The concept of multiplication can be shown visually using Base Ten Blocks. The visualization used for this multiplication example is the "array".
EXPANDED ALGORITHM METHOD (vertical)
The concept of multiplication can also be shown numerically in such a way to directly relate the numbers in the visual "array" method to an easily understandable numeric algorithm which utilizes the same values. This method is a great way to transition to the traditional method of multiplication. In fact, a transition does not need to be made; people who continue using this method can be very successful.
The next example was created for an algebra class to show how similar multiplying polynomials is to multiplying numbers - it is all based on place value!!
DISTRIBUTIVE METHOD (horizontal = FOIL)
This method is very similar to the Expanded Algorithm, except it is worked horizonally. It is based on the distributive property. Anyone who has had some algebra will appreciate the fact they can "FOIL" numbers!