The famous Greek mathematician Pythagoras (you know the one with that theorem) said, “Numbers have a way of taking you by the hand and leading you down the path of reason.” What Pythagoras was getting at, I think, is that numbers–by their very nature–permit us to do things which enable an understanding of the very universe and its intricate laws. Numbers have their roots in arithmetic, and a mastery of this field, particularly the operations of addition, subtraction, multiplication, and–yes that monster operation of division–will certainly pave a smooth road down that path of reason.
For most children, the tedious task of memorizing their number facts evokes long-winded yawns and puts pain-riddled expressions on their cherubic faces. However, rote tasks such as these (see my article Mastering Arithmetic and Singapore – What’s the Connection?) are what insure that children have a chance to progress up the ladder in mathematics. Of the four arithmetic operations, division is the one that children find most uncomfortable as this is the one operation which produces “uneven” results in the form of remainders. Such remainders thrust children into the world of fractions, percents, and decimals (see my article on this topic) and we all know how painful those things called fractions can be.
Given the difficulties that division presents to children learning their arithmetic basics, it would be both expedient and practical to present an approach which would lead them down this path of reason. Of the myriad number tricks and math shortcuts that I have developed over the years, the method of division by ten-multiples is one I am quite fond of. Basically, this method hinges on understanding the basic multiplication facts. After all, mathematics is a building blocks discipline, and this method, by being dependent on having mastered multiplication, clearly shows this fact.
This method shows an effective way to divide a three digit number by a one digit number. Take the example 306/6. A ten-multiple of 6 is 60. What we are trying to do is see how many ten-multiples of 6 go into 306 without going over. To do this effectively, we need to know our 6-times table. We know that 6×5 = 30 and 6×6 = 36. The respective ten-multiples of 30 and 36 are 300 and 360. Since 300 is less than 306, we know that 306 divided by 6 is going to be “50-something.” After we divide out the 300, we are left with 6, which gives another 1 as part of the quotient. Thus 306/6 is 51.
Play with this method a little and teach it to your kids. The more exposure they have to arithmetic techniques, the more they will come to master mathematics. Who knows, they might even become whiz kids.