Combine blueberries, confectioners' sugar, and water in a small saucepan over medium high heat.
Let the mixture come to a boil and then lower the heat and let it simmer for about 10 minutes, stirring from time to time, until the mixture thickens up and the blueberries start to burst. Remove blueberry syrup to a bowl and let cool.
Once cooled, brush a little blueberry syrup on the rims of your glasses. Crush one of the graham crackers and place on a plate. Roll the rims of the glasses into the crushed graham cracker.
Put blueberry mixture, along with 3 cups of ice cream and remaining four graham crackers in a blender and blend until well-combined. Pour into prepared glasses.