No, no need to carry passports or any form of ID, unless you know you will need it. Keep the passports in a safe place, preferably locked away and discreet, and only bring them out when you absolutely need to (i.e. for travelling, or if you need to produce them for any reason, like opening a bank account or for a job application or something).
Don't send your kids to school with their passports!
Yeah, definitely don't send your kids to school with them - they're sure to get lost/stolen/damaged in no time!!