How to explain why one should use lowercase letters for variable names? How can I explain to an Algebra I student why he should use lowercase letters when naming his variables (i.e. $q = $ number of quarters $vs.$ $Q = $ number of quarters?  I am not interested in the historical answer given in this post: Why are variables lowercased? 
I would instead like a simple example and/or rational reason that a rather stubborn 8th grade student would understand.
Thanks all!
N.B. Maybe I am the one who is in the wrong here but I have been told that lowercase letters are better.
 A: While the points below do not apply to the 8th grade, it is preferable to teach the habits of good style early on.
A principle of easily read mathematical typography is that symbols with the same syntactic properties, particularly with regard to concatenation, should belong to the same typographical class (where "class" is loosely defined for convenience in particular applications).
For example, if $\pmb x,\pmb y\in\Bbb R^n$ and $A,B\in\Bbb R^{n\times n}$, then formulae such as $$z=\pmb x^\top\! A\pmb y\pmb y^\top\!B\pmb x+\pmb y^\top\!\pmb y\quad\text{and}\quad Z=\pmb x\pmb y^\top\! A\pmb y\pmb x^\top+B $$are easily read; while, in the same formulae with the typography randomized to $$Z=x^T A Y Y^Tbx+Y^TY\quad\text{and}\quad z=xY^T AYx^T+b,$$where distinction by capitalization and font is dropped, it is harder to see what's going on (albeit easier to type!).
If you are only dealing with real-valued quantities—not operators, sets and spaces, or vectors and matrices (as ab0ve)—then keeping to lower case is less important, especially if you need lots of different variables and constants. Even then, it's better to avoid capitals, or restrict their use to symbols that play a particular role.
In physics, engineering, and other areas where mathematics applies, different priorities hold, and many symbols are capitalized by long-established convention.
A: In my opinion, you should do exactly the opposite.
Teach them that variable names are absolutely arbitrary. You can pick uppercase letters, lowercase letters, little icons, or whatever. The only important thing is that two variables with the same name, or picture, or whatever refers to the same quantity.
It really bugs me that math teaching revolves so much about the syntax of things, instead of focusing on what it actually means. I don't deny that doing math requires some sort of formalism - but it should always be made clear that the formalism is just a convenient way to communicate mathematical ideas, and that what's actually important is the idea behind it.
Once you've established that notation is about communication of ideas, not about their content, it follows (and I think they'll agree) that deviating from universally agreed upon notation is usually a bad idea. But not because the math somehow becomes wrong, but simply because it makes it harder to get your point across. It's like inventing your own, private language, and wondering why nobody understands you.
Though I must say that in the case of variables, saying that they should always be given lowercase letters as names is a gross oversimplication. A variable representing a matrix, for example, will usually be given an uppercase latter. The same often goes for points in geometry. So for variables, what we really do is we try to partition the available letters in such a way that similar things can be recognized as such. Sometimes that means using letters that are close together in the alphabet. Sometimes that means using both upper-case and lower-case letters, because we want to emphasize that $f$ and $F$, respectively $g$ and $G$ are somehow related. What should be taught, I think, is to pick sensible variable names, i.e. ones that make the intention clear, not any particular variable names (which, in a given context, might not be sensible at all).
