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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 5 of 10: Recognizing the symmetry for the two colors across the cases when building unifix towers four-cubes tall [video]. Retrieved from https://doi.org/doi:10.7282/T3862J4T

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 5 of 10: Recognizing the symmetry for the two colors across the cases when building unifix towers four-cubes tall
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, 1996-03-13, c1996-03-13
Persistent URLhttps://doi.org/doi:10.7282/T3862J4T
DescriptionIn the fifth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Referring to the combinatorics notation for each of the five cases for n equal height 4 and r equal to the number of red cubes from zero to four, researcher Carolyn Maher asks Stephanie whether there would not be 16 more towers if one was focusing on r as the number of yellow cubes from zero to four. Stephanie reasons that the solution for that investigation would include the same 16 towers in reverse order. The problems as presented to Stephanie:Based on the number of towers in each case for n equal height 4 and r equal to the number of red cubes from zero to four, will there not be an equal number of towers for n equal height 4 and r equal to the number of yellow cubes from zero to four, resulting in a final total of 32 towers? Justify your answer.
Math ToolColor markers
Math StrandAlgebra
Math ProblemBinomial expansion, Towers
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Constructing a pictorial model, Referencing a previous problem, Recognizing a pattern, Making conjectures
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 Captured1996-03-13
Local IdentifierA68A69-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 five of seven, Clip 5 of 10: Recognizing the symmetry for the two colors across the cases when building unifix towers four-cubes tall
   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