Talk about persistence! James Dyson built 5,127 prototypes before finally developing his bagless vacuum cleaner. This video explains how Dyson's frustration with existing products and persistence in improving them has resulted in over 700 design engineers working with him at his company.
This page allows you to request a free engineering kit for your classroom, and also shows images of the kit so that you can see all the parts. The kit allows you to take apart a vacuum cleaner (reverse engineer) to see how it works.
This site has some great links to ideas on incorporating literature about engineering problems into a STEM project, or vice-versa. For instance, My Side of the Mountain and Hatchet both feature characters who must survive in the outdoors. You could coordinate the literature and writing in Language Arts with a STEM project or unit in science class.
With materials such as duct tape, sponges, scissors, string, paper, and a small hand saw, students brainstorm to build a prosthetic leg. For the project to be successful, a student must be able to use to walk around the classroom. Students sketch prototypes and learn about the different stages of the design engineering process.
This white paper from the National Math and Science Initiative reviews the problem: a lack of racial diversity in STEM jobs in the U.S. It proposes solving this problem by using more STEM projects in k-12 classrooms, and reviews research that shows improvement in test scores in some schools who used National Math and Science Initiative resources and curriculum with their students.