Here's a fun one. (OK, I think it's fun, anyway.) Especially for those who teach macro.
A first year student emails me. Paraphrasing, he asks "For a closed economy, we know that national saving equals national investment, and investing in newly-produced goods counts towards GDP. And "saving" means anything we do with our income other than paying taxes and spending on newly-produced consumption goods. So if I take $100 from my pay and stick it under the mattress, does that count towards GDP?"
Your instinct is to answer "No!" of course. But you should be able to see his logic.