Given a collection of blocks:

• Pack as Much as Possible

• Organize by Size

For example, a collection of 354 single blocks yields (photo)

3 Purple, 5 Blue, 4 Green.

This simple packing operation establishes a key property of the base-10 number system:

Every discrete quantity can be represented by powers of ten, with no more than nine of each size.

(If there were ten of one size, then they should have been packed to create a block of a larger size.)

The quantity is represented by means of the colored digits 1 – 9.

The digits need not be written in any particular order; there is no need for zero!

Addition and subtraction can be executed by kids without any instruction.

Multi-color Digis constitute a decimal model that is not positional.

It is instructive to understand the logic of the decimal system without being confused by the additional idea of positional notation, which requires the introduction of zero.

The introduction of positional notation is done separately, when moving to unicolored blocks.