10

1 Analytic found

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...

11

1 Analytic found

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...

12

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed

DescriptionIn the fourth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie remembers that she had figured out the expanded algebraic expressions for (a+b) for powers up to 6. ...

13

3 Analytics found

TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 5 of 5: Sharing with the Group

Date Created1993-02-26

DescriptionIn this final clip, an exuberant Stephanie presents her understanding of the “doubling rule” to the group of students ( Matt, Michelle I, Michelle R, Milin and Robert) who assembled around a...

14

3 Analytics found

TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 4 of 5: Stephanie and Matt Rebuild the Argument

Date Created1993-02-26

DescriptionIn clip 4 of 5, fifth grade student Matt shares his understanding of Milin’s inductive argument with Robert and Michelle R. who, up to this point, found twelve, four-tall towers. Stephanie...

15

2 Analytics found

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...

16

2 Analytics found

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...

17

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 2 of 11: Stephanie rebuilds Unifix towers 1-cube, 2-cubes, 3-cubes and 4-cubes tall, selecting from two colors

DescriptionIn the second clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues her exploration of early algebraic ideas about binomial expansion with researchers Carolyn...

18

1 Analytic found

TitleBuilding Towers, Selecting from Two Colors for Guess My Tower, Clip 1 of 5: The Meaning of "At Least"

Date Created1993-02-26

DescriptionIn the first of five clips, Milin and Michelle I, two fifth grade students are attempting to find all possible towers three cubes tall when selecting from two colors as the sample space for Question 1...

19

4 Analytics found

TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 2 of 5: Does the Number Double?

Date Created1993-02-26

DescriptionIn the 2nd of 5 clips, Stephanie and Matt, two fifth grade students are attempting to find all possible towers four cubes tall when selecting from two colors as the sample space for Question 2 of the...