The kids walked to the corner store.
prepositional phrase
Being the oldest is a big responsibility.
subject
(tells what)
explains
past tense
Melting in the sun, the ice cream dripped down his arm.
A-OK
Modifies 'ice cream'
prepositional phrase
I would love to get together soon.
direct object
looking and listening
Wagging her tail, the dog begged for a treat.
A-OK
modifies 'dog'
I want to dream the impossible dream!
infinitive phrase
My dream is to own my own business.
subject complement
might be sleeping
past perfect progressive
Barking loudly, the postman jumped when the dog came to the door.
Dangling!
Barking does not modify 'the postman.'
Mom has errands to run.
infinitive phrase
We have several projects hanging over our heads this weekend.
modifies 'projects'
will seek help
Singing too softly, the choir drowned out Sophie's voice.
Dangling!
The choir is not singing too softly.
After being in a coma for three weeks, the patient finally came to.
prepositional phrase
(part of a phrasal verb)
To tell the truth, I always preferred strawberry jam.
adverbial
(how or why)
felt funny
Melting in the sun, the boy licked the ice cream off his arm.
Dangling!
Melting does NOT modify 'boy' -- UNLESS the BOY is the one who's melting!
(This is called 'amphiboly.')