This rhyme is very similar to My Mother and Your Mother, and I believe you play it the same way:

You play it with a child by reciting the rhyme while gently sliding your hand down his/her face. When you get to the last line, you hold the child's nose between your thumb and forefinger, with your other hand you pretend to "chop off" the nose!

Thanks and Acknowledgements

This rhyme can be found in The Little Mother Goose (1912), illustrated by Jessie Willcox Smith, and printed in the USA.