I like to show how the same mathematics shows up in very different contexts. A topic that I've used with quite varied audiences (though never with as much variation in a single audience as you have) is parabolas. They show up as the paths of thrown baseballs (or fired cannonballs), as the shape of (weightless) cables of suspension bridges, as the ideal shape of radio-telescope dishes (or the reflectors at the back of automobile headlights if you want the beams to emerge parallel). And yet, all parabolas are the same, up to scaling and orientation. You can also mention mathematical descriptions in terms of a plane section of a cone, or focus and directrix, or (if the students are OK with graphs) the graph of $y=x^2$. All these aspects of parabolas have nice pictures that you can show.