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A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage [video]. Retrieved from https://doi.org/doi:10.7282/T3XW4MR8
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Description
TitleA34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, 1993-10-29, c1993-10-29
Persistent URLhttps://doi.org/doi:10.7282/T3XW4MR8
DescriptionIn this raw footage, full-session video, Dr. Davis first introduces Gunnar Gjone as a visiting mathematics educator from Norway. The researcher, Carolyn Maher, begins the session by asking the students to review their conclusions from the previous day’s class when they were asked to share a candy bar equally among the students in their small group. Two groups had been composed of eight students while another was composed of nine students, and their task had been to determine how much more candy each person in the smaller group would receive than those in the larger group, which they agreed to be the difference between 1/4 and 1/9, after dividing each candy bar into 10 equal pieces. Based on Cuisenaire Rod models, the students concluded that the difference was 5/36. However, a number of students, including Meredith, still argued that the difference should be 1/5. After the class agrees that 5/36 is the difference, Jessica contends that the earlier distribution was not equitable. Andrew suggests that the 3 candy bars could be divided into 30 rectangular pieces (10 per candy bar) and shared evenly among all 25 students by having each student get one whole rectangular piece and 1/5 of one of the remaining 5 rectangular pieces. A whole-class discussion follows in which the students are asked to compare and order 1/2, 1/3, 1/4 and 1/5. David shares his solutions based on building models with Cuisenaire rods. Various students mark positions for each of these fractions, and also 1/10, on a number line segment from 0 to 1, drawn on an overhead transparency.The class is then asked to work in pairs to produce number line segments and mark the positions of unit fractions from 1/2 to 1/10 and also 1/100 and 1/1000. Several of the students, including Andrew and Jessica, located 1/3 at two different points on their number line. In a final class discussion, Alan shares his number line, which includes 1/100 and 1/1000, and contends that there could be three points for 1/3. The students discuss this and conclude that the same point on the line segment cannot be named both 1/3 and 2/3 or 1/3 and 3/3 although it is appropriate to name the same point 3/3 and 1.
Math ToolCuisenaire rods
Math StrandFractions
NCTM Grade Range3-5
NCTM Content StandardNumber and operations, Measurement
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Referencing a previous problem, Reasoning by analogy, Proportional reasoning, Considering a simpler problem, Recognizing a pattern, Recognizing equivalence
Grade Level4
Student ParticipantsAlan (student), Andrew (student), Audra (student), Beth (student), Brian F. (Colts Neck, student), Caitlin (student), Danielle (student), David (student), Brian C. (Colts Neck, student), Erin (student), Graham (student), Gregory (student), Jackie (student), Jacquelyn (student), James (student), Jessica (student), Kelly (student), Kimberly (student), Laura (student), Mark (student), Meredith (student), Michael (Colts Neck, student), Sarah (student)
MediatorsMaher, Carolyn Alexander (Researcher), Davis, Robert B. (Robert Benjamin) (Researcher), Gjone, Gunnar (Researcher), Phillips, Joan (Teacher)
CorporateConover Road (Colts Neck, N.J.)
SettingClassroom
Student GenderMixed
Student EthnicityWhite
Camera ViewsPresentation 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 Captured1993-10-29
Local IdentifierA34-19931029-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
Related Publication
Type: Excerpt or clip creation
Label: Video clips created from video footage A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
Name: Fraction problems, Sharing and number lines, Clip 1 of 3: Sharing candy bars, Introducing the problem
Type: Excerpt or clip creation
Label: Video clips created from video footage A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
Name: Fraction problems, Sharing and number lines, Clip 1 of 3: Sharing candy bars, Introducing the problem
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
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#sthash.GokJ943B.dpuf
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
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#sthash.GokJ943B.dpuf
Related Publication
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
Date: 2010
Author: Schmeelk, Suzanna E. (Rutgers, the State University of New Jersey)
Name: Tracing students' growing understanding of rational numbers
Reference: http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052898
Type: Related publication
Label: Ed.D. dissertation references the video footage that includes A34, Fraction problems: Sharing and Number Lines (presentation view), Grade 4, October 29, 1993, raw footage
Date: 2010
Author: Schmeelk, Suzanna E. (Rutgers, the State University of New Jersey)
Name: Tracing students' growing understanding of rational numbers
Reference: http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052898