Possible Clues:

• Taking of a vote; partition
• Difference of opinion in The Branch
• Split between a regiment and a corps?
• Class's maths exercise, long or short?
• Mathematical process in class
• Parliamentary vote
• Conflict that's indicated by points put on either side of bar
• Come together in the army; fall apart in politics
• A number of teams grouped together in sport according to ability
• Math function