DescriptionIn the second of five clips from a follow-up interview about his participation in Informal Mathematics Learning (IML), an after-school enrichment program, Ariel, an 8th grade student in an urban middle school, is asked to solve the Ladders problem, which he had worked on as a 7th grader in IML. Researcher Cecilia Arias asks Ariel to read the first parts of the problem and Ariel quickly determines the number of rods necessary to build ladders that have three and then ten rungs. Ariel then proposes the general equation of 3X+2 referring to the first differences for the value of Y and noting that this would describe a linear equation.
The wording for the Ladder Problem as given to Ariel:
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 many rods would you need to build a ladder with 10 rungs?
How could you represent the number of rods needed if you were to build a ladder with any number of rungs?
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 7 of 7, Ariel's 8th grade interview, Clip 2 of 5: Ariel solving the Ladder problem Date: 2009 Author: Baldev, Prashant V. (Rutgers, the State University of New Jersey)
Name: Urban, seventh-grade students building early algegra ideas in an informal after school program Reference: QA.B175 2009
Source Title: B21, Early algebra, investigating linear functions, series 7 of 7, Ariel's 8th grade interview (student view), Grade 8, May 17, 2007, raw footage. Identifier: B21-20070512-PFLD-SV-IFML-GR8-ALG-VAR-RAW