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## Teach Your Kids Arithmetic – The Quick-Add – Part I

In the continuity of my series on arithmetic, I present here a subject which was one of the cornerstones of my book “Arithmetic Magic”. To fully understand how this concept helps us in arithmetic operations, we must first pose some basic ideas. The “Quick-Add” is an extremely valuable tool to help children master quick arithmetic, especially when applied to the summation of numbers. Today, the calculator has paralyzed even the most able student. Hardly does one know his basic multiplication facts, as the ubiquitous calculator does this for him. This situation is understandable, and one comparison I can make relates to memorizing phone numbers. Since ubiquitous cell phones store numbers, I no longer memorize people’s numbers because I don’t need them. Similarly, students can no longer add or multiply because the calculator does it for them. It’s a problem for the following reasons: 1) not mastering arithmetic leads to math problems down the road; 2) not being able to add or multiply leads to frustration during basic homework; and 3) lack of doing = future lack of doing, which further increases the risk of mathematical illiteracy.

The Quick-Add method offers students a viable alternative for performing quick calculations without the aid of calculators or pencil and paper. This method is based on the idea of ”complements”. The word “complete” means “complete”, and that is exactly what these numbers do. A “10’s complement” completes the 10; a “100-Complement” completes the 100, and so on. The reason this idea is so useful is because it aligns with the inherent simplicity of the metric system, in which all units and measurements are based on the number 10 and its multiples. To begin to understand this idea, let me present the following scenario: if I were to say to a child, “What is 8 + 9?” or feverishly trying to count the sum. are quick with this stuff and, pretty quick, can find the answer of 17. However, I’m not focusing on those kids. The healthy don’t need a doctor. I’m focusing on struggling kids. with basic arithmetic operations and experience enormous frustration: which, when germinated, leads to negative attitudes towards mathematics and ultimately crystallizes in self-doubt, fear and dread of this most wonderful subject. consequences are truly dire because many of the students I have worked with realize – after curing them of their math ills – that they were actually good at math. problem solvers we would generally be if we had mathematics on our side rather than against us!

Let’s go back to the idea of complements. In the example 8 + 9, we see that the sum is 17. How quickly would a child find the answer 17, if I said “What is 10 + 7?” Now, the careful analysis of the difference between 8 + 9 and 10 + 7 reveals some very interesting things and shows how the circuitry in the brain capitalizes on some very important mathematical facts. Let’s examine them. It is true that 0 and 1 are two very special numbers, but for addition, 0 is the number whose special property applies here. The number 0 has the “additive identity property”. It simply means that 0 plus any other number gives the given number. It is 0 + 5 = 5; 0 + 4 = 4, etc. (From an addition perspective, I guess you could say 1 is special in that adding 1 to any number is pretty intuitive because we’re only incrementing the number unit one: so 8 + 1 = 9- -you got the idea.)

Now, the complements of a number are the numbers which, when added to the given number, give a sum of 10. For example, the 10’s complement of 8 is 2, since 8 + 2 = 10. 10 of 3 is 7, since 3 + 7 = 10. The way we relate the concept of complements to quick addition is as follows: parsing 10 + 7, we rewrite this example as 10 + 07. We insert a 0 in front of the 7 as a placeholder for the empty “tens column” and to bring the numbers into a parallel structure. Now let’s examine how the brain circuits work when doing 10 + 07. The brain executes 1 + 0 in the “tens column” and 0 + 7 in the “ones column”, thus capitalizing on the “additive identity property” of 0. This is in fact “obvious”. Therefore, our strategic tool for addition will be to convert addition problems into their associated “Quick-Adds”. Once done, this greatly simplifies additions.

Stay tuned, because in Part II I will go into much more detail about this whole procedure.

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