Confessions

I don't understand how the phases of the moon work and I'm too prideful to look it up.

I've taught science for over a decade, I figure I could just visualize it but I get distracted before I can fully picture it in my head.

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Spoiler
It's not the earth's shadow, then every new moon would be a lunar eclipse so...it's the moon's shadow? But the moon is tidally locked? How do you make a crescent shadow? No matter how I look at half a sphere it doesn't look like a crescent.