Backwards Day! What a good idea. Good excuse to wear your cap backwards, practise walking backwards, sitting on a chair backwards...let the children come up with ideas. Try telling a story backwards. Does it work? Is it good to know the solution before the problem?
With older children it can be fun to identify names that are spelled the same forwards and backwards, like Eve; Anna; Hannah; Otto and Elle. When I read Libby Gleeson's Skating on Sand to classes the discussion in the book of Hannah's name being a palindrome always elicits long list of other palindromes. Jill Tomlinson's The Penguin Who Wanted to Know has a penguin called Otto and another called Anna so it too is good to start palindrome discussion. If you just want to keep palindrome discussion brief introduce the picture book Mom and Dad are Palindromes by Mark Shulman and Adam McCauley and leave it out for your students to read.