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**Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 4 of 7: Predicting the number of rods for ladders with 80 and then 120 steps [video]. ** Retrieved from

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TitleEarly algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 4 of 7: Predicting the number of rods for ladders with 80 and then 120 steps

PublisherNew Brunswick, N.J.: Robert B. Davis Institute for Learning, , c2005-12-15

DescriptionIn the fourth of seven clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, continues his exploration of ideas about linear functions. Researcher John Francisco asks Ariel to test the rule he has proposed and written down for finding the number of rods in a ladder with an even number of steps. The procedure that Ariel had articulated and followed for relatively small numbers had the following steps: (1) divide the number by two; (2) build a ladder with that number of steps with actual rods; (3) count the rods; then (4) double that number and subtract two from the product. When Francisco asks him to test his rule for a ladder with 80 steps, Ariel refers back to his answer of 26 for a ladder with eight steps. He then multiplies 26 by 10, justifying this by noting that since 8 times 10 is 80, 26 times 10, or 260. He completes his answer by subracting 2 and asserting that 258 would be the correct number of rods. Despite the researcher' s attempts for him to follow his written procedure more closely, Ariel did not waver from this answer. When Francisco asks him to predict the number of rods for a ladder with 120 steps, Ariel follows a similar path, this time beginning with a ladder with six steps.

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:

Given the rule that you have written for finding the number of rods for a ladder with an even number of steps, test your rule for a ladder with 80 steps.

Test your rule for a ladder with 120 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.

Date Captured2005-12-15

Local IdentifierB17B18-ALG-VAR-CLIP004

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 4 of 7: Predicting the number of rods for ladders with 80 and then 120 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