waxing crescent: first quarter waning gibbous: third quarter
Explanation:
The moon is waxing (getting larger) in the first quarter after the new moon. It is waning (getting smaller) in the third quarter, after the full moon at the end of the second quarter.
The shape of the moon is a "crescent" when it is less than a semicircle. It is "gibbous" when it is more than a semicircle. As it waxes, the crescent grows until the moon is half-full at the end of the first quarter, then it is a waxing gibbous moon through the second quarter until it is full at the end of the quarter. Following the full moon, it is waning gibbous until it becomes half-full again at the end of the third quarter. Finally, it is a waning crescent through the fourth quarter until the new moon.
waxing crescent: first quarter waning gibbous: third quarter
