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Early algebra ideas about binomial expansion, Stephanie's interview one of seven, clip 6 of 9: Testing (x + y)(x + y) = x(x + y) + y(x + y) with numbers. [video] Retrieved from https://doi.org/doi:10.7282/T3VX0FH8

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, clip 6 of 9: Testing (x + y)(x + y) = x(x + y) + y(x + y) with numbers.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1995-11-08
Persistent URLhttps://doi.org/doi:10.7282/T3VX0FH8
DescriptionIn the sixth 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 justify her conjecture that
(x + y)(x + y) could also be represented as x(x + y) + y(x + y). Stephanie substitutes 2 for "x" and 3 for "y" into each side of the equation and performs the calculations to determine that the statement is true for those values. Subsequently she substitutes 4 for "x" and 5 for "y" as a second test.
The problem presented to Stephanie:
You say that (x + y)(x + y) = x(x + y) + y(x + y). How could you test that conjecture?
Math ToolColor markers
Math StrandAlgebra
Math ProblemSimplify expressions
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Considering a simpler problem, 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 ViewsStudent view, Work 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 Captured1995-11-08
Local IdentifierA56A57-ALG-BIEX-CLIP006
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 6 of 9: Testing (x + y)(x + y) = x(x + y) + y(x + y) with numbers
   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