What is mental math and why is it important?
Mental math is a skill that can help you in many aspects of life, from school to work to everyday situations. But what exactly is mental math, and how can you improve it? In this article, we will explore the definition, benefits, techniques, and resources of mental math. By the end of this article, you will have a better understanding of what mental math is, why it matters, and how you can practice it.
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Mental math definition
Mental math is a group of skills that allow people to do math in their head without using pencil and paper or a calculator. Mental math involves using various strategies, such as memorizing facts, rounding numbers, estimating calculations, and visualizing problems, to solve math questions quickly and accurately. Mental math can be used for basic operations, such as addition, subtraction, multiplication, and division, as well as more complex operations, such as fractions, decimals, percentages, algebra, geometry, and more.
Mental math benefits
Enhances concentration and memory
Doing mental math requires strong memory skills. Math facts and other number concepts have to be retrieved from long-term memory. Our brains also use a skill called working memory to keep track of the steps needed to solve a particular math problem. By practicing mental math regularly, we can improve our memory capacity and recall. This can help us with other cognitive tasks, such as learning new information, following instructions, and staying focused. Mental math can also improve our emotional health by engaging the brains prefrontal cortex during mental exercises.
Stimulates interest and confidence in math
Mental math can make math more fun and accessible for students of all ages. By using mental strategies, students can explore different ways of thinking about numbers and operations. They can also discover patterns, relationships, and properties of numbers that may not be obvious when using written or calculator-based methods. Mental math can also boost students confidence in their math abilities by helping them overcome their fear or anxiety of math. By being able to perform calculations quickly and accurately in their heads, students can feel more prepared and competent in various situations that involve math.
Improves problem-solving and reasoning skills
Mental math can help students develop their problem-solving and reasoning skills. By doing mental calculations, students have to think critically and creatively about how to approach a problem. They have to use logic, analysis, synthesis, evaluation, and inference to find the best solution. Mental math can also enhance their reasoning skills by applying mental math to real-world situations. They can use mental math to make sense of data, compare quantities, measure distances, estimate costs, and more. Mental math can also help students develop their spatial reasoning skills by using visualization and mental imagery to solve geometric problems.
Mental math techniques
Basic operations
One of the most common uses of mental math is to perform basic operations, such as addition, subtraction, multiplication, and division. There are many techniques that can help you do these operations mentally, depending on the type and size of the numbers involved. Here are some examples of mental math techniques for basic operations:
Addition: To add two numbers mentally, you can use strategies such as breaking up numbers into smaller parts, adding from left to right, or using friendly numbers. For example, to add 37 and 46 mentally, you can break up 37 into 30 and 7, and 46 into 40 and 6. Then you can add 30 and 40 to get 70, and add 7 and 6 to get 13. Finally, you can add 70 and 13 to get 83. Alternatively, you can add from left to right by adding the tens first (30 + 40 = 70) and then the ones (7 + 6 = 13), and then adding the results (70 + 13 = 83). Another option is to use friendly numbers that are easy to add, such as multiples of 10 or 100. For example, you can round up 37 to 40 and round down 46 to 40. Then you can add 40 and 40 to get 80, and subtract the difference between the original numbers and the rounded numbers (3 + 6 = 9) from the result. So you get 80 - 9 = 71. Then you can add the difference between the rounded numbers and the result (83 - 71 = 12) to get the final answer: 71 + 12 = 83.
Subtraction: To subtract two numbers mentally, you can use strategies such as breaking up numbers into smaller parts, subtracting from left to right, or using friendly numbers. For example, to subtract 53 from 89 mentally, you can break up 53 into 50 and 3, and 89 into 80 and 9. Then you can subtract 50 from 80 to get 30, and subtract 3 from 9 to get 6. Finally, you can subtract 6 from 30 to get 24. Alternatively, you can subtract from left to right by subtracting the tens first (80 - 50 = 30) and then the ones (9 - 3 = 6), and then subtracting the results (30 - 6 = 24). Another option is to use friendly numbers that are easy to subtract, such as multiples of 10 or 100. For example, you can round up 53 to 60 and round down 89 to 80. Then you can subtract 60 from 80 to get 20, and add the difference between the original numbers and the rounded numbers (7 + 9 = 16) to the result. So you get 20 + 16 = 36. Then you can subtract the difference between the rounded numbers and the result (36 - 24 = 12) from the final answer: 36 - 12 = 24.
Multiplication: To multiply two numbers mentally, you can use strategies such as breaking up numbers into smaller parts, using distributive property, or using friendly numbers. For example, to multiply 30. Then you can multiply 40 and 30 to get 1200, and subtract the difference between the original numbers and the rounded numbers (5 x 4 = 20) from the result. So you get 1200 - 20 = 1180. Then you can add the difference between the rounded numbers and the result (840 - 1180 = -340) to get the final answer: 1180 + (-340) = 840.
Division: To divide two numbers mentally, you can use strategies such as breaking up numbers into smaller parts, using inverse operations, or using friendly numbers. For example, to divide 84 by 12 mentally, you can break up 84 into 60 and 24, and divide each part by 12. Then you can add the results to get the final answer: (60 / 12) + (24 / 12) = 5 + 2 = 7. Alternatively, you can use inverse operations to multiply both numbers by a common factor that makes one of them a multiple of 10 or 100. For example, you can multiply both numbers by 10 to get 840 and 120. Then you can divide 840 by 120 by moving the decimal point two places to the left: 840 / 120 = 8.4 / 1.2 = 8.4 / (12 / 10) = (8.4 x 10) / 12 = 84 / 12 = 7. Another option is to use friendly numbers that are easy to divide, such as multiples of 10 or powers of 2. For example, you can round down both numbers to the nearest multiple of 10: 84 becomes 80 and 12 becomes 10. Then you can divide 80 by 10 to get 8, and add the difference between the original numbers and the rounded numbers (4 / 2 = 2) to the result. So you get 8 + 2 = 10. Then you can subtract the difference between the rounded numbers and the result (7 - 10 = -3) from the final answer: 10 + (-3) = 7.
Mental math resources
Books
If you want to learn more about mental math and practice your skills, there are many books that can help you. Some of the most popular and recommended books on mental math are:
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Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks by Arthur Benjamin and Michael Shermer. This book teaches you how to do mental calculations faster than a calculator, as well as how to perform amazing math tricks that will impress your friends and family.
Mental Math: Tricks To Become A Human Calculator by Abhishek V R and Ofpad. This book teaches you how to master mental math using a simple and effective method called Vedic Math, which is based on ancient Indian mathematics.
Mental Math for Pilots: A Study Guide by Ronald D. McElroy. This book teaches you how to do mental math in aviation-related situations, such as flight planning, navigation, fuel management, weight and balance, and more.
Courses and programs
If you prefer to learn from an instructor or a curriculum, there are many courses and programs that offer mental math instruction and practice. Some of the most popular and recommended courses and programs on mental math are:
Mental Math Course by Udemy. This online course teaches you how to do mental math faster and easier using various techniques, such as Vedic Math, Trachtenberg System, Base Method, and more.
Mental Math Program by Kumon. This offline program teaches you how to do mental math using a step-by-step approach that builds your skills gradually from basic arithmetic to advanced algebra.
Mental Math Course by Coursera. This online course teaches you how to do mental math using a scientific approach that combines cognitive psychology, neuroscience, and education.
Apps and games
If you want to have fun while practicing your mental math skills, there are many apps and games that make mental math fun and engaging. Some of the most popular and recommended apps and games on mental math are:
Mental Math Challenge by Peaksel Games. This app challenges you to solve various mental math problems in a limited time, such as addition, subtraction, multiplication, division, fractions, percentages, and more.
Mental Math Cards by Peekaboo Studios LLC. This app helps you improve your mental math skills by using flashcards that show different math problems and solutions. You can customize the difficulty level, operation type, number range, and time limit according to your preference.
Mental Math Master by Florian Loitsch. This game tests your mental math skills by giving you different tasks that require quick thinking and calculation, such as counting coins, finding prime numbers, solving equations, and more. You can compete with other players online or offline.
Conclusion
Mental math is a valuable skill that can benefit you in many ways. It can enhance your concentration and memory, stimulate your interest and confidence in math, improve your problem-solving and reasoning skills, and help you with real-world situations that involve math. To improve your mental math skills, you can use various techniques for basic operations, rounding and estimating, number sense and patterns. You can also use various resources for learning and practicing mental math, such as books, courses, programs, apps, and games. We hope that this article has inspired you to try mental math and enjoy its benefits. Remember, mental math is not only a skill, but also an art and a sport. It can challenge your mind, enrich your knowledge, and entertain your spirit.
FAQs
Here are some frequently asked questions about mental math:
How can I improve my mental math speed and accuracy?
The best way to improve your mental math speed and accuracy is to practice regularly and consistently. You can use various resources, such as books, courses, programs, apps, and games, to practice different types of mental math problems. You can also challenge yourself by setting a time limit, increasing the difficulty level, or competing with others. The more you practice, the more you will develop your mental math skills and confidence.
What are some common mental math mistakes and how can I avoid them?
Some common mental math mistakes are: forgetting to carry or borrow digits, mixing up the order of operations, misreading or misinterpreting the problem, making calculation errors, and losing track of the steps. To avoid these mistakes, you can use various strategies, such as: checking your work, using estimation, writing down intermediate steps, repeating the problem aloud, and using mnemonics or memory aids.
Is mental math useful for standardized tests?
Yes, mental math can be very useful for standardized tests, such as SAT, ACT, GRE, GMAT, and more. Mental math can help you save time and energy by allowing you to solve problems quickly and accurately without using pencil and paper or a calculator. Mental math can also help you check your answers and avoid careless errors. However, mental math is not a substitute for knowing the concepts and formulas that are tested on these exams. You still need to study the content and strategies that are relevant for each test.
Is mental math different from arithmetic?
Yes, mental math is different from arithmetic. Arithmetic is a branch of mathematics that deals with the study of numbers and their properties, operations, and applications. Mental math is a group of skills that allow people to do arithmetic (and other types of math) in their head without using pencil and paper or a calculator. Mental math involves using various strategies, such as memorizing facts, rounding numbers, estimating calculations, and visualizing problems, to solve math questions quickly and accurately. Mental math can be used for arithmetic, as well as other types of math, such as fractions, decimals, percentages, algebra, geometry, and more.
Can mental math help with dyscalculia?
Dyscalculia is a learning disability that affects a person's ability to understand and perform math. People with dyscalculia may have difficulty with number sense, counting, memorizing facts, calculating, estimating, measuring, and more. Mental math can help people with dyscalculia by providing them with alternative ways of thinking about and doing math. Mental math can also help them improve their confidence and motivation in math by making it more enjoyable and rewarding. However, mental math is not a cure for dyscalculia. People with dyscalculia may still need professional support and intervention to overcome their challenges and achieve their goals.
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