A chemical feeder includes a housing having a housing chamber, a sieve plate within the housing chamber, and a cartridge on an upper surface of the sieve plate. The cartridge includes a tubular member with a sidewall outer surface and a plurality of partitions extending from the sidewall outer surface to define a plurality of pockets, at least one of which contains a solid chemical material. The sieve plate includes a plurality of sieve plate inlet apertures, at least a portion of which are in fluid communication with at least one of the plurality of pockets. During operation, a feed liquid passes up through at least a portion of the sieve inlet plate apertures and into at least one pocket where it contacts a solid chemical material, so as to form a treated liquid that includes dissolved chemical material, at least a portion of which is removed through an outlet.