Hi July,
'for a change' --> I can think of two types of situations you may want to use this phrase:
-Reflective
-Sarcastic
This are REALLY poor categories, but they are the only ones that i can think of.
Reflective
1) Lets do some exercise, for a change (the speaker is implying that they have not exercised before/ in a while/ much, and want to 'change' this)
2) We moved to the countryside for a change (the speaker is implying that he/she was bored where they were living and wanted to make 'a change', and moved)
* In this case, 'for a change' is used when you want to do something differently from before or you have done something differently because you want to change something.
Sarcastic
*When you are being sarcastic, you are just over exaggerating something. So in this case:
1) How about we spend all our money on cheesecake, for a change (in this case, the speaker doesn't want to change anything, and doesn't want to spend/ waste money on buying cheesecake)
2) For a bit of a change, i'm drinking Pepsi instead of Coke (the change isn't really a change, since both Pepsi and Coke taste extremely similar)
This is a tough question, since 'for a change' can be used in a lot of ways. These were the only two I could think of. Maybe you can make a couple of sentences using 'for a change' and we can check them to see if they make sense. I hope this was a little helpful :)