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This is a variant of http://en.wikipedia.org/wiki/Lattice_multiplication that does not make it as easy to carry tens a column to the left as that method does.

I also think lattice multiplication makes it easier to understand for pupils why the trick actually performs a multiplication.

So, I would teach them lattice multiplication instead.

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Another approach: http://en.wikipedia.org/wiki/Grid_method_multiplication

Of course it's all multiplication, and all essentially the same thing. I find the grid method the least notation-focused of at least these three, and so I think more accessible to assimilation. Maybe I'm biased, I didn't learn multiplication this way but found myself naturally doing it like this in my head and then was pleasantly surprised to find it had a name. It's also amenable to estimation.

Thanks for the link. The grid is also helpful as a way to visualize things like:

  (1 + a)^2 = 1 + 2a + a^2

There is a square with side 1+a, and the grid consists of four pieces, sizes 1, a, a, and a^2.

Thinking about approximations when a << 1, you can motivate why

  (1 + a)^2 ~= 1 + 2a

really easily by imagining the grid you refer to.

In other words, keeping this grid picture in mind can be helpful to more mature mathematicians/physicists/engineers...probably more useful than the standard multiplication algorithm is.

I learned the lattice method in the 5th grade in 1981 here in a US public school. I loved it and used it for years afterward. I didn't realize until I was in high school that it wasn't part of the curriculum but only something my teacher thought was useful.

It’s also easy to do in your head, and works pleasantly for numbers in any base, including polynomials.

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