I numeri dalla prima alla quinta superiore

In this paper some questions related to teaching and learning arithmetic in High Schools are discussed. Even in High Schools, the structure of natural numbers cannot be neglected. Confidence in using numbers helps in stating and verifying conjectures. Using properties of notation for rational numbers, we give a proof that there are infinitely many prime numbers. About the introduction of real numbers, it seems to be related to measure and topology, rather than to solving algebraic equations. Among other things, Zeno's paradox about Achilles and the Turtle is briefly discussed. At the end of the paper, some problems are posed.