Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.

In the third clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, researcher Carolyn Maher presents Stephanie with base-ten materials, algebra blocks and other rectangular prisms; then asks her how she might use any of the manipulatives to explain volume in general and the volume of cube with side (a+b) in particular. Stephanie uses the small cubic unit and the 100 cubic unit "flat" from the base-ten materials to explain the numerical volume of the large 1000 cubic unit block. She was then asked how she might figure out the volume of the large block if it were to have a side of (a+b). Precision about language and issues of meaning with reference to geometric models that involve two and three dimensions are addressed directly in clip 4 and discussed in each subsequent clip in the series. The problem as presented to Stephanie: How could you use squared materials to show the cube of the quantity (a+b)?Transcript and student work are also available.Robert B. Davis Institute for Learning. (1996). Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives. [video]. Retrieved fro