Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 11 of 11: Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal

In the final clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is challenged by researchers Carolyn Maher and Robert Speiser to extend her ideas about how to build the Unifix-cube towers across cases for towers 4-cubes tall for particular cases when selecting from blue and green cubes to towers that are 5-cubes tall. She describes how the five towers, 5-cubes tall with exactly one green cube, would generate the single tower with five blue. Researcher Speiser concludes the session by pointing out the connections between Stephanie's thinking about the towers and the mathematical thinking of both Fermat and Pascal. The problem proposed to Stephanie is: How could you extend your thinking about towers 4-cubes tall, selecting from blue and green cubes, to towers that are 5-cubes tall?Robert B. Davis Institute for Learning. (1996). Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 11 of 11: Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal. [video]. Retrieved fromTranscript and student work are also available