Staff View
Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 7 of 7: Combining a six step ladder with a two step ladder

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_corporate)
NamePart (type = corporate)
Frank J. Hubbard Middle School (Plainfield, N.J.)
TypeOfResource
MovingImage
Identifier (type = rbdil)
B17B18-ALG-VAR-CLIP007
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 (authority = rbdil_cameraView)
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 7 of 7: Combining a six step ladder with a two step ladder [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 final clip of the series of seven from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, revisits his method for solving a specific example of the Ladder Problem. Researcher John Francisco asks Ariel explain how he had predicted the number of rods for a ladder with 125 steps. The procedure that Ariel had articulated and followed for smaller numbers had the following steps: (1) Find the closest smaller even number to the number posed; (2) divide that number by two; (3) build a ladder with that number of steps with actual rods; (4) count the rods; then (5) double that number and subtract two from the product to find the result for the even number, and finally, (6) add three to the total number of rods to find the amount of rods for the original odd number of steps in the ladder. Ariel explains that, for 125, he would divide 124, the nearest even number below 125, by 2 to find 62. He continued his explanation of using his earlier count of 198 for a ladder with 60 steps, building a ladder with 2 steps and adding the resulting 8 rods to 198 for a total of 206. Francisco challenges Ariel to actually build a ladder of 6 steps and predict the total if he were to add a second ladder of 2 steps. After Ariel completes the ladders, 20 for 6 steps, and 8 for two steps, his first prediction is 28 rods. However, before building and counting the 8 step ladder, Ariel refers to his rule and subtracts 2 from the 28 for a result of 26. When he builds the 8 step ladder, his result is confirmed and he insists that this is the same method that he had used for finding the ladder with 124 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:
Explain again how you found the number of rods for a ladder with 124 steps.
Test your method of adding a two step ladder to a larger ladder (in this case a 60 step ladder) by building a 6 step ladder and then adding a 2 step ladder in order to find the rods for a ladder with 8 steps.
Did you use the same method for both problems?
PhysicalDescription
Extent (unit = digital file(s))
1
InternetMediaType
video/x-flv
RelatedItem (type = host)
TitleInfo
Title
B17, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage
Identifier (type = rbdil)
17-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW
RelatedItem (type = host)
TitleInfo
Title
B18, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage
Identifier (type = rbdil)
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
OriginInfo
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 7 of 7: Combining a six step ladder with a two step ladder
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime (qualifier = exact)
2009
AssociatedEntity
Role
Author
Name
Baldev, Prashant V.
Affiliation
Rutgers, the State University of New Jersey
AssociatedObject
Type
Dissertation
Relationship
References
Name
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 7 of 7: Combining a six step ladder with a two step ladder
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000067229
RelatedItem (type = host)
TitleInfo
Title
Robert B. Davis Institute for Learning Mathematics Education Collection
Identifier (type = local)
rucore00000001201
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers University. Libraries)
NjR
Identifier (type = doi)
doi:10.7282/T39C6W5Z
Back to the top

Rights

RightsDeclaration (AUTHORITY = rbdil1_v1); (ID = rbdil1_v1)
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
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
Back to the top

Source

SourceTechnical
SourceType
Videotape
Duration
00:04:48
Back to the top

Technical

ContentModel
Video
PreservationLevel
full
Generation
Digital preservation master
Duration
00:04:48
System
MS Video
Frame
Height
640
Width
480
Rate
29.97 fps
AspectRatio
4:3
Structure
interlaced
FormatColors
Color
BitRateReduction
Compression
CompressionType
uncompressed
Codec
CodecName
full frame uncompressed
CodecQuality
code regenerating
VideoSampling
SamplingSize
4:2:2
WordSize
3-byte
BitsPerSample
24-bit
SoundPresent
yes
Sound
Channels
NumberOfChannels
2
SoundField
stereo
Sampling
SamplingRate
44.1 kHz
BitsPerSample
16-bit
WordSize
3-byte
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
573440
Checksum (METHOD = SHA1)
c2909089896ce16f043c69a829835418a14413a7
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
1091747840
Checksum (METHOD = SHA1)
98a9439ecb6ebd8002fc03cfe5da22041281fbd2
Back to the top
Version 8.3.13
Rutgers University Libraries - Copyright ©2020