Explaining black holes to neophytes

I'm working on presentations about astronomy for mostly high school students (here they are from ages 12-16) and I want to have a short section about black holes, since they are usually pretty interested in those. I've been generally annoyed at the way they are generally discussed. Singularities are often presented as real objets. I know it is normal to "lie" and simplify things when popularizing science, but I feel in this case it's too big a lie. People accept very young this way of explaining black holes and can feel shocked or betrayed when they learn no physicist believes in actual singularities.

Though the inner solutions of schwartzchild and Kerr black holes can be funny to think about (especially Kerr), they are unphhysical, so I find it odd to say to kids that black holes have singularities in them. Though I think it's important to point out that our model predict them and that it's a sign of trouble with these models.

I was thinking of mentioning that singularities are generally explained (to avoid people from being confused by having conflicting information about black holes), but to point out it's not physical and that we actually don't know what is in black holes.

So I would like people's and other communicator's opinions about this topic. How do you explain black holes? How do you treat singularities?