What are some conceptualizations that work in mathematics but are not strictly true? I'm having an argument with someone who thinks it's never justified to teach something that's not strictly correct. I disagree: often, the pedagogically most efficient way to make progress is to iteratively learn and unlearn along the way. 
I'm looking for examples in mathematics (and possibly physics) where students are commonly taught something that's not strictly true, but works, at least in some restricted manner, and is a good way to understand a concept until one gets to a more advanced stage.

What about all the basic rules of weight & motion--aren't they just simplifications of terribly complex rules that generally work as long as you don't deal with anything too small or going too fast?
It seems that EVERY problem in early physics/calculus is simplified to eliminate most of the variables because the problem would become impossibly complex if you added them?  For instance, falling object calculations don't generally take into consideration wind resistance, and if they do they don't take wind and varying pressure into account.  A ball rolling down a ramp always considers only perfect surfaces.  A draining tub doesn't take into account the speed difference of the funnel created by the flow or how long it will take to form?
Most things are simplified so we can fit them into our heads in one way or another.  I've always had lots of luck imagining electricity as water--I know it's inaccurate for many reasons, but it works extremely well even for things like induction (inertia), even though it's obviously "Wrong".
I also believe every description of what is going on in quantum mechanics is a best guess at this point, doesn't mean it isn't helpful though.
