At, or at any time after, the time of forming a division, any 10 or more freeholders thereof may petition the board to have plans prepared for the construction, improvement, or maintenance of all or any part of any highway lying within the division, whether or not such highway is mentioned in the petition for the formation of the division. In the event that there are 10 or fewer freeholders thereof, such petition will be sufficient if it bears the signatures of at least a majority of the landowners within the proposed division and the signatures of owners of more than 50 percent of the assessed valuation within the division.