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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 2 of 9: Reviewing the algebraic expansion of (a+b) cubed. [video] Retrieved from https://doi.org/doi:10.7282/T3M0449W

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 2 of 9: Reviewing the algebraic expansion of (a+b) cubed.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-21
Persistent URLhttps://doi.org/doi:10.7282/T3M0449W
DescriptionIn the second 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 describes to researcher Carolyn Maher her algebraic expansion of (a+b) cubed. Stephanie first rewrites the expression as (a+b)(a+b)(a+b), then replaces two factors of (a+b) with the quantity (a squared + 2ab + b squared) and uses the distributive property to complete the expansion which she then simplifies.
The problem as presented to Stephanie:
Explain your conclusions about the cube 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-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 four of seven, Clip 2 of 9: Reviewing the algebraic expansion of (a+b) cubed.
   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