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Early algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 3 of 6: Representing a square with side of length (a+b) [video]. Retrieved from https://doi.org/doi:10.7282/T32J69VF

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Description

TitleEarly algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 3 of 6: Representing a square with side of length (a+b)
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-01-29
Persistent URLhttps://doi.org/doi:10.7282/T32J69VF
DescriptionIn the third clip in a series of six from the second of seven interviews in which 8th grade Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn Maher asks Stephanie to draw and label a square with side length (a+b). Stephanie draws and labels the square, marking the lengths "a" and "b" on each side. She then explores ways of partitioning the drawing in order to determine its area geometrically.
The problems as posed to Stephanie:
What is the meaning of the square of the quantity (a+b)? What about a square with side "a"?
What about a square with each side 3 units in length? 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), Muter, Ethel M. (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student view
Date Captured1996-01-29
Local IdentifierA58A59-ALG-BIEX-CLIP003
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 3 of 6: Representing a square with side of length (a+b)
   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