To read over a column of the results of each number is to learn them by heart, and it impresses upon the child's memory the series of multiples of each number from 1 to 100.
With these tables a child can perform many interesting exercises. He has sheets of long narrow paper. On the left are written the series of numbers from 1 to 50 and from 51 to 100. He compares the numbers on these sheets with the same numbers in the tables, series by series, and writes down the different factors which he thus finds; for example, 6 = 2 × 3; 8 = 2 × 4; 10 = 2 × 5. Then finding the same number in the second column and the other columns his result will read, 6 = 2 × 3 = 3 × 2; 18 = 2 × 9 = 3 × 6 = 6 × 3 = 9 × 2.
In this comparison the child will find that some numbers cannot be resolved into factors and their line is blank. By this means he gets his first intuition of prime numbers (Tables C and D).
When the child has filled in this work from 1 to 50 and from 51 to 100 and has reduced the numbers to factors and prime numbers he may pass on to some exercises with the beads.
The children now meditate, using the material, on the results that they have obtained by comparing these tables. Let us consider, for example, 6 = 2 × 3 = 3 × 2. The child takes six beads, and first makes two groups of three beads and then three groups of two.
And so on for each number he chooses. For example:
