Presenting Mapping Reducibility (for P vs NP)
Considering that you teach HS students, many of the reduction examples "off the market" might be conceptually a bit too complex, and can be confusing even for many college students.

I'd suggest that you choose an example between very similar problems, like the (polynomial time) reduction from 4SAT to 3SAT.

So, what are 4SAT and 3SAT? SAT is the Boolean satisfiability problem, or, given a Boolean formula phi, we want to decide if there is a solution to the equation phi = true.

These equations are usually written in conjunctive normal form, or a series of conjunctions of disjunctions, like: "(a or b or c) and (c or d)". When each clause has 3 terms, the problem is called 3SAT. When each clause has 4, it's called 4SAT. Now you might get a sense how one could reduce from 4SAT to 3SAT. One possible reduction (which is extremely simple) is described here on the Math SE.