Simplify the following text for a Grade 3 native English-speaking person.
Original: The terms old moon and new moon are interchangeable , although new moon is more common . Half moon is often used to mean the first - and third-quarter moons , while the term ` quarter ' refers to the extent of the moon 's cycle around the Earth , not its shape .
Simplified: After that , the moon comes out of the darkness and becomes a half moon .