DescriptionIn the second of five clips from this classroom session, Alan worked alone at his desk on a new task that the researcher, Amy Martino, had posed. He built models to find the difference between one half and two fifths. Alan showed the researcher two models that he had built. The first was composed of an orange rod, five red rods, two yellow rods, and ten white rods. Alan used this model to reason that one half is larger than two fifths by one tenth, showing that the difference between the length of one yellow rod and two red rods was one white rod. He then showed the researcher his second model, which used a train of brown and red instead of the orange rod, and explained that that was the only difference between the two models. The researcher asked Alan if he could try to find a model that was of a different length. Using a model that he had built with two blue rods and four purple rods, Alan quickly constructed a model using two orange rods, five purple rods, another set of two orange rods, and ten red rods. He showed the researcher that the difference between an orange rod and two purple rods was one red rod, verifying his original solution. The researcher then asked him why he chose two oranges to be the whole. Alan replied that in his previous model the whole was equal to ten ones, and that if he doubled it, it would equal twenty and he would be able to use the same colored rods for the other parts. Alan used this argument to explain that he had derived the second model from the first, and then predicted what a third model would look like. The researcher encouraged him to test his prediction and build the third model.
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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 2 of 5: Alan finds the difference between one half and two fifths 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 2 of 5: Alan finds the difference between one half and two fifths 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