Joe Pagano

Teach Your Kids Arithmetic - Multiplication Shortcuts - Part I



Posted: Sunday, May 08, 2011

by Joe Pagano
Math by Joe

When Gauss said that mathematics was the queen of sciences and arithmetic the queen of mathematics, he was not lying. Without arithmetic, there could be no mathematics; for the essence of this most challenging discipline lies in the ability to manipulate numbers and figures. Multiplication, division, addition, and subtraction form the core of arithmetic operations. In this article, we will examine some niceties regarding the first of these four operations.

If you have read and followed my "Teach Your Kids Arithmetic" article series, you learned how important the basic arithmetic operations are. An inability to reckon with numbers certainly will pave the way for a rude "a-wreckoning." Of the four operations, multiplication stands as a very powerful one because of its ability to catapult us into the stratosphere, "number-wise." Known as "repeated addition," multiplication permits us to add the same number to itself many times. Thus 36x14 is really the addition of 14 to itself 36 times. In this example, multiplication gives us a shortcut to the answer, which is 504.

There is a way to do the previous multiplication lightning fast in your head without a calculator and without pencil and paper, or the old-fashioned way. However, before one learns to do these lightning fast multiplications, one needs to know the Fundamental Multiplication Table . This table allows us to figure any multiplication of the numbers between 1 and 9. This basic table can be a real bugbear for elementary students. Many adults enter the world without knowing their basic multiplication facts, as dictated by this table. For this reason, illiteracy, number-wise, also known as innumeracy, is prevalent in our society.

Mastering the multiplication table is probably one of the most important educational necessities. Just this ability will give your child a huge advantage in school and in life. So how do you get your kid to accomplish this most important objective? One of the ways to master multiplication is through mastery of addition. In my various writings, I have taken students on a journey through the four pillars of arithmetic. The first pillar is addition. Through mastery of addition and the learning of key addition shortcuts, students become better prepared to tackle multiplication.

Let's look at a specific example to make this point clear. If students wish to master the "six-times" table, then they can do this by using repeated addition techniques. For example, 1x6 = 6 is obvious from the identity property of 1; 2x6 = 12 comes from 6 + 6, and this is learned from a "quick-add." (See my article on "quick-adds")Teach Your Kids Arithmetic: The Quick-Add - Part I. Once this is learned, 3x6 becomes 2x6 + 1x6; 4x6 becomes 2x6 doubled. This is carried all the way through to 9x6, and thus mastery of the six-times table is achieved through addition techniques. All the times tables can be mastered this way, and once this is done, the multiplication table is history.

Moreover, by looking at the interrelationship of addition and multiplication, students start to make important connections between different arithmetic operations and thus start to see new insights into mathematics in general. Once this hurdle is cleared, a student quickly becomes adept in mathematical studies.

Do yourself a favor. Try out these methods and read and study some of my articles mentioned here. If you give your kids these tools, you probably will not have to worry about their performance in mathematics again. This certainly is a better alternative than the most unpleasant one of seeing your kids struggle miserably in math.
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