DescriptionIn the sixth of seven clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, continues to apply his method for solving specific examples of the Ladder Problem. Researcher John Francisco asks Ariel to use his rule for finding the number of rods for ladders with odd numbers of steps specifically for a ladder with 125 steps. The procedure that Ariel had articulated and followed for relatively small 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 insists that he is following his rule and explains that he divides 124, the nearest even number below 125, by 2 to find 62. He then refers to his earlier count of 198 for a ladder with 60 steps. Ariel builds a ladder with two steps, counts the 8 rods in it, and adds that to 198 for a total of 206. He then doubles 206 and subracts 2 from the resulting 412 to end up with 410 as his prediction for 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 and James:
Use your rule to find the number of rods in a ladder with 125 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 6 of 7: How many rods for a ladder with 125 steps? 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