In the sentence "On track and field day, the teacher was very proficient at announcing the events", is the word "proficient" a noun or verb?

Neither. "Proficient" is an adjective, describing teacher. He was a proficient teacher.

A quick way to determine a word's part of speech is to look it up in a dictionary. Find the definition and part of speech that seems to fit in your sentence. Usually, dictionaries have a sentence to show how the word is used.

I usually use http://dictionary.reference.com/

To determine whether "proficient" is being used as a noun or a verb in the sentence "On track and field day, the teacher was very proficient at announcing the events," we can examine its role and function.

1. Look up the word "proficient" in a reputable dictionary.
2. Check for the different definitions and parts of speech listed.
3. Review the context and usage of the word in the sentence.

By following these steps, we can determine the correct answer.