Apparatus and methods for making dental prostheses including a matrix housing that has a plurality of interconnected walls, one of which defines an aperture. The matrix housing houses a dental model of a set of teeth, a wax model of a clasp, and a matrix that defines a sprue. The aperture provides access to the sprue. The matrix housing may be used with a cartridge for containing thermoplastic resin and a resin discharging device. The discharging device includes a body defining a through hole, a cartridge mount attached to the body, a ratchet push rod inserted through the through hole and including a plurality of teeth, a trigger pivotably attached to the body, and a drive tooth connected to the trigger and the body. The drive tooth cooperates with the teeth of the push rod to control the pressure asserted by the push rod to the cartridge.