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A discussion in the Maths Café from 2007 prompted me to start thinking about the various methods for multiplying which our learners may have been taught at school.
You might like to start your examination of multiplication methods by:
The Grid Method
Chinese Multiplication (also known as the Gelosia method or the Lattice method)
Egyptian, Russian and Vedic Multiplication
PS: if you don't know how to multiply the numbers 6 to 10 on your fingers, read Multiplying on your fingers from everything2.com.