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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 8 of 9: Issues related to a physical model for (a+b) cubed and the volume of the model for a=1 and b=2. [video] Retrieved from https://doi.org/doi:10.7282/T3CF9P0P

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 8 of 9: Issues related to a physical model for (a+b) cubed and the volume of the model for a=1 and b=2.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-21
Persistent URLhttps://doi.org/doi:10.7282/T3CF9P0P
DescriptionIn the eighth 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 revisits her physical model of (a+b) cubed. She identifies each piece of the model and points out that the pieces are in one-to-one correspondence with the terms of the algebraic expansion. When researcher Perl raises questions about the small cube, Maher agrees that the specificity of the pieces makes it difficult to use the model to represent the general form. Stephanie responds to their discussion by letting the length of the side of the small cube, "a", be 1 and the length of the longer side of each other piece, "b", be 2, because the physical pieces appeared to be constructed in this manner. She then calculates the volume of the cube with side (a+b) to be 27 and checks her answer by counting the number of small cubes in the total figure.
The problem as presented to Stephanie:
If the side of the small cube is one linear unit, find the volume of the cube constructed from the eight pieces.
Math ToolColor markers, Algebra blocks
Math StrandAlgebra
Math ProblemConstruct volume model
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, Considering a simpler problem, Constructing a physical model
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-CLIP008
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 8 of 9: Issues related to a physical model for (a+b) cubed and the volume of the model for a=1 and b=2.
   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