Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 3 of 7: Investigating the algebraic generalization for building Unifix-cube towers n-tall with exactly two red cubes from towers with exactly one red cube.

In the third clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie continues to investigate the construction of Unifix towers four-cubes tall, selecting from red and yellow cubes, when moving from towers with exactly one red cube to towers with exactly two red cubes. She works with researcher Carolyn Maher to begin to develop and explain a generalized formula based on her physical and numerical representations of the towers. Researcher Donna Weir is observing. The problems posed to Stephanie are: From the four Unifix-cube towers, four-cubes tall, with exactly one red and three yellow cubes, how many towers were generated with two red and two yellow cubes? How could you represent this numerically? After removing duplicates, how many unique towers did you find? How could you represent this step and the entire process numerically? What does each number represent in relation to the towers? For towers of any height n, how might we represent the process of moving from towers with exactly one red cube to towers with exactly two red cubes algebraically?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 3 of 7: Investigating the algebraic generalization for building Unifix-cube towers n-tall with exactly two red cubes from towers with exactly one red cube. [video]. Retrieved fro