This shows the first bead frame which the child uses in his study of arithmetic. The number formed at the left on the frame is 1,111.
When the child fully understands this process he makes up many exercises of his own accord and with the greatest interest. He moves beads to the left at random, on one or on all of the wires, then interprets and writes the number on the sheets of paper purposely prepared for this. When he has comprehended the position of the figures and performed operations with numbers of several figures he has mastered the process. The child need only be left to his auto-exercises here in order to attain perfection.
Very soon he will ask to go beyond the thousands. For this there is another frame, with seven wires representing respectively units, tens, and hundreds; units, tens and hundreds of the thousands; and a million.
This frame is the same size as the other one but in this the shorter side is used as the base and there are seven wires instead of four. The right-hand side is marked by three different colors according to the groups of wires. The units, tens, and hundreds wires are separated from the three thousands wires by a brass tack, and these in turn are separated in the same manner from the million wire.
The transition from one frame to the other furnishes much interest but no difficulty. Children will need very few explanations and will try by themselves to understand as much as possible. The large numbers are the most interesting to them, therefore the easiest. Soon their copybooks are full of the most marvelous numbers; they have now become dealers in millions.
For this frame also there is specially prepared paper. On the right-hand side the child writes the numbers corresponding to the frame, counting from one to a million: 1, 2, 3, 4, 5, 6, 7, 8, 9; 10, 20, 30, 40, 50, 60, 70, 80, 90; 100, 200, 300, 400, 500, 600, 700, 800, 900; 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000; 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000; 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000; 1,000,000.
After this the child, moving the beads to the left on one or more of the wires, tries to read and then to write on the left half of the paper the numbers resulting from these haphazard experiments. For example, on the counting-frame he may have the number 6,206,818, and on the paper the numbers 1,111,111; 8,640,850; 1,500,000; 3,780,000; 5,840,714; 720,000; 500,000; 430,000; 35,840; 80,724; 15,229; 1,240.
When we come to add and subtract numbers of several figures and to write the results in column, the facility resulting from this preparation is something astonishing.
FOOTNOTES:
[6] At the present time, because of the difficulty of getting beads of certain colors, owing to war conditions, the following colors have been approved by Dr. Montessori to replace those originally used: 10 bead bar, gold; 9, dark blue; 8, white; 7, light green; 6, light blue; 5, yellow; 4, pink; 3, green; 2, yellow-green; 1, gold. These same colors are retained for the bead squares and the bead cubes. They will be supplied by The House of Childhood, 16 Horatio Street, New York.