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DescriptionThis clip is the first of six featuring four grade 11 students, Robert, Stephanie, Shelly, and Amy Lynn, as they construct and justify solutions to the Pizza Problem. This clip focuses on Stephanie...
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DescriptionIn the second of 6 clips, the four 11th grade students generate an exhaustive list of pizza options choosing from 4 toppings. They recognize that the 16 choices correspond to the fourth row of...
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DescriptionIn the final clip the students generalize the exponential structure of the Pizza Problem and describe the relationship between two consecutive rows of Pascal’s Triangle with reference both to the...
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DescriptionIn this fifth of six clips, four 11th grade students reconsider Pascal's Triangle as it relates to the Pizza Problem and connect this problem with the Towers Problem. As the students summarize their...
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DescriptionIn the fourth of six clips, the four students develop the structural isomorphism between adding an additional pizza topping choice and the addition rule for successive rows of Pascal’s Triangle and...
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DescriptionResearcher Amy Martino led a whole class discussion that focused on solutions to the task: I'm going to call the orange and light green together one…Can you find a rod that has the number name one...
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DescriptionResearcher Amy Martino posed two related tasks to the students that highlighted the difference between additive and multiplicative reasoning. First, she asked the students: If we call the orange...
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DescriptionIn the last of five clips from a single class session, the researcher reviews with the students how to place whole numbers on a number line. The students are then asked to decide about the placement...
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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...
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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...
