A childrens poem about a Mother and child mouse. First line of poem is
"Once a trap was baited with a piece of cheese". Mother mouse told
baby not to go near but baby mouse did not listen " " first he took a
nibble and then he took a bite" Thats all I can remember

I've found two slightly different versions of the poem that were
posted by people who say they learned the verse from their mothers.

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Once a trap was baited with a piece of cheese.
It tickled so the little mouse, it almost made him sneeze.
"Be careful!" said an old mouse, "There's danger where you go."
"Nonsense!" said the little mouse. I don't think you know."

Then he stepped in boldly, no one in sight.
First he took a nibble. Then he took a bite. 

Snap! The trap was closed there.
Closed as quick as wink,
Catching mousey fast there, 'cause he didn't think.

Personal Pages of Gary and Lynda Crocker: A Eulogy for Doris Potter 
http://home.earthlink.net/~garycrocker/beliefs/eulomom.htm

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Once a trap was baited 
with a piece of cheese 
It tickled so a little mouse 
it almost made him sneeze. 
An old mouse said "There's danger-- 
Be careful where you go!" 
"Nonsense!" said the little mouse, 
"I don't think you know" 
So he walked in boldly-- 
nobody in sight. 
First he took a nibble, then 
he took a BITE 
Then SNAP! the trap together 
closed, as quick as a wink-- 
Catching mousie fast there 
'cause he didn't think." 

Callister History and Families: READING
http://www.digiville.com/callister/mother/read.html

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The original poem was somewhat longer. It was written by the American
poet Phoebe Cary (1824-1871).

They Didn't Think

Once a trap was baited
With a piece of cheese;
It tickled so a little mouse,
It almost made him sneeze.
An old rat said, "There's a danger,
Be careful where you go!
"Nonsense!" said the other,
"I don't think you know!"
So he walked in boldly - 
Nobody in sight -
First he took a nibble,
Then he took a bite;
Close the trap together
Snapped as quick as wink,
Catching mousey fast there,
'Cause he didn't think.

Once there was a robin,
Lived outside the door,
Who wanted to go inside
And hop upon the floor.
"No, no," said the mother,
"You must stay with me;
Little birds are safest
Sitting in a tree."
"I don't care," said Robin,
And gave his tail a fling,
"I don't think the old folks
Know quite everything."
Down he flew, and kitty seized him 
Before he'd time to blink;
"Oh," he cried, "I'm sorry,
But I just didn't think."

WordPower: Selected Poems of Phoebe Cary
http://www.wordpower.ws/poetry/phoebe-cary.html#didnothink

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My Google search strategy:

Google Web Search: "first he took a nibble" "then he took a bite"
://www.google.com/search?hl=en&q=%22first+he+took+a+nibble%22+%22then+he+took+a+bite%22

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I hope this is precisely what you are looking for. If it is not,
please request clarification; I'll gladly offer further assistance
before you rate my answer.

Best regards,
pinkfreud

Excellent I am so very happy the words have been going around in my
head for weeks. Thank you so very much Annielowell

I'm glad I could help. Thank you very much for the five-star rating
and the nice tip!

~pinkfreud