An illuminated film-covered keyboard includes: a backlit keyboard module which includes a plurality of keys that are light-permeable, and at least one backlight source; a frame body disposed on the backlit keyboard module, the frame body including a key area, wherein the top surface of each of the plurality of keys is exposed at the key area; and a cover film disposed at the key area and on top of the top surface of each of the plurality of keys, wherein the cover film includes a light-permeable film, a base color layer, a light-shielding layer that is opaque, and a protection layer disposed on a side of the light-shielding layer opposing the base color layer, and wherein the portions of the light-shielding layer that respectively correspond to each of the plurality of keys are removed so as to form a plurality of light-transparent patterns.

An illuminated film-covered keyboard includes: a backlit keyboard module which includes a plurality of keys that are light-permeable, and at least one backlight source; a frame body disposed on the backlit keyboard module, the frame body including a key area, wherein the top surface of each of the plurality of keys is exposed at the key area; and a cover film disposed at the key area and on top of the top surface of each of the plurality of keys, wherein the cover film includes a light-permeable film, a base color layer, a light-shielding layer that is opaque, and a protection layer disposed on a side of the light-shielding layer opposing the base color layer, and wherein the portions of the light-shielding layer that respectively correspond to each of the plurality of keys are removed so as to form a plurality of light-transparent patterns.

Mathematical teaching apparatuses and methods of use are provided herein. In one embodiment a mathematical teaching apparatus includes a frame having a plurality of spaced apart rods, and an equal number of beads disposed on each of the plurality of spaced apart rods to create beaded rows. Each of the equal number of beads of the beaded rows is identical in size such that the beaded rows form a square when the beaded rows are disposed on a furthermost edge of the frame.

Mathematical teaching apparatuses and methods of use are provided herein. In one embodiment a mathematical teaching apparatus includes a frame having a plurality of spaced apart rods, and an equal number of beads disposed on each of the plurality of spaced apart rods to create beaded rows. Each of the equal number of beads of the beaded rows is identical in size such that the beaded rows form a square when the beaded rows are disposed on a furthermost edge of the frame.

An illuminated film-covered keyboard includes: a backlit keyboard module which includes a plurality of keys that are light-permeable, and at least one backlight source; a frame body disposed on the backlit keyboard module, the frame body including a key area, wherein the top surface of each of the plurality of keys is exposed at the key area; and a cover film disposed at the key area and on top of the top surface of each of the plurality of keys, wherein the cover film includes a light-permeable film, a base color layer, a light-shielding layer that is opaque, and a protection layer disposed on a side of the light-shielding layer opposing the base color layer, and wherein the portions of the light-shielding layer that respectively correspond to each of the plurality of keys are removed so as to form a plurality of light-transparent patterns.