For this to work you will need to either share your Apple ID with your child, or have the username & password to their Apple ID.
Apple have a free feature called Find my iPhone which allows you to locate the iPhone easily. You can also get the free app. The app is located here and the website to locate the phone is https://www.icloud.com/#find
You will need to enable location services & find my iphone on your childs iPhone or iPad. Once enabled you can then use the Find my iPhone app or iCloud to locate your child.