RUcore: Rutgers University Community Repository
Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 2 of 7: Predicting the rods for odd and even numbers of steps
Descriptive
Genre
(authority = RURes_Genre)
Research data
Genre
(authority = RURes_dataGenre)
Observational data
Genre
(authority = RURes_dataLifecycle)
Repurposed data
Genre
(authority = RURes_qualitativeMethod)
Educational interventions (small group)
Genre
(authority = RURes_researchDataType)
Longitudinal data
Genre
(authority = RURes_researchMethodology)
Qualitative research
Genre
(authority = RURes_dataCollectionSetting)
School
Genre
(authority = RURes_dataLifecycle)
Edited data
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Ariel (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
James T. (student)
Subject
Name
(authority = RBDIL_corporate)
NamePart
(type = corporate)
Frank J. Hubbard Middle School (Plainfield, N.J.)
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MovingImage
Identifier
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B17B18-ALG-VAR-CLIP002
Subject
(authority = NCTM Content)
Topic
Algebra
Subject
(authority = NCTM Process)
Topic
Problem solving
Subject
(authority = NCTM Process)
Topic
Reasoning and proof
Subject
(authority = NCTM Process)
Topic
Communication
Subject
(authority = NCTM Process)
Topic
Connections
Subject
(authority = NCTM Process)
Topic
Representation
Subject
(authority = Grade range)
Topic
6-8
Subject
(authority = LCSH)
Topic
Mathematics education
Subject
(authority = LCSH)
Topic
Critical thinking in children--New Jersey--Case studies
Subject
(authority = LCSH)
Topic
Learning, Psychology of--Case studies
Subject
(authority = LCSH)
Topic
Manipulatives (Education)--Case studies
Subject
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Topic
Work view
Subject
(authority = rbdil_cameraView)
Topic
Student view
Subject
(authority = rbdil_mathStrand)
Topic
Algebra
Subject
(authority = rbdil_mathProblem)
Topic
Ladder problem
Subject
(authority = rbdil_mathTools)
Topic
Cuisenaire rods
Subject
(authority = rbdil_mathTools)
Topic
Color markers
Subject
(authority = rbdil_setting)
Topic
Informal learning
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Considering a simpler problem
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recursive reasoning
Subject
(authority = rbdil_representations)
Topic
Physical models
Subject
(authority = rbdil_representations)
Topic
Mathematical expressions
Subject
(authority = rbdil_studentGender)
Topic
Male
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(authority = rbdil_studentEthnicity)
Topic
Mixed
Subject
(authority = rbdil_schoolType)
Topic
Public school
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = rbdil_gradeLevel)
Topic
7
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Proportional reasoning
Subject
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Union County
City
Plainfield (N.J.)
TargetAudience
(authority = RURes_discipline)
Social science
TargetAudience
(authority = RURes_domain)
Mathematics education
Note
(type = supplementary materials)
Transcript and student work are also available.
Note
(type = APA citation)
Robert B. Davis Institute for Learning. (2005). Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 2 of 7: Predicting the rods for odd and even numbers of steps. [video]. Retrieved from
Name
(type = personal)
NamePart
(type = family)
Francisco
NamePart
(type = given)
John
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Affiliation
Rutgers, the State University of New Jersey
Name
(type = personal)
NamePart
(type = family)
Baldev
NamePart
(type = given)
Prashant V.
