Fraction as number, an introduction, Clip 6 of 8: Problem posing for the class

In the sixth of eight clips from this session, researcher Carolyn Maher asked the students to work with their partners to come up with questions to challenge the class. Alan was first to present his challenge. He asked the class to find the rod that would be called one if the red rod was called one fifth. Graham responded that the orange rod would be called one, and explained that five red rods were equal in length to the orange rod Beth and Mark posed two related challenges. Beth asked the students, “If a [light] green was a whole, what would a blue be?” Erik responded that it would be called “three wholes,” but did not justify his solution. Mark asked the students to name the light green rod if the blue rod was called one. Jacquelyn responded that it would be called one third, and explained that three green rods equaled a blue rod, and so each light green rod would be called one third. Next, Jacquelyn, Kelly, and Michael posed their problem to the class. They asked, “If white one is one whole what would the orange be?” Erik responded that the orange rod would be called ten, since only ten white rods equaled (in length) an orange rod. The researcher asked the class to name the white rod if the orange rod was called one. Jacquelyn responded that it would be called one tenth, using a line of reasoning similar to Erik. Meredith asked the class to find the rod that would be called one if the purple rod was called one half. Amy replied that the brown rod would be called one, because the purple rod was one half as long as the brown rod, and two purple rods equaled (in length) the brown rod.Transcript and student work are also available.Robert B. Davis Institute for Learning. (1993). Fraction as number, an introduction, Clip 6 of 8: Problem posing for the class [video]. Retrieved fro