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Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes. [video] Retrieved from https://doi.org/doi:10.7282/T34J0CXH

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-04-17
Persistent URLhttps://doi.org/doi:10.7282/T34J0CXH
DescriptionIn the second clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first predicts the number of Unifix-cube towers with exactly three red cubes to be generated from the six towers with two red and two yellow cubes. In response to questions from researchers Carolyn Maher and Donna Weir, Stephanie predicts and then builds twelve towers from the six and identifies the four sets of three duplicate towers to produce the four unique towers with exactly three red cubes. Stephanie notes that the six towers with two of each color would be multiplied by 2 because of the two possible positions for the third red cube and the resulting 12 would be divided by 3 to account for the duplicates. She then focuses on the four towers with exactly one red cube and recognizes that each of these would produce a single tower with all four cubes yellow. Since the four would be the same, there would be only one such tower. Stephanie concludes by noting that this same process would produce a single tower with four red cubes from the four that she has built with exactly three red cubes.

The problems posed to Stephanie are:
Predict the number of towers with exactly three red cubes that would be generated from the six towers with two red and two yellow.
Confirm your prediction by building the towers and eliminating duplicates. How would you describe this process with numbers?
Predict the number of towers that would be produced moving from three of one color to all four of that color. How can you confirm that prediction?
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, Reasoning by contradiction, Controlling for variables
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-CLIP002
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 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes.
   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