I used to think that because an alkali metal needs to lose one electron to complete its outer shell, when the atom increases in size (atomic radius), the electron would be easier to lose as the attraction between it and the nucleus would be lower, resulting in increased reactivity as you go down the group (the opposite being true for halogens as they need one more electron and so need to retain their electrons).
Now the trouble I am having is that why would the melting point also increase, what does the ability to lose an electron have to do with the intermolecular forces between several atoms?