Music and singing is one of my absolute musts for my children. I also go into their nursery and provide singing and music sessions with the children there. Some people feel very embarrassed at the thought of having to sing but young children are really not bothered if you don't sing in tune!
Simple songs and rhymes teach children so much. They are learning new words, about counting and simple sums, about the world around them, and how to communicate. Songs often use actions and signs which help children to learn the words and remember them. Besides all of which singing is a really fun and uplifting activity which children really enjoy.
Twinkle twinkle little star
The wheels on the bus
Heads, shoulders, knees and toes
If you're happy and you know it
Three brown teddies sitting on a wall
I am the music man - this is a good one to do with percussion instruments
Baa baa black sheep