Collecting conkers was not (to use a phrase unheard in the fifties) gender specific but playing conkers was much more a boys' thing.
Skipping was for the girls. Every girl had a rope, either a fancy one with painted wooden handles or more likely a piece of worn out washing line. We would skip on our own at home but in the playground it was generally a group thing. We had loads of skipping rhymes. They had to be short so no-one would have to wait too long for their turn. One of my favourites was
Mary drank some marmalade
Mary drank some pop
Mary drank some other things
That made her stomach flop.
Whoops went the marmalade!
Whoops went the pop!
Whoops went the other things
That made her stomach flop!
That one was accompanied by an enthusiastic pretence at throwing up.
Being the rope turner was never popular so it became a sort of forfeit if you "missed a link" or made any other mistake.
Skipping ropes also made the walk home more fun too. We would all run home turning our ropes as we ran. Happy days