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Early algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 5 of 9: Beginning to make sense of (x + y)(x + y) [video]. Retrieved from https://doi.org/doi:10.7282/T3GM8696

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 5 of 9: Beginning to make sense of (x + y)(x + y)
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, 1995-11-08, c
Persistent URLhttps://doi.org/doi:10.7282/T3GM8696
DescriptionIn the fifth clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion researcher Carolyn Maher asks Stephanie to multiply (x + y)(x + y). Stephanie conjectures that this would be x "squared" plus y "squared", symbolically represented by the exponent 2 above x and above y, only to disprove her conjecture by substituting numbers.
Stephanie then concludes that, since a(x + y) = ax + ay, (x + y)(x + y) could also be represented as
x(x + y) + y(x + y).
The problem as presented to Stephanie:
What about (x + y)(x + y) ? What would that be?
Math ToolColor markers
Math StrandAlgebra
Math ProblemBinomial expansion
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Additive reasoning, Reasoning by contradiction, Substituting numbers for variables
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.
Local IdentifierA56A57-ALG-BIEX-CLIP005
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early Algebra Ideas About Binomial Expansion, Stephanie's Interview One of Seven: Clip 5 of 9, Beginning to make sense of (x + y)(x + y)
   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: A56, Early algebra ideas about binomial expansion, Stephanie's interview one of seven (student view), Grade 8, November 8, 1995, raw footage.
   Identifier: A56-19951108-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A57, Early algebra ideas about binomial expansion, Stephanie's interview one of seven (work view), Grade 8, November 8, 1995, raw footage.
   Identifier: A57-19951108-KNWH-WV-INT-GR8-ALG-BIEX-RAW