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*9-12*in Subject1

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...

2

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...

3

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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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...

5

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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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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DescriptionThis is the fifth of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) have been discussing Pascal’s Triangle. The researcher rewrites row 3 of Pascal’s...

9

DescriptionThis is the last of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) explain to Brian, a late-comer, the meaning of Pascal’s Identity (the addition rule for...

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TitleNight session, Pascal's identity, clip 1 of 7: thinking about the meaning of combinatorics notation

DescriptionThis is the first of seven clips from the night session. In it, Jeff, Michael, and Romina discuss the coefficients of the binomial expansion, specifically (a+b) to the 10th power. In attempting to...