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Over the years, I have developed independently a series of techniques to help children--adults as well--to do arithmetic with more confidence. After I started cataloguing my system of techniques toward the aim of producing a DVD series, I discovered that certain aspects of my teaching were similar to the methods taught in the Vedic system of mathematics. This system is based on the sutras of Sri Bharati Tirthaji Krishna (1884-1960) and such system is a beautifully catalogued compilation for showing how to do mathematics more naturally and efficiently. A sutra is a Hindu piece of writing meant to teach aphoristically, and such sutras were produced for the purpose of study, meditation, and indeed memorization. When I discovered the Vedic system and immersed myself into some of its sutras, I became quite amused at how pieces of certain discoveries, throughout history, can be made by independent parties.
Armed with the knowledge of the Vedic system as well as my own independently discovered methods, I am placed in a unique position to propagate these methods and to aid children in their efforts to become more efficient and more confident in doing mathematics. Although the arithmetic techniques are interrelated and often build upon one another, the best approach is to teach them in parts, allowing the children to absorb one aspect before moving on to the next. The beauty of these techniques is their simplicity of use and their ability to boost the confidence in students who have incorporated them into their learning repertoire. Toward this end, let's look at one technique, which I have named the "Nifty Five Square Technique." This method teaches students to take the numbers that end in five (called five numbers) and calculate the multiplication of each number by itself. When a number is multiplied by itself, such as 3 x 3, we say we are squaring 3 or squaring the number. Specifically, this method teaches students how to square each of the numbers 15, 25, 35,...,95.
The "Nifty Five Square Technique" takes each of the numbers and produces their square instantly. No calculator required. The method, with appropriate modifications, will work for all "five numbers," even numbers like 115 or 225. For the purposes of this article, however, I will confine myself to the set of five numbers from 15-95. This is a sufficient subset of five numbers for one to garner a particular appreciation of the beauty of this method. Now, let us begin with the method.
In order to calculate the product of 15 x 15, all one need do is take the digit 1, which is the "tens" digit and multiply that by one more than the "tens" digit. Thus 1 + 1 = 2, and 1 x 2 = 2. Then just attach 25 to the number 2 to get your product. Thus 15 x 15 = 225. For the other numbers we have the following:
25 x 25 = 625 (2 x 3 = 6)
35 x 35 = 1225 (3 x 4 = 12)
45 x 45 = 2025 (4 x 5 = 20)
55 x 55 = 3025 (5 x 6 = 30)
65 x 65 = 4225 (6 x 7 = 42)
75 x 75 = 5625 (7 x 8 = 56)
85 x 85 = 7225 ( 8 x 9 = 72)
95 x 95 = 9025 (9 x 10 = 90)
What could be easier than that! Start showing your kids this stuff and you will be amazed at how quickly they start to excel in mathematics. Their defeatist attitudes in mathematics will quickly change to more confident and self-assured ones. Children armed with these techniques will feel a sense of positivity toward the subject and no longer dread doing their basic arithmetic homework. With this shift in attitude, children become successful in a difficult subject, become more poised toward challenges, and ultimately become more effective problem solvers. Try it out.
About the author:
Joe is a prolific writer of self-help and educational material. Under the penname, JC Page, Joe authored the classic of mathematical ABC's Arithmetic Magic. Joe is also author of the charmingly pithy and popular ebook, Make a Good Impression Every Time: The Secret to Instant Popularity; the seminal collection of verse, Poems for the Mathematically Insecure. For more information, visit his website at www.mathbyjoe.com.
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