@lostwanderer92,
To me it depends on the child.
I think overall any child under the age of 18 should be informed that their may check their online activity. Does that mean you do? No.
Put it to you this way - I have two daughters (one now over 18) but when she was younger I do not know if every checked her activity. I do look at her facebook and twitter but more to see her pictures and keep up with her. Why did not check her - she actually would come to me if she received anything inappropriate whether it was something from a friend or whether it was from someone she did not know.
My other daughter not so much - I will open her phone and scroll through her texts. Although she does not get into trouble - she is borderline and I know it - and she knows it. She had some issues with friends due to texting more as a mis-understanding leading to fights between friends so I like to monitor it.
Her texts can be borderline so as long as they stay within say some swearing but nothing sexual or violent I let it go because I understand this is talk with friends.
And she is a teen not a preteen.
A preteen to me should be monitored.
I'd also like to add - I pay for the phone and computer and the services so they are my property. No different than a work computer - work makes it clear they can monitor your usage.