STUDENT'S HOMEWORK:

I go to the park.
I play the badminton
I play the baseball
I play the soccer

TEACHER'S CORRECTION:

I go to the park.
I play soccer
I play baseball
I play soccer

EXPLANATION:

Use the article the for nouns, singular or plural, that are more specific or belongs in a group.

Example:  The dog needs feeding.  (already known)

Example:  Hand me the pencils over there.  (location specific)

But since you used "the" in different way it is understood that you will do a particular sports or activity.