DescriptionDuring this clip, the students discuss a task that had been posed by Erik: If I call the blue rod one, what rod will I call one half? A lively discussion centering on the definition of one half...
DescriptionResearcher Amy Martino posed two related tasks to the students. In this clip, the students work on designing a rod that can be called one half when the blue rod is called one. Erik and Alan discuss...
DescriptionIn this clip, the first of five clips from a single class session, the researcher asks the students to review how they were able to show that 1/4 is larger than 1/9 by 5/36. The students had worked...
DescriptionIn this second of five clips from a single class session, the students consider how 3 candy bars could have been equally distributed among their class of 25. The students had worked on this problem...
DescriptionIn a whole-class discussion in the third of five clips from a single session, students are asked to compare and order 1/2, 1/3, 1/4 and 1/5. David shares his solution that is based on building models...
DescriptionThe third of 6 clips focuses on the four 11th grade students as they map the numbers of pizza choices to the rows of Pascal’s Triangle and attempt to make sense of the addition rule with the...
DescriptionIn clip 4 of 5, fifth grade student Matt shares his understanding of Milin’s inductive argument with Robert and Michelle R. who, up to this point, found twelve, four-tall towers. Stephanie...
DescriptionIn clip three of five, Milin, a fifth grade student, shares his inductive argument for building towers up to 3 cubes tall with researcher Carolyn Maher and his partner, Michelle I. Michelle in turn...
DescriptionIn the 2nd of 5 clips, Stephanie and Matt, two fifth grade students are attempting to find all possible towers four cubes tall when selecting from two colors as the sample space for Question 2 of the...
DescriptionIn this final clip, an exuberant Stephanie presents her understanding of the “doubling rule” to the group of students ( Matt, Michelle I, Michelle R, Milin and Robert) who assembled around a...