Which games do you play with your baby? What games can be played with 0 to 3 month old baby? Which games are suitable for toddlers? Pooja replied. I remember my mother playing an interesting game with my younger brother when he was a little toddler. She used to sing a Marathi rhyme called ' Ithe Naach Re Mora' which means that the baby is asking the peacock to dance on his hand and she used to play with his fingers and hands.