Smashing small pottery pieces in Japan is believed to keep off bad luck. Depending on a place, we might throw the pottery from a cliff, try to throw it through some hole or gate, or just smash it on a stone.
We also might write our fears before throwing, whisper, or just blow our fears into a small clay cup before throwing it.
Stone for smashing bad luck
There are a few words for “offering” in Japanese. The most common is 奉納（ほうのう） written on torii gates, lanterns, sculptures in all shrines and temples, but also 初穂(はつほ) first ears of rice or crops or harvest of the season and offering (to the gods)
Clearly seems as the first harvested rice has been offered to deities, other words for an offering, commonly seen in shrines and temples is 奉納 and when buying amulets or other devotional objects, one usually hears “おおさめになります” which is polite way of saying how much a bill tots up to.