-AIDA means more like the "the whole time"
-AIDA+NI means at some point during a period of time. You also use it to delineate the period of time in which you did some thing a number of times (While I was in Germany, I went to Berlin 3 times).
So with that said, are these example sentences correct? I've putt an explanation for why I chose to use AIDA or AIDA+NI in parenthesis.
1. 授業の間、私たちはメモを取っていた。
We took notes during the class. (The whole time)
2. 僕は京都にいる間に、茶会を見学した。
While I was in Kyoto, I observed a tea ceremony. (Not the whole time I was in Kyoto, once during that period of time)
3. ラジオがつけている間、僕は集中ができません。
I can't concentrate while the radio is on. (The whole time it's on)
4. 先学期の間、僕の日本語がとても進んでいた。
During last semester, my Japanese progressed a lot. (Meaning over the entire semester... I wonder, if I changed this to 間に would it mean more like "at some point during last semester?)
5. 雨が降っている間、出かけたくない。（The whole time it's raining)
６．雨が降っている間に、本を読んでください。(Not sure if this is correct... but my book seems to give a precedent for AIDA+NI here with the sentence "While it's quiet, write a letter").