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Early algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 2 of 9: Distributing a variable over other variables, Does it check out with numbers? [video]. Retrieved from
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TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 2 of 9: Distributing a variable over other variables, Does it check out with numbers?
Publisher: , , c
DescriptionIn the second clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, researcher, Carolyn A. Maher, asks Stephanie, an 8th grade student, whether a variable "a" could be distributed over a quantity composed of the sum of two other variables and how this would be represented symbolically. Stephanie, after conjecturing that a(x + y) would be the same as ax + ay, begins by substituting the numbers 2, 3 and 4 for "a", "x" and"y" in each expression to test her conjecture. When asked whether her conjecture will always work, she questions the usefulness of distributing multiplication over addition in cases where there are numbers, rather than variables, to express the sum. She then tests her conjecture by substituting the numbers 2 and 4 for "a" and "y", setting the resulting expression equal to 14, the result of the earlier substitution, and solving for "x".
The problem as presented to Stephanie:
a (x + y) is written on Stephanie's paper. The researcher asks: What do you think this might be?
Stephanie's equation for checking her conjecture:
2(x + 4) = 14
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.
Local IdentifierA56A57-ALG-BIEX-CLIP002
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview one of Seven, Clip 2 of 9: Distributing a variable over other variables, Does it check out with numbers?
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: A56, Early algebra ideas about binomial expansion, Stephanie's interview one of seven (student view), Grade 8, November 8, 1995, raw footage.
Identifier: A56-19951108-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
Title: A57, Early algebra ideas about binomial expansion, Stephanie's interview one of seven (work view), Grade 8, November 8, 1995, raw footage.
Identifier: A57-19951108-KNWH-WV-INT-GR8-ALG-BIEX-RAW