Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 2 of 7: Predicting the rods for odd and even numbers of steps [video]. Retrieved from https://doi.org/doi:10.7282/T3NP2354
DescriptionIn the second 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 linear functions. In responding to questions from researcher John Francisco, Ariel develops procedures for calculating the number of rods needed to construct a ladder with an even or an odd number of steps. Researcher Francisco poses the question: "How many rods are needed to build a ladder with eight steps"? Ariel predicts 28 steps based on building a ladder with four steps, counting the 14 rods, and multiplying by 2. When he actually constructs an eight-step ladder, Ariel is surprised to count only 26 rods. James notes that this makes sense because each new step requires three rods and four steps times three rods would be 12 additional rods added to the 14. When Francisco asks Ariel if he is sure about his earlier prediction for 100 steps, Ariel constructs a ten-step ladder and counts 32 rods, he adjusts his procedure for predicting the number to counting the rods for a five-step ladder and then to "times two minus two". For an eight-step ladder, Ariel uses his new procedure and predicts (14 x 2) - 2 = 26 rods. When asked about a ladder with 16 steps, he uses the same reasoning: (26 x 2) - 2 = 52. When the researcher asks about a nine-step ladder, Ariel finds half of the ladder with one fewer steps, in this case taking half of eight, counts the rods in that ladder, multiplies that number by 2, then subtracts 2 from it, and adds 3. 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 three-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:
How many rods do you need for a ladder with eight steps? How many rods for a ladder with sixteen steps?
How can you predict the number of rods for a ladder with an odd number of 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 2 of 7: Predicting the rods for odd and even numbers of 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