In the previous article in the series, I approached division by introducing how to break down the dividend into smaller pieces that could be calculated quickly and their results used in summation to find the correct answer. To extend the idea that larger numbers can be divided without using an algorithm and by relying on the relationship between division and multiplication I will present a division problem solution using a cluster of multiplication problems that are easily calculated.
For instance, in a traditional program the division of 782 by 43 is taught as a series of steps and procedures that are long, monotonous, and susceptible to
calculation errors. However, by using a series of multiplication problems this problem becomes easy and quick to calculate. First off, children will learn that, in this instance, 43 x some number will give them either 782 or something close to it. To get that number they need only to start with friendly multiplications. 43 x 10 is a good start because children can easily figure the answer is 430. Once they have that they know 43 x 5 is 215. They're almost there. We have 645 of the total 782. Children at this point can be taught to add groups of 43. If they add three more groups of 43 they will arrive at 129. 430 (10) + 215 (5) + 86 (2) + 43 (1) = 474. That would leave an answer of 18 R 8. It is as easy as baking a cake. The steps are below.
782 / 43 = 43 x ___ = 782
43 x 10 = 430
43 x 5 = 215
43 x 2 = 86
43 x 1 = 43
Answer: 18 R 8
Of course, solving division problems in this manner is not constructed by children overnight. There are several big ideas at work in solving problems this
way, and introducing children to these various strategies over time will help them internalize deeper number sense, which will lead to quicker and more efficient calculating in a manner that they may also find rewarding and fun. Why do children find Sudoku so fun and not algorithms? Do I need to tell you?