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Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes [video]. Retrieved from https://doi.org/doi:10.7282/T3Z036ZZ

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27
Persistent URLhttps://doi.org/doi:10.7282/T3Z036ZZ
Descriptionn the ninth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to describe mathematically how she has generated sets of Unifix-cube towers 4-cubes tall across cases. She first considers the case for all green cubes when generated from the set of cubes with three green cubes and one blue cube and determines that the single resulting tower could be calculated by multiplying four (representing the four towers with exactly 3 green cubes) by 1 (representing the tower formed by exchanging the single blue cube for a green in each tower) and dividing the product by 4 because the four resulting towers are all duplicates. Stephanie then begins to express her observations in writing to explain how the four towers with one blue cube were generated from the towers with two blue and two green cubes.

The problems as proposed to Stephanie are:
How can you determine the number of towers, 4 cubes tall, with four green cubes from your set of four towers with one blue cube and 3 green cubes?
How could you describe with numbers how the single tower with four green cubes is generated?
How could you describe with numbers how the set of our towers with one blue cube and 3 green cubes is generated from the set of towers with two green cubes and two blue cubes ?
Math ToolColor markers, Unifix cubes
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 HeuristicsReasoning by cases, Direct reasoning, Working backwards, Controlling for variables, Recognizing a pattern, Referencing a previous problem
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher), Speiser, R. (Robert) (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsStudent view, Work 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 Captured1996-03-27
Local IdentifierB06B07-ALG-BIEX-CLIP009
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the footage that includes Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes.
   Date: 2011
   Detail: D
   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: B06, Early algebra ideas about binomial expansion, Stephanie's interview six of seven (student view), Grade 8, March 27, 1996, raw footage.
   Identifier: B06-19960327-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: B07, Early algebra ideas about binomial expansion, Stephanie's interview six of seven (work view), Grade 8, March 27, 1996, raw footage.
   Identifier: B07-19960327-KNWH-WV-INT-GR8-ALG-BIEX-RAW