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Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 4 of 7: Predicting the number of rods for ladders with 80 and then 120 steps

Descriptive

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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
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_corporate)
NamePart (type = corporate)
Frank J. Hubbard Middle School (Plainfield, N.J.)
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Identifier (type = rbdil)
B17B18-ALG-VAR-CLIP004
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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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
Subject (authority = rbdil_studentEthnicity)
Topic
Hispanic
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 4 of 7: Predicting the number of rods for ladders with 80 and then 120 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
Subject (authority = rbdil_district)
Geographic
Plainfield Public Schools
Classification (authority = RUresearch); (edition = Data)
Abstract (type = summary)
In the fourth of seven clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, continues his exploration of ideas about linear functions. Researcher John Francisco asks Ariel to test the rule he has proposed and written down for finding the number of rods in a ladder with an even number of steps. The procedure that Ariel had articulated and followed for relatively small numbers had the following steps: (1) divide the number by two; (2) build a ladder with that number of steps with actual rods; (3) count the rods; then (4) double that number and subtract two from the product. When Francisco asks him to test his rule for a ladder with 80 steps, Ariel refers back to his answer of 26 for a ladder with eight steps. He then multiplies 26 by 10, justifying this by noting that since 8 times 10 is 80, 26 times 10, or 260. He completes his answer by subracting 2 and asserting that 258 would be the correct number of rods. Despite the researcher' s attempts for him to follow his written procedure more closely, Ariel did not waver from this answer. When Francisco asks him to predict the number of rods for a ladder with 120 steps, Ariel follows a similar path, this time beginning with a ladder with six 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 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:
Given the rule that you have written for finding the number of rods for a ladder with an even number of steps, test your rule for a ladder with 80 steps.
Test your rule for a ladder with 120 steps.
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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
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DescriptiveEvent
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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 4 of 7: Predicting the number of rods for ladders with 80 and then 120 steps
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Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime (qualifier = exact)
2009
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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
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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 4 of 7: Predicting the number of rods for ladders with 80 and then 120 steps
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Robert B. Davis Institute for Learning Mathematics Education Collection
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doi:10.7282/T3X63KPP
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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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Videotape
Duration
00:04:23
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