Chapter 9: Cross Multiplication: Situation 3 From the MACMTL–CPTM Situations Project

An Algebra 1 class was working through an example, for which the teacher had written the following on the whiteboard:

A student asked, “When we're doing this kind of problem, will it always be possible to cross multiply?”

When learning new content, students often attempt to apply procedures with which they are comfortable even though those procedures may not be mathematically appropriate for the new content. This appears to be the case in the Prompt, in which a student imposes a process used to solve proportions on this problem involving the simplification of a radical involving a fraction. The first Focus explains the student's apparent thinking and the associated misapplication of the process known as cross multiplication. The second Focus gives the conditions that led to the apparent cross multiplication and explains when this condition will arise.