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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 7 of 10: Continuing investigation of Pascal's Triangle to generate rows 5 and 6 and calculate the totals for each row. [video] Retrieved from https://doi.org/doi:10.7282/T3571B0K

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 7 of 10:
Continuing investigation of Pascal's Triangle to generate rows 5 and 6 and calculate the totals for each row.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-13
Persistent URLhttps://doi.org/doi:10.7282/T3571B0K
DescriptionIn the seventh 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. Stephanie is asked by the researcher, Carolyn Maher, to use the addition pattern that she has recognized in the first four rows of her triangle representation of the terms to predict the numbers in row 5 and to check that the total is consistent with the total number of towers 5-cubes tall when selecting from two colors. Maher then asks Stephanie to predict the values and total for row 6 and shares information about the origin of Pascal's Triangle.
The problems as presented to Stephanie:
According to the addition pattern and the values that you have determined for rows 1 through 4, what would be the values in row 5 of the triangle? What is the total of the values in this row? Predict from the addition pattern the values for row 6 and check to determine that the total is consistent with your knowledge of the number of towers 6 cubes tall.
Math ToolColor markers
Math StrandAlgebra
Math ProblemBinomial expansion, Explore Pascal's triangle
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Constructing a pictorial model, Referencing a previous problem, Recognizing a pattern, Making conjectures
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student view
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-CLIP007
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 7 of 10: Continuing investigation of Pascal's Triangle to generate rows 5 and 6 and calculate the totals for each row.
   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