This material is used in the Montessori lower elementary classroom with children between 6-9 years of age).
With the Checkerboard and bead bars (representing numbers 1-9) the children learn long multiplication (2, 3, 4, or more digit numbers). In the problem in Photograph 1, a five digit number was multiplied by a two digit number. The multiplicand is on the bottom horizontal line (in Photograph 2, it is 3,212) and the multiplier is on the vertical line. The children multiply each digit of the multiplicand by each digit of the multiplier and place corresponding bead bars in the corresponding coloured square. Each coloured square represents one level of the hierarchy of numbers: units (green), tens (blue), hundreds (red), units of thousands (green), tens of thousands (blue), and hundreds (red) etc. and this goes up in this way to hundreds of millions. After multiplying each digit of the multiplicand by each digit of the multiplier, and placing the corresponding bead bars in their coloured squares, the children exchange the bead bars to have only one bead bar in each square on the bottom line of squares, representing the answer.
With repeated work using this material, the children come to understand (deeply) the concept of long multiplication and, with time, alongside the tactile work with the material, the children also learn to extract this long multiplication process onto paper, and eventually they work on long multiplication in the abstract, only on paper and without the checkerboard.
The number (the answer) that is on the board in Photograph 1 represents 1,979,191. In Photograph 2, it will end up being 40,756.