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 Triangle in what the students call “choose” notation (1 3 3 1 becomes “3 choose 0, “3 choose 1,” “3 choose 2,” and “3 choose 3”). The researcher then asks the students to write more rows of Pascal’s Triangle in this notation, including a general row (row n). As the students work on this task, they describe connections between Pascal’s Triangle and the binomial expansion and between the n-th row of Pascal’s Triangle and the answer to the n-tall towers problem.
The n-tall towers problem is: How many towers n cubes tall is it possible to make when there are two colors of cubes to choose from?
“Choose” notation is the notation for counting the number of combinations; “n choose r” gives the number of ways of selecting subsets containing r objects from a set containing n objects. When counting combinations, the order of selection is irrelevant. “n choose r” is equal to n!/[(n – r)!r!].
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Related Publication Type: Dissertation Label: Ed.D. dissertation references the video footage that includes Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle Detail: Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection. Author: Uptegrove, Elizabeth B. (Rutgers Graduate School of Education)
Name: To symbols from meaning: students' investigations in counting.
Source Title: A28, Night session, Pascal's identity, grade 11, May 12, 1999, raw footage Identifier: A28-19990512-KNWH-PV-CLASS-GR11-CMB-TW10T-RAW