Talk for K-12 Students + General Audience Reference Request
As one of the topics of your lecture, the problems from combinatorics might be good candidates.Generally, a high school student has some conception on permutation, combination and high school geometry. So, following examples illustrates what i mean.


Take arbitary points on plane. Can we always find a line such that the number of points above and below the line is same? If yes, how ?
Take a point set on plane. How can we find the minimum number of points that should be added to the point set such that it contains 4 points forming a square?


etc. Actually, the many problems in combinatorial geometry are even though hard to solve, but since they mainly focuses on points, lines they can act as motivational problems.