Appendix A
USING THE METHODS IN THE CLASSROOM
Children often ask me, ‘How do I use the methods in the classroom? Won’t my teacher object if I use
different methods?’
It is a fair question. Here is the answer I give.
Firstly, many of the methods taught in this book are ‘invisible’. That is, the difference is what you say
in your head. With addition and subtraction problems the layout and written calculations are the same;
what is different is what you say to yourself in your head. When you are subtracting 8 from 5 and you
borrow 10 to make it 8 from 15; you say to yourself 8 from 10 is 2, plus 5 is 7. You write down the 7.
The students who subtract 8 from 15 write down 7 as well (so long as they don’t make a mistake), so
anyone looking over your shoulder would have no idea you are using a different method.
The same goes for subtracting 3,571 from 10,000. You set the problem out the same as everyone else,
but again, what you say inside your head is different. You subtract each digit from 9 and the final digit
from 10. No-one looking at your finished calculation would know you did anything different.
If you were asked to subtract 378 from 613 you would again write the problem down as usual. Then
you could find the answer in your head by subtracting 400 and adding 22.
613 − 400 = 213
213 + 22 = 235
Using this method there is no carrying or borrowing. You just write the answer and then check by
casting nines.
The same goes for all mental calculation; that is, all calculations where you write nothing down. No-
one knows what method you use. Students and teachers have always used different methods, even for
such simple problems as 56 minus 9, as I pointed out earlier in the book.
Also, the higher the grade you are in, the less of a problem this will be.
Now let’s look at where it can make a difference. Let’s say you are asked to multiply 355 by 52. You
set out the problem as the teacher requires.
Here is the finished calculation. Can you now make use of what you have learnt in this book?
Certainly you can. You can cast out nines to check your answer.
The substitutes are 4 × 7 = 1, which we can see is correct because 4 times 7 equals 28, and 2 plus 8 is
10, which adds to 1.
Had you found you had made a mistake, you could cast out nines to find where you made it. You
would find the substitute number for each part of the calculation. It would look like this.