By public petition. When owners of more than 50% of the frontage within a district or part of a district shall present to the Board of Commissioners a duly signed petition for the amendment, change or modification of said district or part of district, the Board of Commissioners shall act upon said petition within 120 days after the filing of said petition with the Town Clerk. Said petition shall be accompanied by a map showing the lots, buildings and uses of property within the area for which the change of district is requested as well as all of the property within 100 feet therefrom, exclusive of street space. Said petition shall, furthermore, set forth the grounds or reasons for the proposed change.