Maths wizardry with lines

[matgb]

You thought you knew maths? YouTube - Alex Bellos demonstrates a very cool, and strange way to multiply:

How weird is that? (Via)

Can't afford to buy the book, does anyone know more about the method, because if multiplying were that easy surely they'd be teaching it in schools, especially for the less numerically gifted?

Comments

[rho]

It's basically nothing more than standard multiplication. Bottom right corner is units * units, then the next diagonal is ten * units and units * tens, then units * hundreds and tens * tens and hundreds * units, and so on. Add the contents of the diagonals to get your units, tens, hundreds answer, then put them all together for the final answer.

The only thing that you're doing differently is that for each individual pair of digits that you multiply, instead of just doing it in your head, you're drawing lines and counting their intersections. That's fine when you're doing 2*3 and want to draw 2 lines crossing 3 lines and count up that there are 6 intersections, but it really comes unstuck when you need to multiply 7 by 9 when even drawing all the lines becomes difficult, let alone counting up the 63 points.

There's a similar method where you construct a grid, multiply the individual digits and then add up the diagonals, which is essentially the same as the method in the video, but with standard multiplication (either by memory or by repeated addition) instead of lines. I think there is something to be said for teaching that method in schools. It's a little unwieldy, certainly, but it's always good to have different approaches to be able to use since different ways of looking a things will click for different people.

[matgb]

On the LJ copy of the post, a friend who is a primary school teacher says he uses the grid method, also something I've never heard of. So yes, does make more sense when you explain it, I was just boggled that it could work as I'd never encountered it before, now I've thought it through and you've explained it it's a bit obvious.

I've never liked one-size-fits-all methods, mostly they work for me but when they don't I get all confused.

Juggling intersections

[frith]

Personally I'd find having to learn this graphical method of multiplication on top of the usual way confusing, not helpful. But it may fit other people with brains that function differently.

[(Anonymous)]

I did a quick diagram to accompany Rho's description, in case your brain is like mine and prefers images to words!


http://i800.photobucket.com/albums/yy285/poifaerie/GridMultiplication.jpg

~ poifaerie @ LJ

[two-brains.livejournal.com]

I like it a lot. Never seen it before, but very cool.

It's a lot like grid multiplication, but probably great for people who prefer images to symbols. Definitely a tool to remember.

The problem (as I see it) for children's use, particularly those who are perhaps less mathematically skilled, is that I can immagine kids getting very confused about place value, particularly when carrying in the second example.

I always get kids who arent good at multiplying to use the grid method as it turns a hard multiplication into a number of easy ones followed by an addition.

[poifaerie.livejournal.com]

Not only working out how many places to "move" a decimal, I can imagine a fair few would have difficulty in working out which groups to add together- especially if ther have problems with spatial awareness.

A nice trick if you can do it, though!

[lokean.livejournal.com]

Crosswise multiplication. It's a technique in Vedic Mathematics, which has a large number of 'shortcut' or 'trick' techniques in it.

The problem is that this technique is very bad when dealing with large individual numerals. I believe there were other multiplication techniques available though...

[dainul.livejournal.com]

I was going to say something similar - imagine 19*91, you'd have to count up 81 crosses at one corner alone.