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Students Compare 1/4 and 1/9

Descriptive

TypeOfResource
Text
TitleInfo
Title
Students Compare 1/4 and 1/9
Identifier (type = doi)
doi:10.7282/T3N018PN
Abstract
The class is investigating the difference between 1/4 and 1/9. In initial discussions, some students agree with Meredith, who says that the difference is 1/5 because 9 – 4 = 5. Researcher Maher indicates to the class that if they apply Meredith’s rule to 1/2 and 1/4, they would get an answer of 1/2, challenging their earlier reasoning that produced an answer of 1/4.

Some students build one model to show ninths and a second model (of a different length) to show fifths. For example, Alan builds one model where the blue rod represents 1 and so the white rod would have the number name of 1/9 and a second model where the purple rod represents 1and so the white rod would have the number name of 1/4. Alan concludes that 1/9 is smaller than 1/4, but he is unable to determine the difference using these models. After he is unsuccessful in his attempt to construct a model that can be divided into ninths and fourths, Alan conjectures that the reason is that it is not possible to build a model when one denominator is odd and the other is even. Researcher Maher reminds him that in previous sessions, he built a model for comparing 1/2 and 2/3; in another previous session, he built a model to compare 3/4 and 2/3.

Meanwhile, James builds a model consisting of 3 orange rods and a dark green rod (36 cm.) that can be partitioned into ninths and fourths. He presents the model to Researcher Davis. First, James claims that the difference is 1/5, illustrating this difference by 5 white rods. Researcher Davis responds by asking James to clarify what number name is assigned to one white rod, and then of two white rods. James responds 1/36 and 2/36, respectively. James realizes that if the difference between 1/4 and 1/9 is represented by 5 white rods, then that difference must be 5/36. James then presents this finding to the class.
Genre (authority = RULIB)
Effective teaching
Genre (authority = RULIB)
Student model building
Genre (authority = RULIB)
Reasoning
Genre (authority = RULIB)
English translation
RelatedItem (type = host)
TitleInfo
Title
RBDIL Analytics
Identifier (type = local)
rucore00000002136
Name (id = NAME-1); (type = personal)
NamePart (type = family)
Uptegrove
NamePart (type = given)
Elizabeth
DisplayForm
Elizabeth Uptegrove
Role
RoleTerm (authority = marcrelator); (type = text)
Creator
Affiliation
Video Mosaic Collaborative
Name (id = NAME-2); (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn
DisplayForm
Carolyn Maher
Role
RoleTerm (authority = marcrelator); (type = text)
Publisher
Affiliation
Rutgers University
OriginInfo
DateCreated (qualifier = exact)
2016-07-03T18:25:27-0400
OriginInfo
DateOther (qualifier = exact); (type = modified)
2016-07-11T10:19:01-0400
OriginInfo
DateOther (qualifier = exact); (type = published)
2016-07-11T10:22:46-0400
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Rights

RightsDeclaration (AUTHORITY = RULIB); (ID = rulibRdec0007)
The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder
Name (TYPE = personal); (ID = R-NAME_0001)
Elizabeth Uptegrove
Role
Author
ContactInformation
ContactInformationDate
2014-09-04T15:07:19-0400
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Technical

ContentModel
Analytic
PreservationLevel
full
Generation
born digital source
MimeType (TYPE = file)
application/xml
FileSize (UNIT = bytes)
11302
CreatingApplication
CreatingApplicationName
RUanalytic
CreatingApplicationVersion
2.1
CreatingApplicationDateCreated
2016-07-11T10:22:46-0400
Note
Generated using the RUanalytic tool export function.
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