Question

What's it called when matter is broken down into smaller and smaller pieces and you can't break it down anymore?

Answer 1

I believe your answer would be an atom. 
Classical Greek philosophers, notably a man named Democritus, who lived in Greece in the 5th century was interested about the world around us. He thought up a very simple situation: If you cut something in half (like a log), the two pieces left can cut into even smaller pieces, which can cut again, and so on down to splinters. Yet, even a splinter could be cut in half. He questioned, "Whats the smallest that something can be cut?" He answer was that, at some very, very small size, you would reach a piece of the object that was 'atomos', Greek for uncuttable. 
If you had a block of iron and let's say you kept cutting it into pieces, you would, in theory, reach an extremely small piece which could absolutely not be broken down-- it was the basic building block of iron. This was, and is, a powerful idea that gives reason for all sorts of things related to chemistry and the world we live in-- like how our bodies digest food (since everything is made up of just a limited number of types of atoms (the elements), we can ingest food in one form, break the food down into small groups of atoms, and put the atoms back together as parts of our growing bodies). Modern chemistry is formed on atomic theory. Atoms are almost unbelievably small, one of your hairs is about a million atoms wide, and a speck of dust you can see might as well contain trillions of atoms. 
I got my answer and reasoning from a website called "scienceline.ucsb.edu". It goes way more into depth for your answer, you might want to check it out. I just chose bits of info that directly give reasoning as to why your answer would be An atom. 
Good luck on your assignment.