After students have mastered the principle of division through visualization by dividing small numbers, they may be ready for larger number division, but the idea of hundreds or even thousands may be incomprehensible to them. Consider that they have been able to visualize and understand division of very small numbers, such as one dozen cookies among three friends or six apples that have fallen from two trees. It can then be a bit overwhelming to have to visualize the number of people a bakery of cookies will serve, if they each get three cookies or how many apples fall from each tree in an orchard if there are 432 apples. By taking out the hundreds, tens and ones, the student can get a more accurate estimation and understanding of the answer to the division equation.
Learning division in the traditional manner involves more memorization of procedure than the expanded method. For example, to divide 432 by 3, traditionally the equation would be solved by dividing 3 into 4 and then 3 into 13, and then 3 into 12, which may be a laborious process.
To be able to comprehend division of larger numbers, students must have an understanding of them first. Since visualization is one of the easier ways to assimilate knowledge, beads could be used to count out 432 pieces. Indicate that the number 4 is in the hundreds place; 3 is in the tens place and 2 is in the ones place. Follow this with an explanation that to make a necklace of the beads, 100 beads are required for each one. Since 4 is in the hundreds place, four necklaces can be made. Follow that by saying that bracelets can then be made with 10 beads. Three bracelets can be made. If a ring needs two beads, two rings can be made.
Over time, once the expanded method is assimilated, it can be employed to make quick division calculations and to make the process of estimation easier.