A selection of len's - 'lifestream', games & research - from the archive.

'JAPANESE MULTIPLICATION'



I have long been interested 'alternative' methods of 'numeracy', mainly since I realised that the secret embarrassment I harboured when growing up, when I basically could not add up, was totally unfounded. In fact, the method that I was forced to adopt, by said embarrassment, was actually profound and significant.

(Further, to labour the point, I had discovered that the existence of alternative methods of learning existed at many levels of education and understanding - and that makes for a great teacher and creative students.)

That I 'added-up' by counting the graphical elements of a number [• illustration to follow]', was in fact the very way that the morphology of numbers originally evolved. [See: Lundmark, Torbjörn. 'Quirk Qwerty', UNSW Press, 2002.].

So, I was quite delighted when, some time ago, I came across an article describing how multiplication is initially taught to children in schools in Japan.

The method, of multiplying any two integers, initially seems primitive, but on further research it was the very basis on which computer code computes [* reference]. In the end the method comprises just adding up some simple numbers.



EXAMPLES

Take two numbers to multiply, say 42 by 31.

42 can be represented as 4 x 10 (tens)  + 2 x 1 (units), and,
31 can be represented as 3 x 10 (tens) + 1 x 1 (units).

Graphically, this can be seen as:

Now combine these at a 90 degree orientation:

The intersections represent the 100's, the 10's and the units:

As indicated, these total:

[100's] = 3 x 4 = 12 - So, x 100 = 1200 (Or, simply add the number of nodes!)

[10's] = (4 x 1) + (2 x 3) = 4 + 6 = 10 - So, X 10 = 100

[Units] = 2 x 1 = 2 - So, x 1 = 2

Finally, add these together:

1200 + 100 + 2 = 1302

QED

So for some larger numbers to multiply, say 53 by 37:


EXAMPLE (Chop-Sticks)IN THE HEADING:

The top illustration represents 53 x 57

Adding the 'nodes'

[100's] = 5 x 3 = 15 - So, x 100 = 1500 (Or, simply add the number of nodes!)

[10's] = (3 x 3) + (7 x 5) = 9 + 35 = 10 - So, X 10 = 440

[Units] = 7 x 3 = 21 - So, x 1 = 21

Finally, add these together:

1500 + 440 + 21 = 1961

QED


DECIMAL NUMBERS and BINARY MULTIPICATION

Too mind-boggling for me at present.

MAIN REFERENCE for all 'Japanese Multiplication' is Wikipedia.