Question

What is the simple rule of thumb to help children remember where apostrophes go?

Answer 1

Apostrophes are used in replacement of any missing letters.

Explanation:

In English grammar, as far as I know, apostrophes are most commonly used for contractions or possessives. As for remembering where apostrophes go in contractions, the way I was taught to remember it was that the apostrophe replaces the missing letter when two different words are put together to create one word.

Ex. should not `->` should+not `->` shouldn't

As you can see above, the "o" in "not" was removed and replaced with an apostrophe, thus turning "should not" to "shouldn't".
I find that the letter that is substituted with an apostrophe is usually a vowel. Below are a few more examples.

Ex. it is `->` it+is `->` it's

Ex. can not `->` can+not `->` can't
(An alternate version of "can't" is also "cannot")

Ex. could not have `->` could+not+have `->` couldn't've
(In this slightly longer example, you remove the "h" and "a" in "have" instead of just the vowel. The same generally holds true in most three-word contractions.)

Apostrophes can also be used for possessives and the images below are probably able to explain it better than I could and they provide a visual as well!

For the full poster on proper apostrophe usage, you can use this link :)