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Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 3 of 7: Investigating the algebraic generalization for building Unifix-cube towers n-tall with exactly two red cubes from towers with exactly one red cube. [video] Retrieved from https://doi.org/doi:10.7282/T3862F8C

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 3 of 7: Investigating the algebraic generalization for building Unifix-cube towers n-tall with exactly two red cubes from towers with exactly one red cube.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-04-17
Persistent URLhttps://doi.org/doi:10.7282/T3862F8C
DescriptionIn the third clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie continues to investigate the construction of Unifix towers four-cubes tall, selecting from red and yellow cubes, when moving from towers with exactly one red cube to towers with exactly two red cubes. She works with researcher Carolyn Maher to begin to develop and explain a generalized formula based on her physical and numerical representations of the towers. Researcher Donna Weir is observing.

The problems posed to Stephanie are:
From the four Unifix-cube towers, four-cubes tall, with exactly one red and three yellow cubes, how many towers were generated with two red and two yellow cubes?
How could you represent this numerically?
After removing duplicates, how many unique towers did you find?
How could you represent this step and the entire process numerically? What does each number represent in relation to the towers?
For towers of any height n, how might we represent the process of moving from towers with exactly one red cube to towers with exactly two red cubes algebraically?
Math ToolUnifix 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, Recognizing a pattern, Controlling for variables, Generalizing
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher), Weir, M. Donna (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student view
Date Captured1996-04-17
Local IdentifierB08B09-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 seven of seven, Clip 3 of 7: Investigating the algebraic generalization for building Unifix-cube towers n-tall with exactly two red cubes from towers with exactly one red cube.
   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: B08, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (student view), Grade 8, April 17, 1996, raw footage.
   Identifier: B08-19960417-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: B09, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (work view), Grade 8, April 17, 1996, raw footage.
   Identifier: B09-19960417-KNWH-WV-INT-GR8-ALG-BIEX-RAW