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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and geometrically [video]. Retrieved from https://doi.org/doi:10.7282/T3G73CK5

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and geometrically
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-21
Persistent URLhttps://doi.org/doi:10.7282/T3G73CK5
DescriptionIn the first clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie explains the conclusions that she has justified in earlier interviews. In response to the researcher, Carolyn Maher, Stephanie firsts writes out the expanded form of (a+b) squared. She then explains that she had used geometric drawings to illustrate the meaning of the square with side a, first by substituting the value 3 for a and drawing a 3 by 3 array within a square and then representing a square with side (a+b) by sectioning her drawing into four parts.
The problem as presented to Stephanie:
Explain your conclusions about the square of the quantity (a+b).
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
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
Date Captured1996-02-21
Local IdentifierA66A67-ALG-BIEX-CLIP001
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and 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: A66, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (student view), Grade 8, February 21, 1996, raw footage.
   Identifier: A66-19960221-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A67, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (work view), Grade 8, February 21, 1996, raw footage.
   Identifier: A67-19960221-KNWH-WV-INT-GR8-ALG-BIEX-RAW