
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 8 of 10: Rebuilding Pascal's Triangle using n choose r notation.
   Date: 2011
   Author: Aboelnaga, Eman Y. (Eman Yousry) (Rutgers, the State University of New Jersey)

   Name: A case study: the development of Stephanie's algebraic reasoning
   Reference: http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Source
   Title: A68, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (student view), Grade 8, March 13, 1996, raw footage.
   Identifier: A68-19960313-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A69, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (work view), Grade 8, March 13, 1996, raw footage.
   Identifier: A69-19960313-KNWH-WV-INT-GR8-ALG-BIEX-RAW