Seriously: there is something to be said for the claim that mathematics is the search for beautiful tautologies.

Like javelin throwing vs hunting, running vs outrunning a predator, or painting vs making a portrait using paint because that is the only way to do it, there is a difference between being doing math and using math to reach a goal.

I think it would be very nice if one managed to give kids, even those with little mathematical talents, a glimpse of that difference.