What does it mean to say that something is "fair"? Standard usages seems to imply that something is considered fair if it is equal. For example, children almost always consider it unfair if their siblings get a bigger piece of cake, get to stay up later &c. If this is an accurate definition, then I have to wonder whether fairness is worth all the trouble people put into it.
Justice is giving another what they are due. Now, insofar as two people are equally due something, said thing should be given to them in equal amounts or shares. But insofar as people are not equally due something, it would seem to follow that there is no injustice if they are given said thing in unequal or unfair amounts or shares.
Thus, there is no injustice to be found in the unfair examples previously give. If the cake is being given to the children as a gift, then it is entirely gratuitous rather than something owed. There is no cause for complaint if you are given an undeserved gift in a smaller quantity than another is given an undeserved gift. And even if the situation were one where it could be conceivably said that cake was due to the children, such as a birthday party, it might still be due to them in different proportions. A younger child might be due less cake than his older sibling simply because he cannot eat as much. Similarly, a younger child might be due an earlier bedtime than his older sibling simply because he needs more sleep.
How much luck you would have in presenting these arguments to a young child I cannot say. But it is depressing that many modern adults argue like little children, thinking that if they do not get some equal share or some similar benefit they have in some way been treated with injustice. Think of many of the arguments in favor of abortion, homosexual "marriage" &c.