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DescriptionIn the first of five clips, four twelfth grade students develop their initial strategies for approaching the Taxicab Problem. They determine the shortest distances to the three given points: A, B and...

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DescriptionIn the fifth of five clips, Romina, Brian and Michael, describe patterns and relationships identified in their solution to the Taxicab problem to Arthur Powell, a second researcher. The students...

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DescriptionIn the second of five clips, the four twelfth grade students employ various strategies to determine the number of shortest paths to the remaining two points, B and C, on the problem grid. Various...

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TitleNight session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations

DescriptionThis is the third of seven clips from the night session. The four students (Ankur, Jeff, Michael, and Romina) investigate the reason for dividing n! by (n-x)! and x! when calculating “n choose...

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DescriptionThis is the second of seven clips from the night session. In it, Jeff, Michael, and Romina, along with Ankur (who has just arrived), use the analogy they call “people on a line” to investigate...

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DescriptionIn the fourth of five clips, the four twelfth grade students explain their conjecture that Pascal's Triangle can be used to predict the number of paths to any point in the Taxicab grid to Carolyn...

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DescriptionIn the third of five clips, the four twelfth grade students attempt to justify for themselves and then demonstrate the relationship that they have conjectured between the Taxicab problem and Pascal's...

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DescriptionIn this full-session, raw footage video, students have come to school in the evening for a night session. The group, made up of Jeff, Michael and Romina begin discussing the coefficients of the...

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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...