Your paper should be approximately 3 pages double spaced (~750-1000 words).
Papers can talk directly about a mathematical topic related to approximation, they can be a personal reflection, and an expository talk relating approximation to something in history, design, culture…you name it! Above all, make sure your writing is focused and specific. However approximation appears in your paper, write about it with as much precision as you can.
A good paper should include a working definition of approximation that is relevant to your topic, and outside references. Good papers are readable (avoid typos and grammatical mistakes).
Avoid a paper that is a simple laundry list of approximation problems in your life. Write about something you find interesting or that you care about. Try to find a way to quantify the approximation problem that you want to discuss. Looking for interesting approximation mistakes is often very insightful.