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Comparing fractions and evaluating models that represent solutions, Clip 5 of 8: Small group work, comparing one half and one fourth [video]. Retrieved from https://doi.org/doi:10.7282/T30K274D
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Description
TitleComparing fractions and evaluating models that represent solutions, Clip 5 of 8: Small group work, comparing one half and one fourth
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1993-10-01
Persistent URLhttps://doi.org/doi:10.7282/T30K274D
DescriptionIn clip 5, researcher Carolyn Maher then asked the students to compare one half and one quarter and determine the difference between the two. The students worked in their groups to build models that would help them solve the problem. Erik and Alan worked together to find a model that would show the difference between one half and one fourth. Alan built a model and concluded that one half is bigger than one quarter by one quarter. Michael and Brian each built a model of two dark green and four light green rods. Brian exclaimed that it’s not bigger and Michael said that he knew why one fourth was not bigger than one half. He explained that one half has a two in the denominator and one quarter has four as the bottom number and that it would therefore take two dark greens and four light green rods. Michael used reasoning to explain why one fourth is smaller than one half. Brian said that he had never thought of it in that way. Then, Brian asked him to re-explain. Michael used his written notation for one half and one quarter and re-explained it to him.
Graham, whose partner was not present, spoke with the researcher about the solution to the problem. Using the same model as Michael and Brian, he explained directly, upon questioning, that one half was larger than one quarter by one quarter. Alan then built another model that showed the difference between one half and one quarter. He used two orange rods and four yellow rods, and concluded that one could “quarter a train of orange rods”. Erik then tried to build a model using the two brown rods. He found that that model could also be built to show fourths, and told Alan that they could keep going down by two, indicating: “Brown, you minus two, take that rod, and you can quarter that one. Brown, black then dark green!” Erik reasoned to find models that could show halves and quarters. Alan explained their method to the researcher, who asked them to repeat it to researcher Robert B. Davis.
Graham, whose partner was not present, spoke with the researcher about the solution to the problem. Using the same model as Michael and Brian, he explained directly, upon questioning, that one half was larger than one quarter by one quarter. Alan then built another model that showed the difference between one half and one quarter. He used two orange rods and four yellow rods, and concluded that one could “quarter a train of orange rods”. Erik then tried to build a model using the two brown rods. He found that that model could also be built to show fourths, and told Alan that they could keep going down by two, indicating: “Brown, you minus two, take that rod, and you can quarter that one. Brown, black then dark green!” Erik reasoned to find models that could show halves and quarters. Alan explained their method to the researcher, who asked them to repeat it to researcher Robert B. Davis.
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, Recursive reasoning
Grade Level4
Student ParticipantsAlan (student), Erik (student), Michael (Colts Neck, student), Brian F. (Colts Neck, student), Graham (student)
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 Captured1993-10-01
Local IdentifierA83A84A85-FRC-CMPRF-CLIP005
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes Comparing fractions and evaluating models that represent solutions, Clip 5 of 8: Small group work, comparing one half and one fourth
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 5 of 8: Small group work, comparing one half and one fourth
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 5 of 8: Small group work, comparing one half and one fourth
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 5 of 8: Small group work, comparing one half and one fourth
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