How does the reactivity of Group 1 Metals with water change down the group?

This is due to the shielding effect. When a group 1 metal reacts with water the reaction proceeds through the formation of an ionic species MOH where M is any group 1 metal. Since the species formed is ionic, the degree of reactivity of the metal is dependant on its ability to lose its outermost electron. 'Outer shell' electrons are the electrons that are furthest from the nucleus and thus experience a weaker electrostatic attraction to the nucleus than the core electrons. As you move down the group the number of electron shells increases, which as a result increases atomic radius. This is known as the shielding effect and as a result, the higher the number of electron shells, the weaker the attraction between the nucleus and outer electrons is, meaning alkali metals at the bottom of group 1 lose their outer electron more readily than earlier alkali metals, resulting in an increase of reactivity with water while moving down the group.