Students want math on a quick study card. Peano Axioms fit on a 3 x 5 card. The structure of arithmetic without gaps is the path starting from the Peano Axioms and going to place value notation as a structure and fractions as functions and then as numbers in their own right.
There is still need of many study aids, examples, exercises and tests on the Peano Axiom Path through Arithmetic (PAPTA). But it is a path that makes sense because it tells the logical story of arithmetic.
If you go off the Peano Axiom Path then you are in the Random Hills of Skills and Drills. You face one test after another. Each time you climb what you think is the last hill in the forest, you just face another test. You never see the forest for the trees.