✔ 最佳答案
In all of the 3 cases above, there are actions in progress past continuous tense is used. past continuous tense is used when there is progress of actions.
In 1,
both the playing badminton and the fishing were taking place in the past, they were running parallel over a period of time so past continuous tense is used.
In 2,
both making noise and teaching were continuous actions so past continuous tense is used. If the sentence is written as "The students made much noise while the teacher was teaching", there will be change in meaning. It becomes more like "the students only made noise at a specific point of time", without the meaning of continuously making noise.
In 3,
though "cut" is an action at a point of time, "preparing dinner" is a continuous action. it means "cut myself during the process of preparing dinner" so past continuous tense is used.