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Discovering equivalent fractions and introducing fraction notation, Clip 5 of 5: Compare one half and two thirds, establishing equivalence [video]. Retrieved from https://doi.org/doi:10.7282/T3D7990C
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Description
TitleDiscovering equivalent fractions and introducing fraction notation, Clip 5 of 5: Compare one half and two thirds, establishing equivalence
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1993-10-04
Persistent URLhttps://doi.org/doi:10.7282/T3D7990C
DescriptionIn the fifth clip, researcher Carolyn Maher called the class together. At the overhead, Erin, Jackie, and Jessica had built the six and twelve centimeter models. The researcher asked the class to provide the solution to the problem, and they answered in unison that two thirds was larger than one half by one sixth. The researcher then asked if anyone had built a model that gave another solution. Meredith indicated that she had, and she was asked by the researcher to tell the class what she found. Meredith lined twelve white rods against the model using the orange and red train. Before she explained what she had done. Michael began to shake his head in disapproval. The researcher asked Michael what was wrong. Michael said he didn’t think they should use a white rod but rather a red rod to show the difference between two thirds and one half. The researcher asked the class what rod they used to represent one sixth and they replied that they had used the red rod. The researcher pointed out that Meredith had showed it to be bigger by two whites. Michael replied that the two whites together would be one sixth”. Erik then offered his view on the matter. He said that the two whites together could be called two twelfths and if combined they would be called one sixth. The researcher pointed out that Meredith was calling it two twelfths as well as one sixth. Meredith said, “There's two answers." Michael and Erik responded that they were the same answer and Erik elaborated on that explaining that Meredith had taken a red and divided it into half with each half being called one twelfth. The researcher then began to record the students’ arguments using mathematical notation at the OHP. She wrote 1R=2W. Erik then continued his direct argument, saying, And since she's calling a white rod one twelfth and the other white rod one twelfth and the red rod is really one sixth. But, when she calls them two twelfths, the two twelfths are actually just two white rods put together to equal a red, so it should be really, it's really one sixth. The researcher then recorded 1/12 + 1/12 = 2/12, and Erik pointed out that it’s also one sixth. The researcher then said and wrote that Erik had also said that 1/2 of 1/6 = 1/12, and that 1/6 = 2/12. Erik agreed. Brian then added to the argument that there were two answers. Jessica then continued Erik’s argument, saying, that two whites would equal one red. The class agreed that all the statements that the researcher had recorded were true.
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
Grade Level4
Student ParticipantsAmy (student), Meredith (student), Michael (Colts Neck, student), Erik (student), Brian F. (Colts Neck, student), Jessica (student), Erin (student), Jackie (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 Captured1993-10-04
Local IdentifierA86A87A88-FRC-CMPRF-CLIP005
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Discovering equivalent fractions and introducing fraction notation, Clip 5 of 5: Compare one half and two thirds: Establishing equivalence
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 Discovering equivalent fractions and introducing fraction notation, Clip 5 of 5: Compare one half and two thirds: Establishing equivalence
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 Discovering equivalent fractions and introducing fraction notation, Clip 5 of 5: Compare one half and two thirds: Establishing equivalence
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 Discovering equivalent fractions and introducing fraction notation, Clip 5 of 5: Compare one half and two thirds: Establishing equivalence
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: A86, Discovering equivalent fractions and introducing fraction notation (classroom view), Grade 4, October 4, 1993, raw footage.
Identifier: A86-19931004-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Title: A86, Discovering equivalent fractions and introducing fraction notation (classroom view), Grade 4, October 4, 1993, raw footage.
Identifier: A86-19931004-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Source
Title: A87, Discovering equivalent fractions and introducing fraction notation (presentation view), Grade 4, October 4, 1993, raw footage.
Identifier: A87-19931004-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Title: A87, Discovering equivalent fractions and introducing fraction notation (presentation view), Grade 4, October 4, 1993, raw footage.
Identifier: A87-19931004-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Source
Title: A88, Discovering equivalent fractions and introducing fraction notation (side view), Grade 4, October 4, 1993, raw footage.
Identifier: A88-19931004-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW
Title: A88, Discovering equivalent fractions and introducing fraction notation (side view), Grade 4, October 4, 1993, raw footage.
Identifier: A88-19931004-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW