How are some individuals able to solve arithmetic problems faster than others? The truth is, no one is born with this ability. The reason why certain individuals are able to solve such problems with agility is not because they calculate faster, but rather because they use completely different methods and techniques to solve problems.
What is Speed Math?
How are some individuals able to solve arithmetic problems faster than others? The truth is, no one is born with this ability. The reason why certain individuals are able to solve such problems with agility is not because they calculate faster, but rather because they use completely different methods and techniques to solve problems. These unique Speed Math methods can easily be learnt.
Speed Math, refers to the ability to mentally solve basic arithmetic problems (involving addition, subtraction, multiplication, and division) with agility and accuracy, faster than an average person or even a calculator. Speed Math techniques aim to improve students’ ability and fluency in mathematics. With the right training, these techniques can easily be learnt by students at all skill levels. There are myriad different Speed Math techniques and methodologies, in this article we examine a few.
Speed Math Techniques
Perhaps some of the least well known, but most effective speed math techniques are non-traditional techniques. These techniques involve approaching mathematics problems from a unique and creative perspective, and in turn, simplify traditional mathematical thinking and processes. These techniques focus on reducing the number and difficulty of arithmetic operations, and in turn, allow for faster and more accurate mental calculation.
These methods are not constrained by extensive rules, but rather involve approaching problems from alternate perspectives. The advantage of non-traditional methods is that they encourage creativity and help students develop a more thorough understanding of fundamental mathematical concepts. More importantly, non-traditional techniques have been proven to improve students speed and accuracy in solving arithmetic problems within a short period of time, usually within a week.
After learning non-traditional techniques, students are often astonished by the simplicity of these methods and amazed by their ability to solve seemingly impossible questions within a short period of time. For instance, these techniques allow students to calculate two-by-two digit multiplication (i.e. 94 × 97) in less than 5 seconds.
- Step 1:
- How far is each number from 100?
- 94 is 6 away from 100, let’s write 6 underneath 94.
- 97 is 3 away from 100, let’s write 3 underneath 97.
- How far is each number from 100?
- Step 2 (1st part of the answer):
- Cross subtract: (94 – 3) = 91, (97 – 6) = 91, conducting this operation we will find that both numbers will be the same, in this case 91
- Step 3 (2nd part of the answer);
- Multiply: to find the second part of our answer, we multiply the 2 numbers we wrote down ourselves, 6 × 3 = 18
- Final answer: 9118
The Japanese and Chinese Abacus
The Abacus is one of the most well-known tools for Speed Math. There are two types of abacus – the Japanese abacus (Soroban) and Chinese abacus (Suanpan), both which assist in increasing the speed and accuracy of mental calculation.
The Abacus is an extraordinary tool, which allows for the visualization of arithmetic problems. On the Abacus, numbers represented as beads on a rod. Using an abacus to solve mathematics problems is often introduced to children at a young age. The ability to visualize the abacus when contemplation mathematic problems, is similar to having a calculator in your brain. Once familiar with using an abacus and its rules, students can be taught how to move beads and interpret answers visually, allowing for the swift mental calculation of multiple digits.
The downfall of arithmetic learning using an abacus, is that mastering its use, involves years of daily practice and discipline. However, in the long term using the abacus enhances one’s ability to mentally visualize mathematical problems, enhances concentration, increases memory power and in turn improves the speed and accuracy of mental calculation.
The Rules of Speed Math
In many Asian countries, certain rules are developed for mental calculation. There are different rules for addition, subtraction, multiplication, and division. However, often such rules apply only to very specific situations.
For example, to solve 2-digit by 2-digit multiplication, in the case that the two digit numbers end in the same digit and the first digit of each number adds to 10, the following technique is used:
- Multiply the first digit of the first number by the first digit of the second number and add the common last digit
- Next, multiply the last digit of the first number by the last digit of the second number, move this number to the units place and add a zero in front, if it is a single digit.
- Combine the resultant numbers from the first two steps to obtain the final answer.
So, 23 × 83 =
- 2 × 8 + 3 = 19
- 3 × 3 = 9 (leave 2-digit space, it becomes 09)
- Ans: 1909
Such rules and techniques are often created by observing common patterns in calculations and involve significant memorization. For this reason, without regular practice, these methods can easily be forgotten.
Each of the speed math techniques we have discussed, have both pros and cons. Personally, I prefer non-traditional techniques, as I find this innovative and creative approach to mental arithmetic to be an exciting and engaging learning experience. Each time I apply these techniques, I am always amazed by the speed and accuracy with which I am able to solve seemingly impossible problems.
Now that we have a deeper understanding of what speed math is, in our next article we will examine the key benefits of learning speed math.
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Esther Cheung is Co-founder of 3C Learning and the author of numerous online educational programs for gifted elementary students. Passionate about empowering gifted children and growing their unique learning abilities, Esther is dedicated to creating educational resources to develop skills that are not addressed by the conventional school syllabus. Revolutionising gifted education, Esther developed 3C learning to support and empower gifted students to reach their academic potential. Join her Facebook Group for gifted education tips, techniques, ideas, and resources.