DescriptionIn the fourth clip Erik repeated the explanation of his model to the classroom teacher. His model consisted of a train of three orange and one dark green rod and lined up four blue rods. He lined up three blue rods and nine white rods against the model and showed that three white rods could be added to each blue rod to complete the third. Then, he looked at what David was doing and wondered aloud about it. Then, he remembered that David had made a conjecture, and repeated it: that the reds would be twenty fourths and the whites forty-eighths since he doubled everything. At this point, the other students understood David’s argument, and David corrected his previous statement regarding the number name for the light green rod. Erik then demolished his thirty-six centimeter model, turning to concentrate on David’s work. David then explained to classroom teacher why he had built the model and what he had found about the light green rod. David and the others then worked to perfect the model, which was comprised of the train of two blue, two, black, and two brown rods, sixteen light green rods, twenty-four red rods, and twelve purple rods. Toward the end of the session, David showed the model to the researcher Carolyn Maher. Pointing to the red rods and counting by two, David and Erik found directly that the white rods would indeed be called forty-eighths. David noted that he was surprised that the purple was one twelfth, rather than the light green. The researcher asked the students if they could think of other number names for the purple rod aside from one twelfth. David first said that it would be four twelfths, but then Erik said that it would be called four forty-eighths, since four white rods equaled the length of the purple rod. David then said that that was what he had meant. Erik then suggested that it be called two twenty-fourths. The researcher then asked if there were any other number names. Meredith proposed that it would be one sixteenth together plus one forty-eighth. The researcher asked her what number name that would be, but the session ended before they had a chance to continue this discussion. The researcher suggested that they continue to think about this question.
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Related Publication Type: Related publication Label: Ed.D. dissertation references the video footage that includes Building large models to show equivalence, an exploration, Clip 4 of 4: Testing the doubling conjecture 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 Building large models to show equivalence, an exploration, Clip 4 of 4: Testing the doubling conjecture 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: A92, Building large models to show equivalence, an exploration (classroom view), Grade 4, October 7, 1993, raw footage. Identifier: A92-19931007-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
Source Title: A93, Building large models to show equivalence, an exploration (side view), Grade 4, October 7, 1993, raw footage. Identifier: A93-19931007-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW