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Early algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 2 of 6: How could one represent a square geometrically? [video]. Retrieved from https://doi.org/doi:10.7282/T3Q81C26

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 2 of 6: How could one represent a square geometrically?
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-01-29
Persistent URLhttps://doi.org/doi:10.7282/T3Q81C26
DescriptionIn the second clip in a series of six from the second of seven interviews in which 8th grade Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie begins to explore the meaning of the square of the quantity (a+b) by considering geometrical representations for squares, first of a number and then of the variable "a". The researcher, Carolyn A. Maher, asks Stephanie to show with a drawing why the square of 3 is 9 and to identify and explain the concept of a unit square. Stephanie is then asked to represent the square of "a" geometrically.
The problems as posed to Stephanie:
What is (a+b) squared? What about a square with side "a"?
How could you represent these ideas geometrically?
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, Constructing a pictorial model
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 Captured1996-01-29
Local IdentifierA58A59-ALG-BIEX-CLIP002
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 2 of 6: How could one represent a square geometrically?
   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: A58, Early algebra ideas about binomial expansion, Stephanie's interview two of seven (student view), Grade 8, January 29, 1996, raw footage.
   Identifier: A58-19960129-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A59, Early algebra ideas about binomial expansion, Stephanie's interview two of seven (work view), Grade 8, January 29, 1996, raw footage.
   Identifier: A59-19960129-KNWH-WV-INT-GR8-ALG-BIEX-RAW