Does your chewing gum loose its flavor
On the bed post overnight?
When your mother says "don't chew it"
Do you swallow it for spite?
Can you catch it on your tonsils,
and dang it left and right?
Oh, does your chewing gum loose is flavor
on the bed post over night!

I don't know this one, but the tune sure reminds me of the Smarties jingle (sorry to get commercial):
When you eat your Smarties, do you eat the red ones last?
Do you suck them very slowly, or crunch them very fast?
They're candy-coated chocolates
So tell me when I ask
When you eat your Smarties, do you eat the red ones last?

As kids, we used to sing it faster and faster - it was fun at the time.