How does the size of the atoms relate to how reactive it is?

The larger an atom is, the more reactive it will be.

It helps to think about the size of an atom with the location of the electrons and nucleus in mind. You know that protons are positively charged and electrons are negatively charged, therefore there is a level of attraction between these two oppositely charged subatomic particles. This attraction helps stabilize the atom.

Now, in a larger atom, with more electrons are those electrons (specifically the valence electrons) going to be closer or further from the nucleus than in a smaller atom?

They will of course be further from the nucleus and therefore further from the positively charged nucleus. This makes it easier for the valence electrons to leave the atom and form an ionic bond or to interact with another atom to form a covalent bond.

If electrons can leave more easily, then the atom is more likely to react.