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I have seen students from India use this method for small numbers and a partial sum method for larger numbers.

http://wsgfl2.westsussex.gov.uk/Aplaws/maths/multicultural/V...

Google 'Vedic multiplication'. Its all good because it is unusual here in the UK and it looks interesting.

Yes, now that I recall, I believe this was a very popular topic in Japan a few years ago (I wasn't in Japan to see it first hand). It was referred to as "India-style multiplication," and some guy(s) sold millions of instructional books. http://math.hoge2.info/kakezan/pr04.html

However, don't think it involves the drawing of lines like in the post.

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