Probably in math classes across the country no matter what level (algebra through calculus), right now, if you asked a student, "how many feet squared is 100 inches squares?", the majority of them would JUST divide by 12 to get their answer. Right? Right?
I've tried various things throughout the years, and things "stick" for the unit, but later, say the following year or years, I ask the same question, the student reverts back to JUST dividing by 12. Must be hardwired into their heads.
Anyway, this came up again yesterday in geometry class with the following problem:
You want to paint the exterior of a cylindrical container with a 4 inch radius and 15 inch height. Paint costs 86 cents per square foot, how much would it cost.
I had an answer bank on the sheet, and LO AND BEHOLD, their answer was not on there. Hmmmmmm. Then I prompted: be careful with your units. OH! Okay, convert convert. OH! the answer is STILL not on there. Hmmmmmm. The dreaded JUST dividing by 12 dilemma. Anyway, I held up a piece of white paper and basically did what you see here below.
It SEEMED to make sense to the students. I liked the visual and the methodical dividing the side by 12 AND the algebraic equation by 12 right afterward, so they see what happens. It SEEMED to stick, but I'm not going to fall for that again. I'll quiz them again next year or two to see. My optimistic self thinks, "YES! I've solved the problem of world peace." Don't burst my bubble. Anyway, one more example to add to the arsenal.