Chapter 19: Multiplying Monomials and Binomials: Situation 13 From the MACMTL–CPTM Situations Project

The following scenario took place in a high school Algebra 1 class. Most of the students were sophomores or juniors repeating the course. During the spring semester, the teacher asked them to do the following two warm-up items:

Roughly one third of the class stated that both pairs of expressions were equivalent because of the distributive property.

This Situation highlights differences between multiplying monomials and multiplying binomials. The students' incorrect responses to the warm-up problem demonstrate a possible misunderstanding of important differences. The students appear to be misusing the distributive property by applying a procedure, “take the exponent on the outside of the parentheses and multiply it by the exponent of what is inside the parentheses,” when that procedure does not apply. Ironically, the students' difficulty with Item 2 may have occurred because they did not use the distributive property. The Foci that follow demonstrate several approaches for exploring the mathematics involved in the two warm-up items, including application of the properties of real numbers, geometric representations, graphical representations, and numerical exploration.