We don't hatch eggs, so just need to keep track of them for freshness. Our system is to fill a carton (usually takes 2 days), move that carton to the "eat these eggs!" portion of the refrigerator, with the oldest on top. We don't start a new carton until the previous one is empty. As a previous post stated, when we accumulate 2 or 3 extra dozen, we give them to friends and family who can hardly wait for the eggs.
We never have over 4 dozen in the fridge at any time.
I keep track of the number of eggs per day on a spreadsheet - it's fun to graph the output and I have the students use the data when they are studying graphing.