I had a children's record when I was growing up, with a story about a little boy who wanders away in the forest and gets lost. He meets various woodland animals who tell him he has to find all the parts of the song in order to find his parents again, and I remember four frogs, some chipmunks and some dachshunds, but that's all. As far as I can remember, the lyrics go like this:

I'll sing you one-O
Every day we grow I-O
What is your one-O?
One is one and all alone and ever more shall be so.
Two's two for two pretty eyes looking at the wide world O.
Three's three for Daddy, Mommy and me.
Four's for the wheels on automobiles.
Five's for the fingers on each hand.

and then I forget the rest.

There were also the following songs:

Oh, my mother runs a butcher shop
My father cuts the meat,
and I'm the little hot dog
who runs around the street.

also:

Misty, moisty was the morn,
chilly was the weather.
There I met an old man
dressed all in leather.
Dress all in leather against the snow and rain,
Saying "How do you do" and "How do you do" and "How do you do" again.
Saying "How do you do" and "How do you do" and "How do you do" again.

and that's all I can remember.