Form F-404 is primarily used for as an essential practice sheet of paper to carry out long division problems with two or three digits at the divisor. This form has the color-coded columns to the units of millions on the right side of the paper, while on the left the same columns are blank, leaving space for the student to work out a long division problem with the pencil. The student may still be working with the distributing method of division by using the Montessori Long Division Test Tubes and Hierarchic Bead Boards. However, it is precisely at this point when proficiency with the Montessori materials is achieved that the students is fully prepared to use the color-coded paper to make the transition to the more efficient and less laborious method of group division, which is essentially the achievement of abstraction.

In distributing division students have to literally and concretely distribute quantities (the dividend) to a receiving number (the divisor). Group division, on the other hand, teaches students that the divisor is the size of each group that the student must create. Therefore, the students learn that the key question for getting an answer is how many equal groups can be made with the dividend. This is an ingenious bridge that leads students to treat division as the inverse of multiplication. In other words, if the dividend is 20 and the divisor is 4, the question to ask is: how many groups of 4 can I make with 20? If the student has mastered the multiplication tables, group division is nothing more than relying on multiplication. The color-coded paper helps treat each quantity to be divided by group rather than by distribution.      

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