9

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...

10

1 Analytic found

TitleEarly algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 2 of 6: Beginning to build a general rule

Date Created2005-12-15

DescriptionIn the second of six clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy completing a unit about linear functions, continues his work on the Museum problem....

11

1 Analytic found

TitleDivision of Fractions, Clip 3 of 3: A Whole Class Discussion About Number Sentences

DescriptionAmy Martino leads a whole class discussion during which they talk about ways of writing number sentences for two problems: 1) How many one sixths are in one? and 2) How many one twelfths are in one?...

12

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 3 of 11: Comparing towers, selecting from two colors, built inductively and corresponding to the addition rule of Pascal's Triangle

DescriptionIn the third clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues a discussion of ideas about binomial expansion with researchers Carolyn Maher and Robert...

13

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 1 of 11: Stephanie revisits combinatorics notation for building towers

DescriptionIn the first clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie revisits her earlier exploration of particular algebraic ideas about binomial expansion with...

14

TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 7 of 7: Finding a general direct "rule" for the number of Unifix-cube towers, selecting from two colors, for any height.

DescriptionIn the final clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie responds to questions from researcher Carolyn Maher about problems that she and her classmates had...

15

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...

16

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. ...

17

1 Analytic found

TitleRevisiting construction of large models to compare fractions, Clip 4 of 5: Alan reasons about the third model he constructed

DescriptionIn the fourth of five clips from this classroom session, the researcher, Amy Martino, returned to Alan and questioned him about the third model that he had built for finding the difference between one...

18

TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 6 of 7: Making sense of the Pascal Triangle addition rule with Unifix cube towers .

DescriptionIn the sixth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first revisits her investigation of the number of duplicates that would be produced when building...