Want to incorporate science and math into the classroom that make for engaging activities? Pamela Truesdell, a Research Fellow for the Cincinnati Engineering Enhanced Mathematics and Science Program has written a book titled: "Engineering Essentials for STEM Instruction: How do I infuse real-world problem solving into science, technology, and math?" Some good examples are: "Cell Phone Drop", "Changing the Shape of Breakfast", "Harvest Helpers" just to name a few.
Have a gander at the many activities there are for students of all grade levels. Some lessons I find particularly interesting due to the high level of engagement and creativitiy are:
""What? No cars?"" (Sci); ""How much is too much?"", ""Model Cities and You"" (Math); ""Energy Jeopardy"", ""Available and Distribution"" (Sci).
Here you can find free lesson plans for projects in physics and engineering. There are three that I really like because it allows students to get their creative currents flowing! There are three particular activities that I like, could also inspire healthy competition, are: Bristle Bots, Dance Pad Mania and Electric Gambox. Be sure to show the Hidden Alarm video first.
How to build interesting STEM projects with using real world examples. You can use the resources listed in the article, or ask your class to come up with real world examples all on their own. This is an interesting take because you can see how engaged they are with the world around them.