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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 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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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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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 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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DescriptionThe third of 6 clips focuses on the four 11th grade students as they map the numbers of pizza choices to the rows of Pascal’s Triangle and attempt to make sense of the addition rule with the...

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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...

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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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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...