What does this participial construction mean?

Question

"I think I've got a good idea of what's been going on," said Professor McGonagall. "It doesn't take a genius to work it out. You fed Draco Malfoy some cock-and-bull story about a dragon, trying to get him out of bed and into trouble. I've already caught him. I suppose you think it's funny that Longbottom here heard the story and believed it, too?" (Harry Potter and the Sorcerer's Stone)

The bold phrase seems to say about the intention of the action in main clause. Can a participial construction denote the meaning?

Answer 1

Firstly, let's clarify what we mean by the term...

a participial phrase is always used as an adjective phrase to modify a noun or pronoun. It includes the participle together with its modifiers, objects, or predicate words.

And here are the first few few examples from that link...

1. Having been on the road for four days, the Todds were exhausted.
2. That hymn, sung by many generations of churchgoers, is my favorite.
3. Climbing slowly, we approached the top of the hill.
4. Surprised by my question, Mrs. Osmond blushed.

Note that in all cases, the participial phrase provides additional information that could grammatically (and usually logically) be omitted. But other than that there's no particular restriction on the kind of information it provides, or how it relates to the noun it modifies (the Todds, that hymn, us, Mrs. Osmond).

Although examples #1 and #4 don't actually embody "intention", they do explain why the main clause arises. And #3 could have been Hoping for a better view, we climbed to the top of the hill, in which case rather than saying how we climbed, the participial phrase would convey intention (i.e. - why we did it).

OP's example explains why [the boys?] fed Draco Malfoy a cock-and-bull story. Perfectly ordinary.