From how many “things” to how much “stuff.”

The fundamental step: Choose a unit of stuff; then count how many units.

(This “trick” must be explicitly explained. It allows the use of discrete counting to quantify things that by their nature cannot be counted.)

(Many points have to be addressed: How to extend the base-ten representation; how to extend the operations; emphasize that now all numbers are relative to the chosen unit.)

Easiest to visualize when the stuff is liquid. Can then pour it into unit containers.

Obviously, the last unit container might not be completely full. What then?

For base-ten, it is natural to continue the pattern downwards: introduce increasingly smaller containers, such that ten of a smaller containers fit into one larger container.