What is Mental Math?

What is Mental Math?

Mental math, often referred to as mental arithmetic, is the ability to perform calculations in one's mind without the aid of tools such as calculators, pencil, paper, or other devices. It encompasses a wide range of mathematical operations including addition, subtraction, multiplication, and division, among others. Mental math is not only a fascinating skill to develop for academic purposes but also a practical one for everyday life, enhancing one's ability to quickly solve problems and make decisions based on numerical information.

Definition and Importance

Mental math is defined as the process of performing mathematical calculations using only the human brain, with no help from any supplies or devices. This skill is crucial for developing a strong number sense, which is the intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations. A well-developed number sense enables individuals to think flexibly and critically about numbers, making mental math a foundational skill not just for academic success in mathematics, but for practical problem-solving in daily life.

Techniques and Strategies

Several techniques and strategies can be employed to improve mental math skills. These include:

  • Breaking Down Complex Calculations: Simplifying calculations by breaking them down into smaller, more manageable parts.
  • Using Number Patterns: Recognizing and applying patterns in numbers to solve problems more efficiently.
  • Estimation: Developing the ability to quickly estimate the answers to calculations, which is particularly useful for checking the reasonableness of answers.
  • Memorization of Basic Facts: Memorizing basic addition, subtraction, multiplication, and division facts to speed up calculations.
  • Visualization: Using mental imagery to represent numbers and operations, aiding in the manipulation of numbers in one's mind

Short History

The history of mental math is as old as mathematics itself, with evidence of its practice dating back to ancient civilizations. However, formal competitions and systematic methods for mental calculation have developed more recently. The Mental Calculations World Championship, for example, began in 1997 and includes a range of tasks such as addition, multiplication, and calculation of square roots. The Trachtenberg system, developed by Jakow Trachtenberg while he was a prisoner during World War II, is a well-known method designed to speed up basic arithmetic operations.

Applications in Education and Daily Life

In educational settings, mental math skills are developed from an early age, with specific strategies taught to plan how to solve problems mentally. For instance, children learn to add by putting the largest number first and then counting up by the smaller number. These skills are not only tested in academic assessments like the SATs but are also invaluable for everyday tasks such as making payments, telling time, and cooking.


Mental math is a critical skill that enhances number sense, promotes quick thinking, and aids in everyday problem-solving. By employing various techniques and strategies, individuals can improve their mental math abilities, making calculations faster and more accurate. Whether for academic purposes or practical applications in daily life, the ability to perform mental calculations is a valuable asset.