How does Percy Jackson and the Lightning Thief communicate ideas of value?
This is a good question. There are several different places you can go to see values. First, there is the love between parents and children. Percy's mother loves him and he does her. We also see that Percy's divine father, Poseidon, loves him greatly as well. So, we can say that there is this fundamental characteristic of love woven in the book.
Second, as we follow the storyline, there is a stolen master bolt, which Zeus needs. This is seen a evil and wrong. So, the very fact that Percy wants to find it and make it right shows moral value in honesty and truth telling.
A third example comes in the importance of friendships. For example, Grover is Percy's best friend, and he is willing to give his life. Also Percy is willing to sacrifice his life for him as well. Finally, when Annabeth is comes along, the faithfulness is enhanced even more.