Your first example ("from elementary school") is not an idiom. However, if you want to say "from first grade," adding "elementary school" after it makes it completely redundant. That doesn't make any sense.
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Grammar GeekThe same reason you don't hyphenate "very good."
Hyphenate when you have nouns that modify other nouns, or when you need to show that two words modifying go "together" and do not each modify the noun.
I am a red car fanatic means I am red, and that I like cars. I am a red-car fanatic means that I have a love of red cars. This is