I know my students have trouble with deciding which operations are linear and which operations are not linear. I am thinking about using a survey like the one on fractions that I have described here. Here is a possible worksheet.
I am of two minds. I do not like to let my students see any erroneous mathematics. It goes into their brains whether they or I want it to or not. Some of the constructions in the worksheets are fairly bizarre and why create uncertainty where there was none before. Yet this exercise would require students to really scrutinize algebraic expressions and draw distinctions. And I know they will still attempt to generalize. With my guidance maybe they can remember the correct rules (generalizations). The Linearity Survey would have to be followed by plenty of time for discussion not a rush job at the end of class. I would also have my students do it in sections – first, the first block, then the next two blocks, and finally the lower right block first on page one then on page two. I have a summary of algebraic distribution rules that I could hand out at the end of the session to reinforce what they have learned. I think I will give it a try.
At the end of a precalculus class, I think this survey would be useful.