How to do Mental Addition in 5 seconds | NSMQ Manipulating Figures
Why Learn Mental Addition
In a day, we are pushed countless times to add numbers without a calculator. A high percentage of these moments are harmless situations where we could do with even an estimate, so the stress of having to do these tasks on a calculator is unbearable. Just by learning to do mental addition, we have save time without sacrificing accuracy. When it comes to exams (SAT, GRE, BECE, WASSCE, etc) and quiz competitions (NSMQ, Sharks, Olympiad, etc), your greatest advantage will be to calculate faster than a calculator.
Addition is one of the six (6) arithmetic operations you need to master if the goal is fast calculation. In fact, it is the most fundamental of them all. For the lesson's sake, the other operations are subtraction, multiplication, division, exponents (powers) and roots. Without the basics of addition, it becomes very difficult to manipulate figures.
Talking about Manipulating Figures, the superpower lies in the how fast you can produce the result after the given question. This means any second that goes by without the answer affects your calculation speed. It, frankly, does not matter what causes the delay, whether it is due to scribing (or "air" scribing), thinking or just blanking. Ideally, the fastest way can only be achieved through mental calculation because it completely eliminates the time-consuming physical steps that introduce delays in addition to the unavoidable cognitive processing.
Mental addition is the process of calculating the sum of two or more numbers purely “in your head”. That we already know. However, the most important thing I need you to remember throughout the lessons is our working definition of addition.
To add means to increase a number (augend) by a certain amount (another number, addend).
This insight will be very instrumental in our pursuit to do any addition within 5 seconds.
What We Want To Achieve
If we want to tell apart what works from what does not, then we need to define what success looks like in this journey. The two measures are simply Speed and Accuracy. We do not want to give a fast answer which is inaccurate and neither do we want to take too long to reach the correct answer when time is of essence.
Being fast opens more doors for you to earn points, but it is being accurate that actually earn the points. There may be trade-off sometimes, but that is a more reason why handling both feels like a superpower.
We know we have to get our correct answer (accuracy) within 5 seconds (speed) in order to say we can do mental addition.
Now, we can synthesize our lessons to gear towards achieving the feat.
What's Stopping Us
The school method of adding numbers is the biggest obstacle to mental addition. From childhood, we are trained to line up numbers, place each digit in its correct column, and solve from right to left. We begin with the ones, carry when necessary, then move to the tens, hundreds, and beyond. For written work, this method is excellent. It is accurate, organized, and easy to follow.
This written method depends on the page to keep track of the calculation. On paper, we can see the columns, write down carries/overflows, and look back whenever we need to. In our minds, none of those supports exist. We must remember every carry and every intermediate result while continuing with the next step.
It also makes the process slow. The school method is designed to prioritize accuracy, not speed (tremendous speed, in this case). We cannot confidently state the answer until every digit has been processed because each carry has the potential to change the next column. In other words, we must complete the entire calculation before we know the final answer. When we try to perform this same process mentally, the delay becomes even more noticeable. We slow down, double check ourselves, and carefully guard against forgetting a carry. We sacrifice speed for accuracy.
Left-to-Right Method
A more natural approach is to work from left to right, just as we naturally read and understand numbers. By starting with the largest place values, we can begin building our answer immediately instead of waiting until the end. This gives us an estimate of the final result from the very first step and allows the answer to grow naturally as we continue.
So why don't we all calculate this way?
The reason is hesitation. As soon as we begin from the left, a question enters our minds: What if there is a carry later? If the ones produce a carry, won't that change the tens? If the tens change, won't that affect the hundreds? To avoid making a mistake, many of us abandon the approach and return to familiar methods. In doing so, we exchange speed for the comfort of guaranteed accuracy.
Think about why we are so comfortable with single-digit addition. When we see a problem like 7 + 5, we do not wait until the end of a process before trusting ourselves. We immediately recognize the answer because the entire calculation is already in front of us. There is no need to hold a temporary result, no next step to worry about, and no fear that the answer will suddenly change.
The same confidence is what we are trying to achieve with large numbers.
The key to fast mental addition is not choosing between speed and accuracy. It is learning how to overcome the carry problem while still working from left to right. Once we can do that, we no longer have to wait until the end to know the answer. We gain the speed of natural thinking without giving up the accuracy we expect. That is what we explore in the various variations of addition problems to develop efficient mental addition.