I finally figured it out. 

One lime makes 2. 

Cut it into 1/16s. Put half in an iced tea glass. 

Fill the glass with fresh mint leaves. (Ours is Sweet mint.) Mash it all up with a pestle. Mash it a LOT because the oils in the lime skin are important. This will squash down to fill a quarter of the glass. 

Fill the glass with crushed ice. 

Add equal parts rum, 1:1 sugar syrup and tonic water. 

Give it a stir and enjoy the evening.