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Early Algebra Ideas About Binomial Expansion, Stephanie's Interview Six of Seven: Clip 7 of 11: Generating towers 4-cubes tall, selecting from blue and green cubes, from towers with exactly one green cube to towers with exactly two green cubes. [video] Retrieved from
https://doi.org/doi:10.7282/T3PG1QJC
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TitleEarly Algebra Ideas About Binomial Expansion, Stephanie's Interview Six of Seven: Clip 7 of 11: Generating towers 4-cubes tall, selecting from blue and green cubes, from towers with exactly one green cube to towers with exactly two green cubes.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27
DescriptionIn the seventh 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 consider how the Unifix-cube towers 4-cubes tall, selecting from green and blue cubes, that correspond to row four of Pascal's Triangle (given rows from 0 to n), could be generated horizontally. Taking each of the four towers with exactly one green cube, Stephanie generates three new towers by holding the green cube constant and replacing one of the blue cubes with a green one. After successfully generating one group of towers with exactly two green cubes from the first tower with one green cube, Stephanie recognizes that one of the towers in the group of three generated from the second tower with one green cube is a duplicate of one in the earlier group, two towers generated from the third tower are duplicates, and all three generated from the fourth tower with one green cube have duplicates in the towers already generated. After removing the duplicates, Stephanie is left with six towers, each with exactly two green and two blue cubes.
The problems as proposed to Stephanie are:
For each tower 4-cubes tall, selecting from blue and green cubes, with exactly one green cube, if you hold the single green cube constant, how many towers, 4-cubes tall with two green cubes, can be produced by exchanging one of the three blue cubes with a green cube?
Are any of the towers duplicates? If so, how many? How many unique towers 4-cubes tall with exactly two green cubes result from this process?
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-CLIP007
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 7 of 11: Generating towers 4-cubes tall, selecting from blue and green cubes, from towers with exactly one green cube to towers with exactly two green 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