You may have seen this guy on TV or on the web:

He makes a big show out of squaring and multiplying large numbers in his head. I had seen Arthur Benjamin several times and was dismissive of his shtick because I, as a rather accomplished mathlete, had never before needed to be able to make these rapid calculations in the course of my many competitions. So if I didn’t need these methods…

But recently I started reading his book – Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks – and I must say that after using his shortcuts to multiply….I now see profound value in them. Like most math in general, it’s not that anyone will have to actually do these calculations for anything important in life, it’s rather that this is a terrific brain-smashing exercise. I had to ban myself from reading the book right before bed because trying to multiply 78 times 49 all in my head and whatnot was revving me up and keeping me wide awake!

I’ve already started my son on the first easy lesson – squaring 2-digit numbers that end in 5.

For example, to square 45 you take the first digit, ‘4’, multiply it by ‘4+1′, which is 5….and you get ’20’.

Now juxtapose ’25’ to the right of it to get ‘2025’. Thus:

652 = (6 x 7) 25 or 4225

852= (8 x 9) 25 or 7225

752= (7 x 8) 25 or 5625

352= (3 x 4) 25 or 1225

Etc.

There are more hacks like this, but they get progressively more challenging.

Timed math exams (SAT, math competitions,…) are all about that – time.  The more net shortcuts someone has, essentially the more time they have to get through the questions than everyone else- AND the more time they have to check their work.