How does reactivity change as you move from one side of the periodic table to the other or if you move from the top to the bottom?
I'm assuming you're asking about how the CHARACTER changes as we move all about the periodic table, and based on that how does the reactivity change.
As we move from left to right, the electropositive character decreases, and the electronegative character increases. For example, take the 3rd period. Sodium's reactivity is pretty high, because it readily gives away an electron to get a stable configuration. As we move towards the right, the reactivity decreases, but again it starts rising and reaches a high vue when we get to chlorine, which readily accepts an electron to get a stable configuration.
When we go down a group, electropositive character increases, but electronegative character decreases. Thus, if we may see the Li-family, reactivity increases down the group, but if we look at the halogen family, i.e. the F-family, reactivity decreases.