Exercise 1: sample answer

Twelve lunar months last about 354 days, which is roughly eleven days shorter than the solar year of about 365 days, so a purely lunar calendar slides backwards through the seasons by about eleven days a year (check the figure). After a few years, a festival tied to spring would fall in winter. Calendars have dealt with this by adding an extra "leap" month every few years (as in lunisolar calendars), or by dropping the Moon altogether and fixing the months to the solar year, as the modern calendar does.