This answer is from a student taking a math course for elementary school teachers. The assignment: Give an example of a math problem that would be difficult to calculate mentally, then give a strategy for calculating it mentally along with the mathematical properties used. And I quote:
An example of this would be as follows it is very hard to do it mentally however here is an example (165 x 2) - (180 x 2) = this is asociative property of multiplication.
I would ahve to mulitply each one whics gives me the answer of 330 - 360=
This would lead to me then having to carry over 1 from the first 3 to add to the other then subtracting 13-6 which gives 8 then 0-0 is 0 so the final answer would be 80.
This tragedy would be hard to accomplish mentally.