DescriptionIn the fourth of five clips from this classroom session, the researcher, Amy Martino, returned to Alan and questioned him about the third model that he had built for finding the difference between one half and two fifths. Alan reasoned from this model to show that two of four orange rods would be called one half. He explained that since he had doubled the length of his model, the purple rods were now called tenths, the brown rods were called fifths, and the red rods were twentieths. Alan had lined up as many white rods as were available (about twenty) and explained that there should be forty white rods in the model, and that they would be called fortieths. Alan then placed five blue rods on top of his model and argued, “You can't make the model any bigger than this, you would have to use one blue. It wouldn't be the exact size. So you can't make a model any bigger than this, without making a train, making all these uneven. So basically, this is the only model you can make that's even without using trains, like this one here, that would make all of these unequal.” In other words, Alan pointed out how each row of rods lined up end-to-end in his model consisted of a single colored train, rather than a train of more than one color of rods. Alan then reasoned that the next size model would need another four orange rods added to the train to be called one.
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Related Publication Type: Related publication Label: Ed.D. dissertation references the video footage that includes Revisiting construction of large models to compare fractions, Clip 4 of 5: Alan reasons about the third model he constructed Date: 2009 Author: Yankelewitz, Dina (Rutgers, the State University of New Jersey)
Related Publication Type: Related publication Label: Ed.D. dissertation references the video footage that includes Revisiting construction of large models to compare fractions, Clip 4 of 5: Alan reasons about the third model he constructed Date: 2008 Author: Reynolds, Suzanne Loveridge (Rutgers, the State University of New Jersey)
Name: A study of fourth-grade students' explorations into comparing fractions Reference: QA.R465 2005
Source Title: A73, Revisiting construction of large models to compare fractions (classroom view), Grade 4, October 8, 1993, raw footage. Identifier: A73-19931008-CNCR-FV-CLASS-GR4-FRC-CMPRF-RAW