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Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 1 of 7: How many rods for 10 step and 100 step ladders?

Descriptive

Genre (authority = RURes_Genre)
Research data
Genre (authority = RURes_dataGenre)
Observational data
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Repurposed data
Genre (authority = RURes_qualitativeMethod)
Educational interventions (small group)
Genre (authority = RURes_researchDataType)
Longitudinal data
Genre (authority = RURes_researchMethodology)
Qualitative research
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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_personal)
NamePart (type = corporate)
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B17B18-ALG-VAR-CLIP001
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
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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
Subject (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
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 1 of 7: How many rods for 10 step and 100 step ladders? [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 first 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 functions. Researcher John Francisco begins the session by arranging five Cuisenaire rods of the same length to form the shape of an “H”. The researcher adds one more rod to each side with a third rod between them and asks Ariel and James what they think this structure might represent. The students agree that the shape could represent a ladder and that the parallel center rods could be called “steps”. Researcher Francisco poses the question: “How many rods would be needed to build a ladder with ten steps?" Ariel and James each build a ladder with five steps, count the 17 rods in it, and conclude that a ten-step ladder would need 34 rods. Francisco next asks "How many do you have for a hundred steps?" Both Ariel and James conclude that such a ladder would require exactly 340 rods. Notice that both boys misunderstand the researcher's question and first solved the problem for four hundred steps. 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 3-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:
What does the arrangement of Cuisenaire rods remind you of?
Can you imagine that this arrangement of eight green rods might be a ladder with two steps?
How many rods would be in a ladder with ten steps?
How many for a hundred steps?
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1
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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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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
RelatedItem (type = is referenced by)
TitleInfo
Title
Urban, seventh-grade students building early algebra ideas in an informal after school program / by Prashant V. Baldev.
Identifier (type = lccn)
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
Label
Ed.D. dissertation references the video footage that includes Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 1 of 7: How many rods for 10 step and 100 step ladders?
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime (qualifier = exact)
2009
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Name
Baldev, Prashant V.
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Rutgers, the State University of New Jersey
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Urban, seventh-grade students building early algebra ideas in an informal after school program
Identifier (type = lccn)
QA.B175 2009
Reference (type = physical)
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 1 of 7: How many rods for 10 step and 100 step ladders?
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Identifier (type = doi)
doi:10.7282/T3HX1BDZ
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Rights

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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
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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
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

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Duration
00:06:38
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