Every once in a while, I'll try to post some math tips that may or may not be helpful to people. We'll start with a couple of simple ones this time, and you'll have to trust me when I say I'm not using a calculator for any of the examples.
Multiplying By 12
I never memorized the multiplication facts for 12 when I was a kid. Why bother? It's easy to multiply by 11, then just add one more of whatever number your multiplying by. For example, for 12 × 7:
11 × 7 = 77
77 + 7 = 84
so 12 × 7 = 84
In third grade, I was able to do that process quickly enough to still complete the timed multiplication tests, so my teachers never knew I hadn't actually "memorized" those facts. (Do they still do those timed tests in elementary?) Of course, that assumes you can add a single-digit number to a larger number without counting it out.
What if you need to multiply something by 12 that's beyond the typically memorized math facts? It's a little trickier, but in a pinch, you can still do it in your head. Multiplying by 10 is even easier than 11. Then you just double whatever you're multiplying by, and add the two together. For example, 12 × 15:
15 × 10 = 150
15 × 2 = 30
150 + 30 = 180
Maybe that one was too easy. Let's try 12 × 43:
43 × 10 = 430
43 × 2 = 86
430 + 86 = 516
Again, this requires some mental addition ability. So let's look at one of the simplest cases of this to start with.
Adding (or Subtracting) 9
As crazy as it makes me to see teenagers in advanced math classes add by counting on their fingers, it's the worst when they do it for something as easy as adding or subtracting 9. Our base-10 number system is a marvelous thing. It makes adding/subtracting 10 super-easy. To add/subtract 9, just do 10, then move one space back the other direction.
For 27 + 9:
27 + 10 = 37
37 - 1 = 36
For 82 - 9:
82 - 10 = 72
72 + 1 = 73
Yes, pretty much all of us have cell phones with calculators these days. But seriously, for simple calculations, I bet you can do it in your head more quickly than you can take out your phone and punch it in. ;)
I'll see if I can come up with more tips and tricks another week.