Group one elements are more reactive further down the group.
Group one elements need to loose an electron- the one on the outer shell- to react. Electrons are held to an atom by the protons in the nucleus. If an electron is close to the nucleus the force holding it in will be very strong, if it is further away it will be weaker.
So bigger atoms (towards the bottom of the group) with the outer orbital far from the nucleus will loose their electron more easily: this means they react more easily/quickly/more/vigorously.
Smaller atoms with the electron closer to the pull of the nucleus (at the top of group one) will be less reactive as it takes more to lose the electron.