Language Point 23
As he began to fall asleep, ...(Para. 9)
fall asleep: become asleep; go into a state of sleep
"Asleep" is an adjective that is used as a predicative (表語(yǔ)).
One after another, all three of the children fell asleep.
三個(gè)小孩一個(gè)個(gè)地都睡著了。