For metals, reactivity as you go from in a period.

Reactivity - Reactivity refers to how likely or vigorously an atom is to react with other substances. This is usually determined by how easily electrons can be removed (ionization energy) and how badly they want to take other atom's electrons (electronegativity) because it is the transfer/interaction of electrons that is the basis of chemical reactions.  

Metals  

Period - reactivity decreases as you go from left to right across a period.  

Group - reactivity increases as you go down a group  

Why? The farther to the left and down the periodic chart you go, the easier it is for electrons to be given or taken away, resulting in higher reactivity.  

Non-metals  

Period - reactivity increases as you go from the left to the right across a period.  

Group - reactivity decreases as you go down the group.  

Why? The farther right and up you go on the periodic table, the higher the electronegativity, resulting in a more vigorous exchange of electron