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**Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 2 of 11: Stephanie rebuilds Unifix towers 1-cube, 2-cubes, 3-cubes and 4-cubes tall, selecting from two colors [video]. ** Retrieved from

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 2 of 11: Stephanie rebuilds Unifix towers 1-cube, 2-cubes, 3-cubes and 4-cubes tall, selecting from two colors

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

DescriptionIn the second clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues her exploration of early algebraic ideas about binomial expansion with researchers Carolyn Maher and Robert Speiser. After reviewing the meaning of the combinatorics notation, Stephanie begins to logically build sets of Unifix towers of different heights when selecting from green and blue cubes. She asserts that there would be exactly two towers that are one-cube tall and positions these two cubes as a first row. She then constructs the four towers that could be generated from those two by adding either a green or a blue cube onto the original cubes and positions them as a second row. Stephanie then repeats this process to produce a third row of towers 3-cubes tall. Finally, she rebuilds the set of towers 4-cubes tall that she had built earlier and positions them in a fourth row, according to the correspondence between each of the 8 towers in row 3 with the pair that it could have generated

The problems, as generated by Stephanie for her discussion with the researchers:

Explain the meaning of the symbolic notation for selecting a particular number of items from a set of items.

Beginning with towers one cube tall, build each successive set of towers from towers that are two-cubes tall through towers that are 4-cubes tall, showing how each successive set of towers is generated from the row with height of one fewer cube.

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-CLIP002

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 2 of 11: Stephanie rebuilds Unifix towers 1-cube, 2-cubes, 3-cubes and 4-cubes tall, selecting from two colors.

__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