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*Indirect reasoning*in Subject1

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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DescriptionAmy Martino leads a whole class discussion during which they talk about ways of writing number sentences for two problems: 1) How many one sixths are in one? and 2) How many one twelfths are in 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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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. 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...

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DescriptionIn the fourth clip from this session, Jessica reported that Jackie and Kelly’s argument was different than their original argument in which they had showed the difference between one half and one...

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DescriptionIn the first clip a visitor worked with Danielle and Gregory on the second task of comparing two third and one half. Danielle showed her using the twelve-centimeter long model, that three fourths was...

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DescriptionDanielle 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...

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DescriptionIn the fourth clip Michael and Brian worked together to compare one half and three fourths.
Michael built a model of an orange and red train, two dark green rods, and four light green rods. He then...

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DescriptionResearcher Carolyn Maher leads a whole class discussion after the students' exploration of the problem: Which is larger, one fourth or one ninth, and by how much? Several students described their...