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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle. [video] Retrieved from
https://doi.org/doi:10.7282/T31G0K7D
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TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-13
DescriptionIn the sixth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Researcher Carolyn Maher asks Stephanie to represent towers one-cube tall using the combinatorics notation introduced earlier for n choose r, and records this in a form that is the first row of Pascal's Triangle. As Stephanie continues to develop this correspondence for towers 2 and 3-cubes tall, she recognizes the addition property of the triangle. Using this pattern to predict the entries for the 4th row of the triangle, Stephanie recognizes that the predicted entries correspond correctly to the numbers of towers that she had built for each case. She uses this representation and the recognized pattern to predict the entries in the 5th row.
The problems as presented to Stephanie:
Does the number of towers in each case for n equal 1 to 3-cubes tall and r equal to the number of red cubes from zero to n, when selecting from two colors, match the corresponding entry in each of the first 3 rows of Pascal's Triangle?
How can this representation be used to predict rows 4 and 5 in the Triangle and the corresponding number of towers 4 and 5-cubes tall?
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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 Captured1996-03-13
Local IdentifierA68A69-ALG-BIEX-CLIP006
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle.
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: A68, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (student view), Grade 8, March 13, 1996, raw footage.
Identifier: A68-19960313-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
Title: A69, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (work view), Grade 8, March 13, 1996, raw footage.
Identifier: A69-19960313-KNWH-WV-INT-GR8-ALG-BIEX-RAW