One fragment reads "SAT DOWN BESIDE"--obviously a quotation from Little
Miss Muffet. In fact, you can see the legs of the spider.
Another reads "ACK AN". By itself, maybe not identifiable. But in the
context of the Little Miss Muffet quotation, this seemed likely to be
from Jack And Jill.
And, thanks to Google, here are images of the linoleum tiles:
<http://radioguy.1stdibs.com/store/furniture_item_detail.php?id=391470>.
--Charles