A first quarter moon looks like half a pie. It rises at noon and is high overhead at sunset. It sets around midnight.
First quarter moon comes a week after new moon. Now, as seen from above, the moon in its orbit around Earth is at right angles to a line between the Earth and sun.
A first quarter moon is called "first quarter" because it is one quarter of the way around in its orbit of Earth, as measured from one new moon to the next. Also, although some people call this a "half moon," and although it really does appear half-lit to us, it's good to recall that the illuminated portion of a first quarter moon truly is just a quarter. On the night of first quarter moon, we see half the moon's day side, or a TRUE quarter of the moon. Another lighted quarter of the moon shines just as brightly in the direction opposite Earth!