Mr. Miyagi's Moon Phases - "Wax on! Wane off!"
Beware the dark side! Do phase fractions confuse you?
The moon is a 3-D sphere and not just a 2-D circle in the sky.
Remember that only the front half or "face" of the moon is visible when illuminated by the sun.
So a "quarter moon" is really 1/4 of a sphere (the other 3/4 is dark), even though it may look like 1/2 of a circle. (1/2 of 1/2 = 1/4)