Comparing fractions and evaluating models that represent solutions, Clip 8 of 8: Comparing one half and one fourth, multiple models

Danielle and Gregory presented their model to represent the solution to the problem: Which is larger one half or one fourth and by how much. They built a model of an orange and dark green train, two brown rods, and four purple rods. Danielle explained that if one half, or the brown rod, was compared with one fourth, or the purple rod, it was larger by one purple rod, or one fourth. Andrew presented a fourth model. Using a purple rod, two red rods, and four white rods, he reasoned directly that one half was larger than one fourth by one fourth. He then said that he thought the solution would always be one fourth. Researcher Carolyn Maher asked him why he thought that. Andrew said that all the models that had been built always had the room for one more fourth and that two fourths equaled one half. As he spoke, he showed that on his model, two white rods equaled the length of the red rod. Erik and Alan then presented their method of building models to represent the solution. Erik explained that if the length of two white rods were subtracted from the length of the rod used previously, a model for the problem could be built. Alan and Erik displayed their work on the overhead. Andrew then challenged the validity of their models, saying that that they didn’t show halves on their model. Erik replied that he thought that other students had already shown the difference between one half and one fourth, and they were simply presenting a method of finding models. The researcher then closed the session by asking the students to think about whether it is possible to build more than six models using the rods that they had.Transcript and student work are also available.Robert B. Davis Institute for Learning. (1993). Comparing fractions and evaluating models that represent solutions, Clip 8 of 8: Comparing one half and one fourth, multiple models [video]. Retrieved fro