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Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 10 of 11:
Developing mathematical expressions for generating the number of towers 4-cubes tall selecting from green and blue cubes for exactly 2 green cubes, exactly 3 green cubes, and for 4 green cubes
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TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 10 of 11:
Developing mathematical expressions for generating the number of towers 4-cubes tall selecting from green and blue cubes for exactly 2 green cubes, exactly 3 green cubes, and for 4 green cubes
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27
DescriptionIn the tenth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie works with researchers Carolyn Maher and Robert Speiser to synthesize her ideas about how to build the Unifix-cube towers across cases and to describe mathematically how she has generated the number of towers 4-cubes tall for particular cases when selecting from blue and green cubes. She explains how the number of towers for each case -- exactly 2 green cubes, exactly 3 green cubes, and all four green cubes -- can be generated consecutively mathematically, beginning with the knowledge that there are four towers with exactly one green cube.
The problems as proposed to Stephanie are:
How can you determine the actual towers 4 cubes tall selecting from blue and green cubes, for towers with exactly 2 green cubes, given that you know that there are four towers with exactly one green cube?
How could you describe mathematically the number of towers and what does each number in your expression represent?
Knowing that there are six towers with exactly 2 green cubes, how can you determine physically and symbolically the number of towers with exactly 3 green cubes?
Given that there are four towers with 3 green cubes, how can you determine physically and symbolically the number of towers with 4 green cubes?
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-CLIP010
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 10 of 11: Developing mathematical expressions for generating the number of towers 4-cubes tall selecting from green and blue cubes for exactly 2 green cubes, exactly 3 green cubes, and for 4 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