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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...
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DescriptionThis is the sixth of seven clips from the night session. After Jeff draws Pascal’s Triangle in what the students call “choose” notation, the researcher asks the students to express an instance...
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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 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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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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Date Created2000
DescriptionThis video comes from the Rutgers-Kenilworth Study, and edited for the The Private Universe Project in Mathematics (PUP-Math). It includes narrative voice over and an interview with Researcher, Robert...
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Date Created2014-03-15
DescriptionAt an after-school session in the middle of their junior year, Ankur, Brian, Jeff, Michael, and Romina were introduced to the World Series problem [the problem statement is below]. The students...
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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 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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Date Created1998-01-09
DescriptionIn this edited and narrated episode from the Private Universe Project in Mathematics, five tenth-grade students consider two different problems. FIRST PROBLEM STATEMENT: “Choosing from two colors...
