In positional counting, cleaning up is the best part. Getting rid of accumulated quantity by exchanging it for more powerful tokens instead of hauling it on forever—this is what makes a positional system so helpful. The counters reveals its two-dimensional soul. Every position is a separate number line. A regular number—a string of digits—obscures this fact.

The kids who understood quantity start solving small problems one by one. This makes them ready to learn big numbers. Positional counting is the gateway to this magnificent world.

Important: don't nudge your students into addition before their understanding of big quantity and the different ways of counting is firmly established. Only then follow to the green pages.

In particular, 2+2 is not 22. The "+" sign means counting forward. 2+2 is 1+1+1+1. Make the student count to 22 and compare.