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Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 7 of 7: Testing the algebraic expansion of (a+b) cubed with numbers and beginning to imagine a physical model [video]. Retrieved from https://doi.org/doi:10.7282/T3JW8CTC

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 7 of 7: Testing the algebraic expansion of (a+b) cubed with numbers and beginning to imagine a physical model
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-07
Persistent URLhttps://doi.org/doi:10.7282/T3JW8CTC
DescriptionIn the final seventh clip from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie checks her completed symbolic expansion for (a+b) cubed by letting a=3 and b=7. She substitutes the values into each term of the expression, calculates the values for each and adds to find a total of 1000. When researcher Carolyn Maher asks if she is convinced that her expression is the same as (a+b) cubed, Stephanie says that she is and that she could have substituted any other pairs of numbers. As the interview ends, the researcher challenges Stephanie to consider how she might construct a physical model for (a+b) cubed that would include each of the four algebraic terms in her expansion.
The problem as presented to Stephanie:
Test the expansion of the quantity (a+b) cubed for a=3 and b=7.
How could you construct a physical model for (a+b) cubed?.
Math ToolColor markers, Base 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-CLIP007
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 7 of 7: Testing the algebraic expansion of (a+b) cubed with numbers and beginning to imagine a physical model
   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