A matoi is a banner used in Edo period Japan by firemen to notify people of a fire nearby or within a building. They were placed on the nearby roof of the burning building by the machibikeshi (fire brigade). Each local brigade of firemen in the Edo period had their own matoi to identify themselves. They were also used to identify the place where the brigade would meet. In modern Japan, the matoi is used mainly for ceremonial purposes. The matoi are seen as symbols of courage, hope, and leadership for firefighters.
In Japan, the houses were often made of wood and paper, with thatched roofs so fires were a common occurrence and a real worry (Tokyo/Edo and other Japanese cities have burnt down repeatedly in the past, the Japanese just rebuild). The only way to stop the spread of fires was often to tear down nearby houses to keep them from catching fire and burning as well. The tool used to tear down these buildings was often large wooden mallets such as the one Kodachi uses or the one Kasumi gives to Akane in the Ranma ½ manga.
Kodachi's school in the Ranma ½ manga (pictured above) has a Matoi symbolizing that it was a place where a fire brigade would meet.