Alternative to Memorizing Times Tables

Date: 01/13/2004 at 19:09:56
From: Samantha
Subject: how do you remember 12's in just one day

How do you remember the 12's times table in just one day?  I have to
do a times test tommorow and I only have one minute.

Date: 01/14/2004 at 10:14:23
From: Doctor Ian
Subject: Re: how do you remember 12's in just one day

Hi Samantha,

In general, you can't memorize that many things in a single day, and
have them stick.  Memorization takes lots of repetition and practice.
 It's kind of like digging a hole--you have to do it one shovelful at
a time. 

However, you don't always have to memorize every little thing.  For
example, I haven't really memorized my 12's, except for 

  12 * 12 = 144

because the rest of them are pretty easy to figure out when you need
them.  For the first few, you can just multiply the individual digits:

  2 * 12 = 24            Double the 1, double the 2

  3 * 12 = 36            Triple the 1, triple the 2

  4 * 12 = 48            Quadruple the 1, quadruple the 2

Multiplying 10 by anything is easy--just add a zero at the end:

  10 * 12 = 120

So 5 times 12 will be half that:

  5 * 12 = half of 10 * 12 = half of 120 = 60

For 6 and 8, we can use doubling:

  6 * 12 = twice 3 * 12 = twice 36 = 72

  8 * 12 = twice 4 * 12 = twice 48 = 96

That leaves only 7, 9, and 11.  And since each of them is just 12 from
something we know, we don't really have to memorize those, either:

  7 * 12 = 6 * 12, plus 12   = 72 plus 12   = 84

  9 * 12 = 10 * 12, minus 12 = 120 minus 12 = 108 

 11 * 12 = 10 * 12, plus 12  = 120 plus 12  = 132

Also, if you're multiplying by a single digit, you can use the
distributive property to turn one hard multiplication into two easy
ones, e.g., 

  7 * 12 = 7 * (10 + 2)

         = 7*10 + 7*2

         = 70 + 14

         = 84

This works for _all_ of them, and although it's not as quick, it's a
good backup strategy.  While memorizing them probably gives you the
fastest way to recall them when needed, practicing thinking about them
like I just described is a nice alternative.  It may be easier that
way at first and it will help you not only to understand why the
answers are what they are, it might even help you memorize them faster
as you keep practicing.

I hope this helps!  Write back if you'd like to talk more about this,
or anything else. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/