I showed my students this incredible video of Arthur Benjamin doing Mathemagic (cue up to about the 13:00 mark for the big finale). In it, he multiplies 57683 by 57683, and he does it all in his head in less than a minute. We used this as a little motivation for trying to work through some mental math problems of our own. We also analzed his strategy and how we can apply his work (though way above our level) to our own. We found that:
a) he breaks the numbers in smaller units that are easier to work with (friendly numbers)
b) he stores these numbers in his head and then adds them all together when he has worked out a couple of sums
c) he must have practiced for a long time to get this good, and therefore perseverance is an important trait in learning math
With these observations in mind, he took off and tried to develop our own mental math strategies, and recorded them in our math journal to help us remember.