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Early algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 5 of 6: Testing the geometric solution for the square of (a+b) [video]. Retrieved from https://doi.org/doi:10.7282/T3FQ9VKR

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Description

TitleEarly algebra ideas about binomial expansion, Stephanie's interview two of seven, Clip 5 of 6: Testing the geometric solution for the square of (a+b)
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-01-29
Persistent URLhttps://doi.org/doi:10.7282/T3FQ9VKR
DescriptionIn the fifth 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 substitute numbers in order to test the geometric solution that she has developed for the square of (a+b). When substituting 2 for "a" and 3 for "b" give the correct answer, the researcher asks whether this is sufficient to justify her solution. Stephanie tries another pair of numbers that also result in a correct answer, and affirms that she is convinced, partly because of the numbers, but primarily because of the logic of her geometric solution.
The problems as posed to Stephanie:
Test your solution, that the square of the quantity (a+b) is equal to the square of "a" plus 2 times the product of "a" and "b" plus the square of b, by substituting numbers for "a" and "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, Substituting numbers for variables
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 ViewsStudent view, Work view
Date Captured1996-01-29
Local IdentifierA58A59-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 two of seven, Clip 5 of 6: Testing the geometric solution for the square of (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: 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: Early algebra ideas about binomial expansion, Stephanie's interview one of seven (work view), Grade 8, January 29, 1996, raw footage
   Identifier: A59-19951108-KNWH-WV-INT-GR8-ALG-BIEX-RAW