Appendix B
WORKING THROUGH A PROBLEM
What you say inside your head while you perform mental mathematical calculations is very important.
You can double the time it takes to solve a problem by saying the wrong things, and halve the time by
saying the right things. That is why I tell you what to say, for instance, when you are multiplying by 11
in your head. To multiply 24 by 11, you would automatically see that 2 plus 4 is less than 10, so you
would look at the 2 and immediately start saying, ‘Two hundred and . . .’. While you are saying that you
would see that 2 plus 4 means you should say, ‘. . . sixty-. . .’, and in the same breath you would say,‘. . .
four.’ So you would just say, ‘Two hundred and sixty-four.’
To multiply 14 by 15 you would simply add 5 to 14 to get 19. You say in your head, ‘One hundred
and ninety . . . ’. Four times 5 is 20. Adding 20 gives, ‘Two hundred and ten.’ You would say ‘One-
ninety, two-ten.’ The less you say, the faster you will be. Practise by yourself.
You don’t need to recite the whole procedure. You wouldn’t say, ‘Fourteen plus five is one hundred
and ninety. Now we multiply four times five. Four times five is twenty. One hundred and ninety plus
twenty is two hundred and ten.’ That would take you much longer, and seems like a whole lot more
work. Just say the subtotals and totals or, if you can, just the answer.
When you practise any of the methods — especially if you want to show off in front of your friends
or class — try to anticipate what is coming. If you see you will have to carry, say the next number with
the carried number already added. For instance, let’s multiply 11 times 84. You would immediately see
that 8 plus 4 is 12 or, at least, more than 10. So you would know to carry 1 and start calling out, ‘Nine
hundred and . . .’ You provide the 2 from 12 to give ‘. . . twenty- . . .’, and then say the 4 at the end,
giving 924. You would call the answer in one breath: ‘Nine hundred and twenty-four.’
Often it helps to call carry numbers what they are. That is, if you are carrying 3 and the 3 represents
300, say three hundred. If it represents 30, say thirty. This can be useful in multiplication and addition.
Usually, the biggest hurdle to calling immediate answers is the feeling that the calculation is ‘too
hard’. Practise for yourself and you will see how easy it is to give immediate answers off the top of your
head. This applies if you are saying the answer out loud or just calculating in your head. Practise some
of the strategies with your closest friend — someone who won’t embarrass you if you make a mistake.
Practise the problems in this book in your head. The first time may seem difficult, the second time is
easier, and by the fifth time you will wonder why you ever thought they were hard. You will also find
that this will build your concentration skills.