Essentially that's what I did -- the way I taught this was:
1. All operators are written explicitly, and parentheses are used around every operation. (Order of operations is a huge tripping stone.)
2. All allowed algebraic manipulations were clearly named and diagrammed, and we applied them step by step (no leaps of intuition allowed -- another tripping stone).
3. Save all arithmetic to the end. I.e. numbers and variables function identically. But -- try to move numbers around so they're in operators together.
4. Once the equation is solved (or whatever task is required), now take out the calculator and do the arithmetic required.
I completely agree subtraction is a more useful real world skill. But like you said -- calculators exist. So no reason to let that be the reason to hold kids back from learning algebra.
1. All operators are written explicitly, and parentheses are used around every operation. (Order of operations is a huge tripping stone.)
2. All allowed algebraic manipulations were clearly named and diagrammed, and we applied them step by step (no leaps of intuition allowed -- another tripping stone).
3. Save all arithmetic to the end. I.e. numbers and variables function identically. But -- try to move numbers around so they're in operators together.
4. Once the equation is solved (or whatever task is required), now take out the calculator and do the arithmetic required.
I completely agree subtraction is a more useful real world skill. But like you said -- calculators exist. So no reason to let that be the reason to hold kids back from learning algebra.