Is walking a verb or a gerund in the sentence: "We will be walking a mile during recess today."?
Walking in this sentence is a verb not a gerund
What are gerunds?
He was writing a poem(writing is used as a verb).
The writing is good(writing used as a noun that is ).In this sentence writing is a noun and these types of nouns are called gerunds
More examples are
The morning walk was pleasant
Sometimes it is better to walk than to run.
Her cooking was delicious
The chefs are cooking food in the back side of the restaurant.
In your sentence
"We will be walking a mile during recess today."
Walking is used as verb because nouns usually don't come after
will be in most of the sentences. They come after will be or there is an article before it thus it is a verb