Science fair project suggestion: illustrating different ways to do something in assembly, to show which libraries and compilers are more clever and which approaches fit specific processors and use cases.
You should analyze a task that is:
- easy to understand (to avoid losing public)
- non-obvious to implement, with some difficulties and tradeoffs (to find interesting differences between implementations)
- simple to test (because you'll have to run performance measurements)
BLAS routines, for example dense matrix multiplication, should be good choices.