Things to consider when doing an inquiry-based STEAM activity:
Is there more than one correct strategy to solve the problem? Does the activity require my child to explain their reasoning or solution? Can the activity be done several times with different outcomes each time? Does the activity provide a sense of frustration and then accomplishment because the answer was not found immediately? Does the activity ask my child to look at the world in a new way? Does the activity require my child to check their work? Does the activity help my child learn to ask questions? Does the activity encourage my child to be original and to elaborate on their ideas?
Books such as 65 Short Mysteries You Can Solve With Math and 65 Short Mysteries You Can Solve With Science (by Yoder), Stories to Solve (by Shannon), Sir Cumference stories (by Neuschwander), The Phantom Tollbooth (Juster), Leonardo DaVinci Gets A Do-Over (Friedlander), Numbed (Lubar), The Race to the Moon: An Interactive History Adventure (Lassieur), anything by Marilyn Burns or Greg Tang
How To Think Like Leonardo Da Vinci by Gelb (book AND workbook)
Professor Noggin's Knowledge Card Games ($10 online)