Multiplicative structure of the block of numbers 1–-100 is designed here as an activity of comprehension of multiplicative (and divisional) schemes, followed by their symbolic coding. At this stage, arithmetic operations and their properties gain their meaning as pull-outs from intuition. To help grasp that meaning and recognition of outer space appearances, we are elaborating here a system of iconic signs upon which such a learning process is founded. In particular, based on this system of signs, a method (that we call Pythagorean) for establishing properties of multiplication and division has been developed and discussed in depth here. A step-by-step building of the multiplication table, iconic representation and explanation of its entries are elaborated as to facilitate learning and retention in memory. At the end, two-box place holders have also been designed and digits in colour used for developing calculation skills in the case of addition and subtraction of two-digit numbers.