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9
Transcript
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...
10
Transcript
TitleNight session, Pascal's identity, clip 4 of 7: An example of Pascal's identity
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...
11
Transcript
Student Work
TitleB81, Counting tasks: Pizza problems with four and five toppings with isomorphism solution (people view), Grade 11, March 1, 1999, raw footage
Date Created1999-03-01
DescriptionThis raw footage features four eleventh-grade students - Amy Lynn, Robert, Shelly, and Stephanie - engaged in a challenging problem-solving experience with a combinatorics task referred to as the...
12
Transcript
Student Work
TitlePizza problems with four and five toppings, clip 5 of 6: Explaining solutions
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...
13
Transcript
Student Work
TitlePizza problems with four and five toppings, clip 3 of 6: Why does it work?
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...
14
Transcript1
Student Work
TitleB80, Counting tasks: Pizza problems with four and five toppings with isomorphism solution (work view), Grade 11, March 1, 1999, raw footage
Date Created1999-03-01
DescriptionThis raw footage features four eleventh-grade students - Amy Lynn, Robert, Shelly, and Stephanie - engaged in a challenging problem-solving experience with a combinatorics task referred to as the...
15
Transcript
TitleNight Session, Pascal’s Identity, Clip 7 of 7: Generating and generalizing Pascal’s Identity
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...
16
Transcript
Student Work
TitlePizza problems with four and five toppings, clip 6 of 6: Connecting pizzas and towers
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...
17
Transcript
Student Work
TitlePizza problems with four and five toppings, clip 4 of 6: Justifying the isomorphism
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...
18
Transcript
Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 5 of 10: Recognizing the symmetry for the two colors across the cases when building unifix towers four-cubes tall
Date Created1996-03-13
DescriptionIn the fifth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Referring to the...