And I know that kids shouldn't stretch the same as adults. How do you know this to be the case?

You are wanting the kids to stretch to stop muscle tightness to prevent injury. But even as adults this is why we stretch. I'm not sure why there should be any difference.

In my opinion if we taught children to stretch at an early age and showed them the benefits then injuries could be prevented in later life. I would treat them the same as you would an adult. Make sure they are feeling the stretch where they are meant to, and if they aren't look at their techinique to find out why and correct it.