I teach high school engineering and my students often are equation hunters, as well, especially as I allow them to bring an equation sheet with them to assessments. They have a significant problem with units. I believe too many years of “x” and “”y with math classes has left them with little understanding of the necessity of concepts having a unit associated with them. Typically, they solve a problem, leaving the units out as they go through the mechanics of equation manipulation, then tack on what they perceive as the appropriate unit at the end.
Although when I solve problems on the board I invariably include units, and show how they can indicate a wrong answer (getting units of kg/(m*s^2) is a good indication that you did not calculate force), most do not include units in their work.
I have found a useful exercise is analyzing equations using dimensional analysis. This involves breaking all concepts into a combination of seven fundamental units: length, time, mass, temperature, electric current, quantity of matter, and luminous intensity. This helps them see relationships, though they struggle with it. Without thinking they know that a specific weight can only be added to a specific weight, but understanding that it reduces to [mass/(length^2*time^2)] helps them make connections. Eventually, they see it as a tool of building and deriving equations, instead of pulling them off a "cheat sheet".
Helmut Thielsch
Virginia Governor’s Academy for Engineering Studies