Cut the 1/2 lime into 4 wedges.
De-stem and cut strawberries in half lengthwise
Place lime wedges and strawberries in a chilled martini shaker (or glass with cover)
Pour in simple syrup
Muddle lime, strawberries and syrup to blend
Add crushed ice until shaker is about half filled
Pour gin over ice.
Shake vigorously until well blended