Summer break is around 3 months and in that time, kids our age go on vacations, play video games, work, go out, ect. Some kids still test themselves over the summer like going to an arts academy or a different subject academy to get them ready for the future. Other kids might not see collage as their future and go into full time work after they graduate high school. I think the student can decide whether or not they'd be interested in working on a project in the summer. It wouldnt be a lot of work but maybe some type of project the kids would be passionate about and want to learn or present that subject.

The project should be student-designed and one of the reasons should be, what are they doing over the break?

depending on the subject the teacher can ask them to make a project including either what they learned that year or something that correlates to that subject. The kids should be able to have fun, still learning, and do a project in their own style and use their creativity. The teacher can steer them in the right direction of help them with ideas but I still think the student should really pick on what they'd like to do. If the teacher assigned the project to the kids I wouldn't think it would be exiting to do, especially over summer break. I'd have so much more fun if I got to choose what I get to write or present about than for a teacher to give me limited creativity and how they'd want it done. You can see when a kid is really passionate about a project compared to a kid who just wants to get it over with, that being said when its student-designed it really has no limit on what they can do. We can have fun with our projects and the teacher will hopefully enjoy them after the break. The project and show, what school subject it is, what did I choose to present that subject, how they go together, and how the school subject taught me about their subject(what they chose). I believe it should be student-designed rather than teacher-designed so the student can really be engaged in the learning process.

This does depend on the subject or how the kid is doing academically, i'd say the teacher should design the project if the kid is failing the class, also depends on what they are planning for the future. If the kid is struggling the teacher should step in and figure out a project that might motivate the student into learning more about the subject.

For the most part I think if the student has to complete a project over the break than they should have some fun with it and show their teacher the potential they have.