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DescriptionAmy Martino introduced division of fractions by asking students to describe how many white rods equal an orange and red train. She then asked the students to name the white rod if the orange and red...

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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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DescriptionIn the first of three clips from a single class session, the researcher asks the 4th grade students to explain the mathematical task of the previous day when each of the three small groups within the...

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TitleAlan's Infinity

DescriptionIn this clip from 4th grade classroom study, students discuss the placement of numbers between zero and one on a number line. A debate ensues as to how many numbers exist between zero and one. Andrew...

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DescriptionIn the sixth clip Erik and Alan worked on the task: Which is larger, one half or three fourths. Erik showed, using the orange and red train as one, that the difference between the two fractions was...

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DescriptionIn the seventh clip, Erik and Alan worked to extend their model using the orange and red train to show fourths and halves. They concluded that three fourths was larger than two thirds by one twelfth....

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DescriptionIn the fifth clip Michael and Brian extended their model using the orange and red train to show thirds and twelfths in addition to fourths. They showed that the difference between two thirds and three...

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DescriptionIn the third clip, researcher Amy Martino then worked with Mark and Laura. Mark justified his solution using each model he built. The researcher asked Mark if he thought that a different model might...

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DescriptionIn the second clip, researcher Carolyn Maher asked the students to build a model to show which is bigger, two thirds or one half, and by how much. The students worked with their partners to solve the...

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DescriptionIn the second clip, Kimberly and Audra worked together on the task: Which is larger one half or three fourths. Kimberly built a model using an orange and red train, two dark green rods, and four light...