PurposesEffective teaching; Student engagement; Student model building; Reasoning; Representation
DescriptionThe class is investigating the difference between 1/4 and 1/9. In initial discussions, some students agree with Meredith, who says that the difference is 1/5 because 9 - 4 = 5. Researcher Maher indicates to the class that if they apply Meredith’s rule to 1/2 and 1/4, they would get an answer of 1/2, challenging their earlier reasoning that produced an answer of 1/4. James offers a model consisting of 3 orange rods and a dark green rod (36 white rods) that can be partitioned into ninths and fourths. He presents the model to Researcher Davis. First, James claims that the difference is 1/5, illustrating this difference by 5 white rods. Researcher Davis responds by asking James to clarify what number name is assigned to one white rod, and then of two white rods. James responds 1/36 and 2/36, respectively. James realizes that if the difference between 1/4 and 1/9 is represented by 5 white rods, then that difference must be 5/36. James then presents this finding to the class.
