Having arranged their plumage, they moved off towards their roosting-places, and the rest of the birds which had been watching their departure darted down, hoping to pick up some of the fish they might have left. (In the Wilds of Florida by W.H.G. Kingston）注：they = 鳥たち
動画の後半部分でリスニング用音声が流れます。
英文を前から読んでいくために、語句のかたまりを作ります。こんな具合に課題文をスラッシュ（斜め線）で区切ります（スラッシュリーディング）。語句のかたまりを意識すると、リスニングで英語の意味をつかむのが楽になります。
Having arranged their plumage,／（主語が文頭にないときの主語の前）they moved off towards their roosting-places,／（接続詞の前）and the rest of the birds which had been watching their departure darted down,／（動詞のing形の前）hoping to pick up some of the fish／（関係代名詞［省略］の前）they might have left.
語句のかたまりを前から訳していきます。
Having arranged their plumage,
羽を整え終えると
they moved off towards their roosting-places,
鳥たちは、ねぐらへ飛び立っていった
and the rest of the birds which had been watching their departure darted down,
そして、彼らが去っていくのを見ていた残りの鳥たちは、さっと下降した
hoping to pick up some of the fish
魚を拾いたいと思いながら
they might have left.
彼らが残していったかもしれない
Having arranged their plumage, they moved off towards their roosting-places, and the rest of the birds which had been watching their departure darted down, hoping to pick up some of the fish they might have left.
the rest of the birds which had been watching their departure darted down→ the rest of the birds を which had been watching their departure が後ろから修飾しているので、主部が長くなっています。
some of the fish they might have left→ the fish と they の間の関係代名詞（which か that）が省略されています。
鳥たちは羽を整え終えると、ねぐらへ飛び立っていった。彼らが去っていくのを見ていた残りの鳥たちは、彼らが残していったかもしれない魚を拾いたいと思いながら、さっと下降した。
今回の課題文には、２つの分詞構文が使われていますが、それぞれ訳し方が異なります。
Having arranged their plumage→ ここは「〜し終えると」と訳せます。接続詞を使って書き換えると After they had arranged their plumage になります。
hoping to pick up some of the fish→ この分詞構文は付帯状況（〜しながら）で訳せます。
