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Continuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths [video]. Retrieved from https://doi.org/doi:10.7282/T3X63KHF
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Description
TitleContinuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1993-10-06
Persistent URLhttps://doi.org/doi:10.7282/T3X63KHF
DescriptionIn the fourth clip Michael and Brian worked together to compare one half and three fourths.
Michael built a model of an orange and red train, two dark green rods, and four light green rods. He then compared the length of three light green rods and one dark green rod and concluded directly that three fourths is larger than one half by one fourth. Two minutes later, researcher Amy Martino asked Michael and Brian to explain their model. Michael repeated his direct argument, and Brian agreed with his justification. Brian built a second model using the purple rod, two red rods, and four white rods. Michael tried to find another model, and he followed Brian’s suggestion to use another length train that was “even.” Michael built a model using a blue and yellow train as one, and two black rods as halves. He then tried to find a rod that could be one fourth of the train. After trying the purple rods and seeing that they would not work, he used reasoning to explain to Brian that the model didn’t work. Brian then built another model using a train of two blue and one red rod, two orange rods, and four yellow rods. He reasoned that this model also showed that three fourths was larger than one half by one fourth. Brian and Michael then decided to record their solution to the problem. Michael, with some assistance from Brian, found a fourth model, and they each set out to record two models and explain why their solution made sense. As in the previous session, Brian and Michael used their models to write a general solution and justification to the problem. As they spoke, they referred to the models that they had built to ensure that their justification paralleled the specific model that they had used to think about the problem. The researcher then approached them and Brian read his justification to her.
Michael built a model of an orange and red train, two dark green rods, and four light green rods. He then compared the length of three light green rods and one dark green rod and concluded directly that three fourths is larger than one half by one fourth. Two minutes later, researcher Amy Martino asked Michael and Brian to explain their model. Michael repeated his direct argument, and Brian agreed with his justification. Brian built a second model using the purple rod, two red rods, and four white rods. Michael tried to find another model, and he followed Brian’s suggestion to use another length train that was “even.” Michael built a model using a blue and yellow train as one, and two black rods as halves. He then tried to find a rod that could be one fourth of the train. After trying the purple rods and seeing that they would not work, he used reasoning to explain to Brian that the model didn’t work. Brian then built another model using a train of two blue and one red rod, two orange rods, and four yellow rods. He reasoned that this model also showed that three fourths was larger than one half by one fourth. Brian and Michael then decided to record their solution to the problem. Michael, with some assistance from Brian, found a fourth model, and they each set out to record two models and explain why their solution made sense. As in the previous session, Brian and Michael used their models to write a general solution and justification to the problem. As they spoke, they referred to the models that they had built to ensure that their justification paralleled the specific model that they had used to think about the problem. The researcher then approached them and Brian read his justification to her.
Math ToolCuisenaire rods
Math StrandFractions
Math ProblemFraction as number, Comparing fractions, Equivalent 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, Reasoning by upper and lower bounds, Generic reasoning
Grade Level4
Student ParticipantsMichael (Colts Neck, student), Brian F. (Colts Neck, student)
MediatorsMartino, Amy Marie (Researcher)
CorporateConover Road (Colts Neck, N.J.)
SettingClassroom
Student GenderMale
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 Captured1993-10-06
Local IdentifierA89A90A91-FRC-CMPRF-CLIP004
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Continuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths
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 Continuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths
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 Continuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths
Date: 2008
Author: Reynolds, Suzanne Loveridge (Rutgers, the State University of New Jersey)
Name: A study of fourth-grade students' explorations into comparing fractions
Reference: QA.R465 2005
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Continuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths
Date: 2008
Author: Reynolds, Suzanne Loveridge (Rutgers, the State University of New Jersey)
Name: A study of fourth-grade students' explorations into comparing fractions
Reference: QA.R465 2005
Source
Title: A89, Continuing to explore fraction comparisons (classroom view), Grade 4, October 6, 1993, raw footage.
Identifier: A89-19931006-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Title: A89, Continuing to explore fraction comparisons (classroom view), Grade 4, October 6, 1993, raw footage.
Identifier: A89-19931006-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Source
Title: A90, Continuing to explore fraction comparisons (presentation view), Grade 4, October 6, 1993, raw footage.
Identifier: A90-19931006-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Title: A90, Continuing to explore fraction comparisons (presentation view), Grade 4, October 6, 1993, raw footage.
Identifier: A90-19931006-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Source
Title: A91, Continuing to explore fraction comparisons (side view), Grade 4, October 6, 1993, raw footage.
Identifier: A91-19931006-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW
Title: A91, Continuing to explore fraction comparisons (side view), Grade 4, October 6, 1993, raw footage.
Identifier: A91-19931006-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW