beyond the sniff test
While this doesn't specifically address spotting fake news, this is one of the intentional ways in which we are attempting to build the critical thinking skills necessary to do that.
We use a simple protocol to identify and vet primary sources, based on similar protocols that you would use for any kind of inquiry activity: observe, describe, question, research, make inferences, repeat as necessary. This is easily scaled for age, discipline, and activity. (It's part of an effort on our part to define and create a school-wide critical thinking protocol that everyone can use. Still in the development stages, but promising!)
By observing closely (reading, viewing, listening) students begin the process of describing the basic features of a claim or artifact or source. In their descriptions, they look for distinguishing features (statistics in an article, details in a photograph) and develop questions based on what they find. Then, they research the questions, which leads them, either to make an inference about a source's veracity, or they research some more.
We use this is projects throughout the school (I'm in a preK-12 school.) We've begun using this protocol with our youngest students and our oldest; with museum artifacts, primary source documents, images, and science labs.
Our goal is getting kids to understand that good critical thinking can be applied in every discipline in roughly similar ways, including spotting fake news.