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Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 6 of 7: Making sense of the Pascal Triangle addition rule with Unifix cube towers . [video] Retrieved from https://doi.org/doi:10.7282/T3NG4PFF

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 6 of 7: Making sense of the Pascal Triangle addition rule with Unifix cube towers .
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-04-17
Persistent URLhttps://doi.org/doi:10.7282/T3NG4PFF
DescriptionIn the sixth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first revisits her investigation of the number of duplicates that would be produced when building Unifix-cube towers 4-tall with three red cubes from the six towers with two red and two yellow cubes. Researcher Carolyn Maher asks Stephanie to justify her conclusion that there would be four sets of three duplicates. Maher then challenges Stephanie to use the sets of towers 3-tall and 4-tall that she has built to model the addition rule of Pascal's Triangle. She then is asked to describe what she has modeled algebraically using combinatorics notation. Researcher Donna Weir is observing.

The problems posed to Stephanie are:
For the towers, 4-cubes tall, with exactly three red cubes, how many duplicates did you find?
How can you explain why there were sets of three duplicates?
As you make a correspondence between the sets of towers of a particular height and each row of Pascal's Triangle, how can you use the towers to show the addition rule as you generate towers of the next height?
How could you describe what you have built using combinatorics notation?
Math ToolUnifix cubes, Color markers
Math StrandAlgebra
Math ProblemBinomial expansion
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsReasoning by cases, Direct reasoning, Recognizing a pattern, Recursive reasoning, Controlling for variables
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher), Weir, M. Donna (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student view
Date Captured1996-04-17
Local IdentifierB08B09-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 seven of seven, Clip 6 of 7: Making sense of the Pascal Triangle addition rule with Unifix cube towers.
   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: B08, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (student view), Grade 8, April 17, 1996, raw footage.
   Identifier: B08-19960417-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: B09, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (work view), Grade 8, April 17, 1996, raw footage.
   Identifier: B09-19960417-KNWH-WV-INT-GR8-ALG-BIEX-RAW