Question

give an example of an addition problem in which you would and would not group the addends differently to add

Answer 1

If you're adding positive numbers together, then the order in which you write or group the addends doesn't matter.

If you're "adding" a negative number to a positive number, it's a little easier to visualize this problem if you write the positive number first, followed by the negative number.

But if you're "adding" -15 to 8, it'd make sense to write the -15 first (because its magnitude is greater) and then the 8:  -15 + 8 = -7