Why are only certain parts of the moon lit up at different times?

Depends on the way the moon is facing the sun

Explanation: The moon is lit up by the way the moon is facing the sun. So, for example, when there is a full moon, the earth ius facing the sun compleatly. When there is a half, half of the moon is facing the sun.

Hope this helps

a "theory" a suggestion that is not 100 % accurate, or a figure. some people say its a theory because they of all the passed theory's about one subject. it depends sometimes theory might be accurate and sometimes they are.