A method for counting spatially arranged, moving markers, wherein the markers being arranged to move along a movement axis parallel to a sensors axis of sensors for detecting the markers during movement. The number of sensors is lower than the number of markers in order to decrease the cost of the sensors system. The present system supports stacks having objects, associated with the markers, of different sizes such as weight plates of increasing height) or different weights.

A method for counting spatially arranged, moving markers, wherein the markers being arranged to move along a movement axis parallel to a sensors axis of sensors for detecting the markers during movement. The number of sensors is lower than the number of markers in order to decrease the cost of the sensors system. The present system supports stacks having objects, associated with the markers, of different sizes such as weight plates of increasing height) or different weights.

Provided is an apparatus for teaching calculation skills. The apparatus may include a plurality of beads and a set of columns of the cells being configured to be occupied by one of the beads. The apparatus may include a set of sensors configured to determine occupation of the cells by the beads, and a processing unit electronically coupled to the set of sensors. The processing unit can be configured to: receive from a server at least one array of integer numbers. Each of the integer numbers represents an intermediate result of solving of a sequence of mathematical operations displayed to a user; determine, via the set of sensors, occupation of the cells by the beads; translate the occupation of cells to a check number; and compare the check number to a current number in array to determine whether the current operation is solved correctly.

A manually operable calculating device is provided. The device includes a plurality of rods vertically disposed relative to one another. At least ten rings are slidably disposed on each of the plurality of rods. The at least ten rings include a first set of five rings including a first color and a second set of five rings including a second color. The plurality of rods each include a front surface opposite a rear surface. A plurality of numerals are disposed on the front surface and correspond to the number of rings. The rear surface is unnumbered.

A method for counting spatially arranged, moving markers, the markers being arranged to move along a movement axis parallel to a sensors axis of sensors for detecting the markers during movement. The number of sensors is lower than the number of markers in order to decrease the cost of the sensors system. The present system supports stacks having objects, associated with the markers, of different sizes (such as weight plates of increasing height) or different weights.

A method for counting spatially arranged, moving markers, the markers being arranged to move along a movement axis parallel to a sensors axis of sensors for detecting the markers during movement. The number of sensors is lower than the number of markers in order to decrease the cost of the sensors system. The present system supports stacks having objects, associated with the markers, of different sizes (such as weight plates of increasing height) or different weights.