The Maya Indians had several calendars, the one I have used here is their calendar over the year (haab). It was used in conjunction with the more famous tzolkin (for their sacred year), which was composed by the numbers from 1 to 13 prefixed to one of their 20 daynames, for instance as 13 Ahau - the last of the 13 numbers conjoined with the last of the 20 daynames (Ahau). This gave 13 * 20 = 260 possible dates according to the tzolkin.

In the picture below (ref.: Midonick) is explained how a more definite date is generated by combining tzolkin with haab:

Also the ordinal number in the month according to the haab calendar was prefixed (see B cogwheel). But the counting began with 0 instead of with 1 (cfr for instance 1 Imix in the A cogwheel, the tzolkin). The last (19th) haab month (Vayeb - or as spelled in the picture: Uayeb) had only 5 days, and its highest number therefore became 4. Otherwise the highest number in a month was 19. Months were defined in the haab calendar, not in the tzolkin.