DescriptionIn 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?
RightsThe 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.
Related Publication 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? Date: 2009 Author: Baldev, Prashant V. (Rutgers, the State University of New Jersey)
Name: Urban, seventh-grade students building early algebra ideas in an informal after school program Reference: QA.B175 2009
Source Title: B17, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage Identifier: 17-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW
Source Title: B18, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage Identifier: B18-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW