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**Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 8 of 9: Issues related to a physical model for (a+b) cubed and the volume of the model for a=1 and b=2. [video]** Retrieved from

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 8 of 9: Issues related to a physical model for (a+b) cubed and the volume of the model for a=1 and b=2.

PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-21

DescriptionIn the eighth clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie revisits her physical model of (a+b) cubed. She identifies each piece of the model and points out that the pieces are in one-to-one correspondence with the terms of the algebraic expansion. When researcher Perl raises questions about the small cube, Maher agrees that the specificity of the pieces makes it difficult to use the model to represent the general form. Stephanie responds to their discussion by letting the length of the side of the small cube, "a", be 1 and the length of the longer side of each other piece, "b", be 2, because the physical pieces appeared to be constructed in this manner. She then calculates the volume of the cube with side (a+b) to be 27 and checks her answer by counting the number of small cubes in the total figure.

The problem as presented to Stephanie:

If the side of the small cube is one linear unit, find the volume of the cube constructed from the eight pieces.

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 Captured1996-02-21

Local IdentifierA66A67-ALG-BIEX-CLIP008

Related Publication

__Type__: Related publication

__Label__: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 8 of 9: Issues related to a physical model for (a+b) cubed and the volume of the model for a=1 and b=2.

__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__: A66, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (student view), Grade 8, February 21, 1996, raw footage.

__Identifier__: A66-19960221-KNWH-SV-INT-GR8-ALG-BIEX-RAW

Source

__Title__: A67, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (work view), Grade 8, February 21, 1996, raw footage.

__Identifier__: A67-19960221-KNWH-WV-INT-GR8-ALG-BIEX-RAW