As part of a science project, I have to give a presentation to my classmates about a topic of my choice (within some constraints) - and I chose symmetry, and it's importance in physics. One important aspect that I think must be talked about is Noether's Theorem.
Now, of course the statement of the theorem itself is very impressive, but I feel like it lacks intuitional backing. I could go up there are start talking about infinitesimal transformations of fields, but even that gets very complicated very quickly (and the mathematics can't be over an Algebra 1 level or I'll completely lose them).
What I'm instead thinking is taking one specific example of a system, and showing that if some symmetry is true, then something else is conserved.
But I can't think of any examples. Is there any specific example of a system where it is easy to explain why translation symmetry implies conservation of momentum in that system, or some other symmetry implies some other conservation? If not, how can I go about demonstrating Noether's Theorem in an intuitive way to a class of 8th graders?