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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 10 of 10: Generating the exponents in the expansion of (a + b) to the seventh power. [video] Retrieved from https://doi.org/doi:10.7282/T3JD4VRX

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 10 of 10: Generating the exponents in the expansion of (a + b) to the seventh power.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-13
Persistent URLhttps://doi.org/doi:10.7282/T3JD4VRX
DescriptionIn the final 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. Researcher Carolyn Maher asks Stephanie to use the relationships that she has recognized between Pascal's Triangle and both unifix-cube towers and expansions of the binomial (a + b) to predict the exponents for each term of (a + b) to the 7th power.
The problems as presented to Stephanie:
Use the symmetries that you see in the successive expansions of (a + b) and your knowledge of unifix-cube towers, selecting from 2 colors, to generate the exponents for each term in the expansion of (a + b) to the 7th power.
Math ToolColor markers
Math StrandAlgebra
Math ProblemTowers, Binomial 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, Constructing a pictorial model, Referencing a previous problem, Recognizing a pattern, Recognizing an isomorphism, Making conjectures
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 Captured1996-03-13
Local IdentifierA68A69-ALG-BIEX-CLIP010
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 10 of 10: Generating the exponents in the expansion of (a + b) to the seventh power.
   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: A68, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (student view), Grade 8, March 13, 1996, raw footage.
   Identifier: A68-19960313-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A69, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (work view), Grade 8, March 13, 1996, raw footage.
   Identifier: A69-19960313-KNWH-WV-INT-GR8-ALG-BIEX-RAW