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Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 3 of 7: Modeling the square of (a+b) for the case of a=3 and b=7. [video] Retrieved from https://doi.org/doi:10.7282/T3X63KTG

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 3 of 7: Modeling the square of (a+b) for the case of a=3 and b=7.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-07
Persistent URLhttps://doi.org/doi:10.7282/T3X63KTG
DescriptionIn the third clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn Maher, asks about the square of (a+b) for the particular case when a=3 and b=7. Referring to the symbolic expansion that she had figured out earlier, Stephanie calculates the value of each part of the expression after substituting 3 and 7 for each "a" and each "b" and finds that the total of the four sums is 100. Stephanie then builds a model of this expression with the base-ten flat partitioned into the four areas.
The problem as presented to Stephanie:
Find the area of each of the four parts of the square of (a+b) for a=3 and b=7 and calculate the total area.
Math ToolBase ten blocks, Algebra blocks
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, 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 ViewsWork view, Student view
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Date Captured1996-02-07
Local IdentifierA64A65-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 three of seven, Clip 3 of 7: Modeling the square of (a+b) for the case of a=3 and b=7.
   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: A64, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (student view), Grade 8, February 7, 1996, raw footage.
   Identifier: A64-19960207-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A65, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (work view), Grade 8, February 7, 1996, raw footage.
   Identifier: A65-19960207-KNWH-WV-INT-GR8-ALG-BIEX-RAW