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notes in keys

That's the pattern, but why are you getting ahead of your teacher. Sometimes there is a reason for what they do. Teachers measure their success by your success if they are any good.
What's he teaching you C and Am? If so, that's the scales with the naturals and makes it easy to learn the rest.
 
I know why C, there is no sharps or flats, I had an instructor start me out with G too. I don't know why. That pattern he gave you should help it make sense. Start with the root note and it's always the same pattern, just different notes. That will help you learn the fretboad.
I'm not new at this but I still take lessons, just advanced ones. We're writing songs now. Be patient it gets better.
He gives me a key, tells me to write 3 or 4 songs and we record one. He plays guitar along with me. It's great while I'm in between bands.