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Affiliation
Rutgers, the State University of New Jersey
Subject
(authority = rbdil_district)
Geographic
Plainfield Public Schools
Classification
(authority = RUresearch);
(edition = Data)
Abstract
(type = summary)
In the second of seven clips from an after-school enrichment session in an urban middle school, two 7th grade boys, Ariel and James, are exploring ideas about linear functions. In responding to questions from researcher John Francisco, Ariel develops procedures for calculating the number of rods needed to construct a ladder with an even or an odd number of steps. Researcher Francisco poses the question: "How many rods are needed to build a ladder with eight steps"? Ariel predicts 28 steps based on building a ladder with four steps, counting the 14 rods, and multiplying by 2. When he actually constructs an eight-step ladder, Ariel is surprised to count only 26 rods. James notes that this makes sense because each new step requires three rods and four steps times three rods would be 12 additional rods added to the 14. When Francisco asks Ariel if he is sure about his earlier prediction for 100 steps, Ariel constructs a ten-step ladder and counts 32 rods, he adjusts his procedure for predicting the number to counting the rods for a five-step ladder and then to "times two minus two". For an eight-step ladder, Ariel uses his new procedure and predicts (14 x 2) - 2 = 26 rods. When asked about a ladder with 16 steps, he uses the same reasoning: (26 x 2) - 2 = 52. When the researcher asks about a nine-step ladder, Ariel finds half of the ladder with one fewer steps, in this case taking half of eight, counts the rods in that ladder, multiplies that number by 2, then subtracts 2 from it, and adds 3. Researcher Prashant Baldev is observing.
The worksheet wording for the Ladder Problem:
A company makes ladders of different heights, from very short ones to very tall ones. The shortest ladder has only one rung, and looks like this (we could build a model of it with 5 light green Cuisenaire rods.) A two-rung ladder could be modeled using 8 light green rods, and looks like this. Build a rod model to represent a three-rung ladder.
How many rods did you use? How could you represent the number of rods needed if you were to build a ladder with any number of rungs?
The questions as posed to Ariel and James:
How many rods do you need for a ladder with eight steps? How many rods for a ladder with sixteen steps?
How can you predict the number of rods for a ladder with an odd number of steps?
The worksheet wording for the Ladder Problem:
A company makes ladders of different heights, from very short ones to very tall ones. The shortest ladder has only one rung, and looks like this (we could build a model of it with 5 light green Cuisenaire rods.) A two-rung ladder could be modeled using 8 light green rods, and looks like this. Build a rod model to represent a three-rung ladder.
How many rods did you use? How could you represent the number of rods needed if you were to build a ladder with any number of rungs?
The questions as posed to Ariel and James:
How many rods do you need for a ladder with eight steps? How many rods for a ladder with sixteen steps?
How can you predict the number of rods for a ladder with an odd number of steps?
PhysicalDescription
Extent
(unit = digital file(s))
1
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video/x-flv
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TitleInfo
Title
B17, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage
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17-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW
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TitleInfo
Title
B18, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage
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B18-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW
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TitleInfo
Title
Urban, seventh-grade students building early algebra ideas in an informal after school program / by Prashant V. Baldev.
Identifier
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QA.B175 2009
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Place
PlaceTerm
(type = text)
New Brunswick, N.J.
Publisher
Robert B. Davis Institute for Learning
CopyrightDate
2005-12-15
Extension
DescriptiveEvent
Type
Related publication
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Ed.D. dissertation references the video footage that includes Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 2 of 7: Predicting the rods for odd and even numbers of steps
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Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime
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2009
AssociatedEntity
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Author
Name
Baldev, Prashant V.
Affiliation
Rutgers, the State University of New Jersey
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Dissertation
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References
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Urban, seventh-grade students building early algebra ideas in an informal after school program
Identifier
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QA.B175 2009
Reference
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QA.B175 2009
Detail
Dissertation is available in paper format in the Rutgers University Libraries' dissertation collection
TitleInfo
Title
Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 2 of 7: Predicting the rods for odd and even numbers of steps
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http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000067216
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Identifier
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doi:10.7282/T3NP2354
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Rights
RightsDeclaration
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The 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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Publication
Status
Unpublished
RightsHolder
(type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-8848
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2013-02-11
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore
Place
New Brunswick, NJ
DateTime
(qualifier = exact)
2009-11-03
Detail
Non-exclusive license to digitize and make openly available the videos and other collection resources of the Institute is on file in the office of the RUcore Collections Manager.
AssociatedEntity
Role
Licensor
Name
Maher, Carolyn A.
Affiliation
Director, Robert B. Davis Institute for Learning, Rutgers Graduate School of Education
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Source
SourceTechnical
SourceType
Videotape
Duration
00:07:13
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