In a rocks size glass (8-10 oz.) place ½ fresh lime and muddle until it has released all it's juice. If you do not have a cocktail muddle you can use the handle end of a wooden spoon.
Add the ½ inch seeded cucumber chunk and muddle until it is well bruised and you can smell the cucumber in the glass.
Pour in 1 part tequila and ½ part triple sec. Give it a stir.
Add ice to the top of the glass. Float in lime soda water to the top. Give it another stir.
Garnish with a thin slice of cucumber.
Notes
Parts in a cocktail: A part is an inexact measurement in a cocktail. It can mean 1 ounce or 1 cup, depending on how much you are making. The key is to keeping it equal. In this drink it calls for 1 part tequila and ½ part triple sec. I usually pour about 1.5 ounces of tequila and .75 ounces of triple sec. FOR A SWEETER COCKTAIL: If you prefer a sweeter cocoktail you can make your cucumber margarita with equal parts tequila and triple sec and also sub ginger beer or Sprite for the lime soda water.