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Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 5 of 7: Testing the partial symbolic expansion of the cube of (a+b) for a=3 and b=7. [video] Retrieved from https://doi.org/doi:10.7282/T39C6WB6

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 5 of 7: Testing the partial symbolic expansion of the cube of (a+b) for a=3 and b=7.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-07
Persistent URLhttps://doi.org/doi:10.7282/T39C6WB6
DescriptionIn the fifth clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie is asked by researcher Carolyn Maher to represent the expansion of the quantity (a+b). After Stephanie rewrites the expression (a+b) cubed, first as (a+b)(a+b)(a+b) and then as (a+b)( a squared + 2ab + b squared), she tests her work by letting a=3 and b=7, uses the distributive property to simplify and then calculates the result.
The problem as presented to Stephanie:
Given the expression: (a+b) cubed: what does that mean? If (a+b) cubed = (a+b) (a cubed + 2ab + b cubed), substitute 3 for a and 7 for b and use the distributive property to simplify and then calculate your answer.
Math ToolBase ten blocks
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 HeuristicsDirect reasoning, Substituting numbers for variables, Considering a simpler problem
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
Date Captured1996-02-07
Local IdentifierA64A65-ALG-BIEX-CLIP005
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 5 of 7: Testing the partial symbolic expansion of the cube of (a+b) for a =3 and b=7.
   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: A64, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (student view), Grade 8, February 7, 1996, raw footage.
   Identifier: A64-19960207-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A65, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (work view), Grade 8, February 7, 1996, raw footage.
   Identifier: A65-19960207-KNWH-WV-INT-GR8-ALG-BIEX-RAW