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Comparing fractions and evaluating models that represent solutions, Clip 7 of 8: Meredith's challenge, does the model work? [video]. Retrieved from https://doi.org/doi:10.7282/T380516K
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TitleComparing fractions and evaluating models that represent solutions, Clip 7 of 8: Meredith's challenge, does the model work?
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1993-10-01
Persistent URLhttps://doi.org/doi:10.7282/T380516K
DescriptionIn the seventh clip Amy, Jacquelyn, and James built another rod model at the overhead to show their solution to the problem: Which is larger one half or one quarter. Amy explained that they had tried to find a model that did not include a train of rods. She said that the brown rod was called one, the purple rods were one half, the red rods were one quarter, and the white rods were one eighth. James then said, using faulty reasoning, that one half was larger than one quarter by one eighth. Meredith countered the team’s argument. She asked them if they were calling the white rod one eighth, and they answered that they were. She built a model of one purple rod and a train of one red and one white rod. She then said that it couldn’t be bigger by one eighth “because there is still negative space” on the model that she had built. She added a second white rod onto her model and said that the difference could be two eighths, and then substituted a red rod for the two white rods and said that an alternative name could be one quarter. She concluded that either it could be called one quarter or two eighths. The researcher asked the three students what they thought of Meredith’s argument. Jacquelyn said that the group meant that when they put the rods together they equaled one eighth. Meredith asked if they meant that two white rods were one eighth. Jacquelyn clarified that they thought that all of the whites put together were one eighth. Jacquelyn used faulty reasoning to revise their argument. In response, Meredith moved the train of eight white rods onto her model comparing the purple and red rods. She asked rhetorically, “You think it’s bigger than one eighth and all these are one eighth? So that’s how much you think it’s bigger by?” Jacquelyn laughed. Here Meredith showed that their claim could not be true. Jacquelyn then revised her argument, and explained what Meredith had presented. She said that one half was larger than one quarter by two eighths or one quarter. Researcher Carolyn Maher asked her how she knew it was one quarter. She explained directly that the red rods were each one quarter and that two white rods viewed together can also be called one quarter.
Math ToolCuisenaire rods
Math StrandFractions
Math ProblemFraction as number, Comparing fractions
NCTM Grade Range3-5
NCTM Content StandardNumber and operations
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Indirect reasoning
Grade Level4
Student ParticipantsAmy (student), Kelly (student), James (student), Meredith (student), Jacquelyn (student), Jessica (student)
CorporateConover Road (Colts Neck, N.J.)
SettingClassroom
Student GenderMixed
Student EthnicityWhite
Camera ViewsClassroom view, Presentation view, Side 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 Captured1993-10-01
Local IdentifierA83A84A85-FRC-CMPRF-CLIP007
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Comparing fractions and evaluating models that represent solutions, Clip 7 of 8: Meredith's challenge, does the model work?
Date: 2009
Author: Yankelewitz, Dina (Rutgers, the State University of New Jersey)
Name: The development of mathematical reasoning in elementary school students' exploration of fraction ideas
Reference: http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000054787
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Comparing fractions and evaluating models that represent solutions, Clip 7 of 8: Meredith's challenge, does the model work?
Date: 2009
Author: Yankelewitz, Dina (Rutgers, the State University of New Jersey)
Name: The development of mathematical reasoning in elementary school students' exploration of fraction ideas
Reference: http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000054787
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Comparing fractions and evaluating models that represent solutions, Clip 7 of 8: Meredith's challenge, does the model work?
Date: 2001
Author: Steencken, Elena Perrone (Rutgers, the State University of New Jersey)
Name: Tracing the growth in understanding of fraction ideas
Reference: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000055125
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Comparing fractions and evaluating models that represent solutions, Clip 7 of 8: Meredith's challenge, does the model work?
Date: 2001
Author: Steencken, Elena Perrone (Rutgers, the State University of New Jersey)
Name: Tracing the growth in understanding of fraction ideas
Reference: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000055125
Source
Title: A83, Comparing fractions and evaluating models that represent solutions (classroom view), Grade 4, October 1, 1993, raw footage.
Identifier: A83-19931001-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Title: A83, Comparing fractions and evaluating models that represent solutions (classroom view), Grade 4, October 1, 1993, raw footage.
Identifier: A83-19931001-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Source
Title: A84, Comparing fractions and evaluating models that represent solutions (presentation view), Grade 4, October 1, 1993, raw footage.
Identifier: A84-19931001-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Title: A84, Comparing fractions and evaluating models that represent solutions (presentation view), Grade 4, October 1, 1993, raw footage.
Identifier: A84-19931001-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Source
Title: A85, Comparing fractions and evaluating models that represent solutions (side view), Grade 4, October 1, 1993, raw footage.
Identifier: A85-19931001-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW
Title: A85, Comparing fractions and evaluating models that represent solutions (side view), Grade 4, October 1, 1993, raw footage.
Identifier: A85-19931001-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW