``The number you have dialed is imaginary. Please divide
by zero and try again.''

This system has been designed with the overall goal of making it possible for the student to confidently multiply any size number by from between one and twelve without having to carry any value higher than two. It is aimed at making it possible for students whose knowledge of mathematics includes only addition, doubling, and subtraction to solve complicated multiplication problems.
Therefore, the lessons are organized such that each presents you with only one new step for solving each new problem, building up from the simple to the somewhat more complex (combinatory) rules for solving any sized multiplication problem.
Terms  
Carry
 the value of the "tens" place of the number you intend next to write in the solution area. In this system of multiplication, the "carry" will never be larger than a 2. 
Half
 a simplified half, throw out fractions. (ex. half of 5 is 2), this is only done when multiplying by 3,4,5,6 or 7... as you will see. 
Multiplicand
 the value to be multiplied. 
Multiplier
 the value by which to multiply. 
Neighbor
 the digit of the multiplicand which is to the right of the "number" (see below), if there is no neighbor then this is zero. 
Number
 when working right to left to achieve the product, this is the digit of the multiplicand under which the next digit of the solution is to be written; if there is no digit in this position, then treat it like a zero. 
Product
 the answer to a multiplication problem. 