On the day of new moon, the moon rises when the sun rises. It sets when the sun sets. It crosses the sky with the sun during the day.
Why does the moon seem to change its shape every night? Remember that the moon is a world in space with a day side and a night side.
A waning crescent moon is sometimes called an old moon. It’s seen in the east before dawn.
You know it when you see it, but what makes a full moon full?
A first quarter moon rises at noon and is high overhead at sunset. It sets around midnight.
When you see the moon as a slim crescent – in the west after sunset – it’s a waxing moon. Is that Earth’s shadow on the moon? No, it’s the moon’s own shadow.
A last quarter moon looks half-illuminated. It rises around midnight, appears at its highest in the sky at dawn, and sets around noon.
In the few days after full moon, you’ll often see a waning gibbous moon in the west in early morning, floating against the pale blue sky.