When I was a child, the first thing that made sense to me was that "x is the number that makes the statement true". That is, 100 = 100, so if 25 * x = 100, you need to figure out what value of x multiplied by 25 gives you 100. I didn't even understand the manipulations or how you would really solve for x at first, but I did understand that you were trying to figure out the number that would do that. I would just phrase it like a puzzle, like "what plus 9 equals 14" or "3 times what equals 42"?

For some reason, one of my earliest memories I have is from when I would try to show off to older kids that I understood algebra.