Segmented coffee cartridge

This coffee cartridge would be three times the size of the kind that fit into well-known cup-at-a-time coffee makers, but it would contain twice as much coffee. The difference is, this cartridge would contain sixteen separate partitions. Used in the linked cup size coffee maker, it would limit coffee brewing to one tablespoon at a time. (optional: twice the size again for two cup's worth)

The cup sized coffee maker would puncture one partition every time the reservoir were dry and push hot water through that partition only. In this way each tablespoon of coffee would be hot and fresh-tasting.