Is Washington elementary a common noun?

This depends on how you're using the word "Washington Elementary".

* If you're referring to a specific school: Then it is a proper noun because it is a unique name.

* If you're using "Washington Elementary" as a general term for any elementary school named after Washington: Then it is a common noun because it's not a specific name.

For example:

* Proper Noun: "I went to Washington Elementary School in my childhood." (Refers to a specific school)

* Common Noun: "Many schools across the country are named Washington Elementary." (Refers to a type of school)

So, the answer depends on the context!