Algebra can be taught to young children by making it concrete. Call the variable boxes, and give them actual boxes to represent them. Color code the units, and don't allow them to mix colors. Tell them to play fair: "You may only give something to the right side, if you also give the same thing to the left side. Same goes for taking things away, or splitting into shares, or asking the teacher for a copies of one of those boxes. Yes, you can do that, just share it fairly between the two sides of the play area." Kids get the rules of fairness really quickly, and those rules map closely to the basics of algebra.

I was part of a study where this was attempted, at about age 8 or 9. IIRC, it worked well for about half of us. The teacher totally blew my mind when she took all of my boxes and tokens, put them in her larger pencil container, and told me that my game was now just a piece in a bigger game.