Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and yellow cubes.

In the fifth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie and researcher Carolyn Maher extend their earlier investigation of how to represent the number of Unifix cube towers for cases from no red cubes to four red cubes for towers 4-cubes tall to towers 5-tall and then towers 6-tall, still selecting from red and yellow cubes. For each case, Stephanie builds or imagines the actual towers and records the numerical expression that would calculate the number of towers. After completing her lists for towers 5-tall and 6-tall, Maher points out that, while the calculated results for each case correspond to the entries in Pascal's Triangle, they have been developed for towers of 5-cubes tall and 6-cubes tall based on patterns rather than a logical correspondence between the numbers and the towers. She challenges Stephanie to think about how to justify her conclusions. Researcher Donna Weir is observing. The problems posed to Stephanie are: How might the reasoning that you used for numerically representing Unifix-cube towers 4-cubes tall, when selecting from red and yellow cubes, for each case be helpful in determining the number of towers, 5-cubes tall, for each case? Use similar reasoning to numerically represent the numbers of 6-tall towers in each case. How could you justify your answers? ; Transcript and student work are also available ; Robert B. Davis Institute for Learning. (1996). Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and yellow cubes. [video]. Retrieved from