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**Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 6 of 11: Generating towers 3-cubes tall, selecting from blue and green cubes, from towers with exactly one blue cube to towers with exactly two blue cubes [video]. ** Retrieved from

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 6 of 11: Generating towers 3-cubes tall, selecting from blue and green cubes, from towers with exactly one blue cube to towers with exactly two blue cubes

PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27

DescriptionIn the sixth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is challenged by researchers Carolyn Maher and Robert Speiser to consider how the eight Unifix-cube towers, selecting from green and blue cubes, that correspond to the third row of Pascal's Triangle (given rows from 0 to n), could be generated horizontally. Taking each of the three towers that have exactly one blue cube, Stephanie generates two new towers by holding the blue cube constant and replacing one of the green cubes with a blue cube. After successfully generating one pair of towers with exactly two blue cubes from the first tower with one blue cube, Stephanie recognizes that there is one duplicate in the pair generated from the second tower with one blue cube and that both towers generated from the third tower with one blue cube are duplicates. After removing the duplicates, Stephanie is left with three towers, each with exactly two blue cubes and one green.

The problems as proposed to Stephanie are:

Building on your knowledge of the third row of Pascal's Triangle and the corresponding towers that you have built, you have convinced us that there are only three towers, 3-cubes tall, with exactly one blue cube, when selecting from green and blue cubes because there are exactly three positions in which to place the blue cube.

For each of those three towers, holding the single blue cube constant, how many towers, 3-cubes tall with two blue cubes, can be produced by exchanging one of the two green cubes with a blue cube?

Are any of the towers duplicates? If so, how many? How many unique towers 3-cubes tall 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-CLIP006

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 6 of 11: Generating towers 3-cubes tall, selecting from blue and green cubes, from towers with exactly one blue cube to towers with exactly two 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