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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives. [video] Retrieved from https://doi.org/doi:10.7282/T3QR4W1X

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-21
Persistent URLhttps://doi.org/doi:10.7282/T3QR4W1X
DescriptionIn the third clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, researcher Carolyn Maher presents Stephanie with base-ten materials, algebra blocks and other rectangular prisms; then asks her how she might use any of the manipulatives to explain volume in general and the volume of cube with side (a+b) in particular. Stephanie uses the small cubic unit and the 100 cubic unit "flat" from the base-ten materials to explain the numerical volume of the large 1000 cubic unit block. She was then asked how she might figure out the volume of the large block if it were to have a side of (a+b). Precision about language and issues of meaning with reference to geometric models that involve two and three dimensions are addressed directly in clip 4 and discussed in each subsequent clip in the series.
The problem as presented to Stephanie:
How could you use squared materials to show the cube of the quantity (a+b)?
Math ToolColor markers, Base ten blocks, Algebra blocks
Math StrandAlgebra
Math ProblemConstruct volume model
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 physical model, Constructing a pictorial model
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsStudent view, Work 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 Captured1996-02-21
Local IdentifierA66A67-ALG-BIEX-CLIP003
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.
   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: A66, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (student view), Grade 8, February 21, 1996, raw footage.
   Identifier: A66-19960221-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A67, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (work view), Grade 8, February 21, 1996, raw footage.
   Identifier: A67-19960221-KNWH-WV-INT-GR8-ALG-BIEX-RAW