Wash berries; remove green caps. Place about half the berries in a Dutch oven. Use a slotted spoon or potato masher to crush berries; add remaining berries and crush again.
Add water. Bring to boiling; reduce heat. Cook, uncovered, over low heat for 5 minutes, stirring occasionally.
Line a strainer or colander with a double layer of 100-percent-cotton cheesecloth; set over a bowl. Pour berry mixture into strainer. Press to drain all juice. Discard strawberry mixture. Measure 6 cups juice.
In a 3- or 4-quart saucepan or Dutch oven heat the juice to rolling boil; stir in the sugar. Continue boiling until mixture is slightly thickened, about 30 minutes, stirring occasionally to prevent sticking.
Pour syrup into hot, sterilized half-pint jars, leaving 1/4-inch headspace. Wipe jar rims and adjust lids. Process in boiling-water canner for 5 minutes. Remove jars from canner; cool on racks.