Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 1 of 7: Stephanie revisits generating Unifix-cube towers 4-tall from exactly one to exactly two red cubes.

In the first clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie revisits her earlier exploration of how to generate Unifix-cube towers across cases with researchers Carolyn Maher and Donna Weir. Selecting from red and yellow cubes, Stephanie builds the four towers with exactly one red cube and explains that from each of the four, holding the single red cube constant, she can build three new towers with exactly two red cubes. After building the three towers corresponding to the original four, she points out that the twelve resulting towers include duplicates. She identifies pairs of towers that are the same and shows the researchers that there are actually six unique towers with exactly two red and two yellow cubes. In response to a question from researcher Maher, Stephanie indicates that the mathematical expression describing what she has built would be the quantity 4 times 3, referring to the 3 towers generated from each of the 4 originals, divided by 2 to account for the duplicates. The problems posed to Stephanie are: Explain how you generated the towers across cases (from four-cube towers with exactly one red to four-cube towers with exactly 2 red cubes). How would you describe what you did using numbers?Transcript and student work are also availableRobert B. Davis Institute for Learning. (1996). Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 1 of 7: Stephanie revisits generating Unifix-cube towers 4-tall from exactly one to exactly two red cubes. [video]. Retrieved fro