DescriptionIn this edited and narrated episode from the Private Universe Project in Mathematics, five tenth-grade students consider two different problems. FIRST PROBLEM STATEMENT: “Choosing from two colors of Unifix® cubes, red and yellow, how many total combinations exist for towers 5 tall, that each contains two red? Convince us that you have found them all.” SECOND PROBLEM STATEMENT (Ankur’s Challenge): “How many towers can you build four tall, selecting from cubes available in three different colors of Unifix® cubes, so that the resulting towers contain at least one of each color?” During the session Ankur and Michael work together at one end of the table and Jeff, Romina, and Brian work at the other end. Ankur and Michael use binary notation to solve the first problem. While waiting for Jeff, Romina, and Brian to complete the first tower problem of five-tall with a choice of two colors, Ankur poses a new question about towers four tall with a selection of three colors: “How many with at least one of each color?” Romina develops a notation that she calls “ones, zeroes, and Xs” to represent the three colors in the problem. First at the table and then at the chalkboard, Romina presents her reasoning to the others as she works to convince them that there thirty-six total towers that meet Ankur’s criteria. She shows them her representation to justify the six possible arrangements for two “1s” in the four positions of the tower. She fills the blank positions with “X0” or “0X” for the other two colors. She then explains that the resulting twelve towers would be multipied by three to account for the three different colors of cubes available.
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: Related publication Label: Ed.D. dissertation references the video footage that includes PUP Math Romina's proof to Ankur's challenge Date: 2010 Detail: Available in electronic form in RUcore, the Rutgers Community Repository. Author: Steffero, Maria. (Rutgers Graduate School of Education)
Related Publication Type: Related publication Label: Ed.D. dissertation references the video footage that includes PUP Math Romina's proof to Ankur's challenge Date: 1999 Author: Muter, Ethel M. (Rutgers Graduate School of Education)
Name: The development of student ideas in combinatorics and proof : a six year study
Related Publication Type: Related publication Label: Workshops (web-based) utilize the video PUP Math Romina's proof to Ankur's challenge Publisher: Annenberg Learner Creator: Harvard-Smithsonian Center for Astrophysics