Important Mental Math Examples, Strategies, And Activities

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If you find math intimidating, and figuring out the square of 23 or solving the multiplications like 152 x 16 in your head makes you lose your sanity, then you may be someone who thinks mental math is a forte that is difficult to perfect. Luckily, you can hone mental math skills with a few tricks, strategies, and activities.

Are you looking to master solving problems effortlessly? Although this may be a slow process, you can improve your ability to solve arithmetic problems without external aid by constant practice along with engagement in activities and learning strategies.  Accordingly, we have listed a set of handpicked mental math-based activities, and strategies with examples that may aid your students to become mental math masters.

Mental Math – Why is it a chief skill?

The practice of doing calculations in one’s mind without the need of a calculator, paper, or any sort of gadget is known as Mental Math. It can be as simple as calculating the time, adding values to the bill, or even thinking about the number of runs needed in a cricket match so that the favorite team can win the game! Despite these daily life applications, here are some value additions of Mental math:

  1. Improves observation skills: When individuals try to calculate numbers in their minds, they form a relationship between two things or digits. This helps build an important observation skill where one carefully analyses and examines how numbers correlate and interact with each other. 
  2. Improves mental health: Calculating digits mentally stimulates the dorsolateral prefrontal cortex this is the part of the brain which has been linked to anxiety and depression. Therefore, when individuals indulge in mental math, they try to adapt to their circumstances, thereby coping with the emotional challenges. This keeps their mental health intact.
  3. Ameriolating Memory: Mental Math is all about a good memory. Having to remember how to calculate and keep certain formulas in mind for quick calculation plays a key role in this skill. For example, if an individual needs to take out an area of a house, they would have to just recall the formula to calculate the same in their mind. 
  4. Enhances Self-Confidence: When an individual calculates mentally and does not use any external device or gadget for the same, they grasp a sense of accomplishment, which makes them more confident about their capabilities.
  5. Sharpens the brain: Practicing mental math can boost the brain power in many ways, as the individual is putting it to the test and use. The left side of the brain takes care of mathematics, but the right side is all about imagination and creativity. But, doing mental math involves the right side avidly as individuals tend to look for creative solutions to answer more promptly. Thus, it involves the entire brain, thereby making it sharp. 

Mental Math – Can this skill be mastered?

If mental math is such an important skill, you might ask— can it be mastered? From the early years, children must be engaged in calculating without the help of paper and calculators so that they can acquire this skill early in life. There are numerous strategies out there for students. Mental math strategies and activities may require only a little while to think about and come up with, but they can be very helpful to break down a complex problem structure and solve it by focusing on one part at a time. Here are some ways students can benefit from using mental math tricks:

  • Math tricks make tables of multiples, squares, and cubes easy to remember and recall quickly when necessary.
  • When presented with difficult problems, students may find it harder to solve them, so a mental math strategy will help them persevere and get to the end of the problem.
  • Mental math will help students solve problems more efficiently, boosting their self-confidence and self-esteem.
  • Higher-level problems can be solved with much more ease as students will be equipped with the knowledge and skills to make basic calculations.

Science behind Mental Math

Depending on their knowledge level, some students will solve these problems more easily while others may find it harder. However, they can build efficient and time-saving strategies with the help of mental math tricks. They can raise their awareness and build better methods to solve problems.

Computational gems can break addition and subtraction challenges into smaller parts, may change numbers to nearest rounded numbers, and gradually develop abilities to compute larger figures. Kids with dyslexia and dyscalculia may not find math that easy, probably due to the lack of these techniques. 

According to research by Hevda Meiri,[1] the frontal lobe in the brain is crucial for making arithmetic calculations. Since disabilities like Dyscalculia are caused due to issues in the intraparietal sulcus and often in the frontal lobe, they may face certain challenges in their expedition with math. But preaching with appropriate skills before adolescence can ameliorate their math abilities. The NeuroScientific[2] model lets us comprehend that the development of numerical processing in the brain happens over the course of childhood and adolescence, thus preaching valuable tips at this age would work.  Evidently, effective strategies and activities will help every student learn hints and techniques of mental math to solve complex problems effortlessly. 

Activities & Strategies For Boosting Mental Math Skills

Despite several pedagogies, activities improve students’ learning experience profoundly. Among these, Mental math activities have a separate place since they aid students who struggle with a crucial subject- Maths. Here are some tailor-made activities and strategies to upscale your student’s mental math abilities:

1.  Number Search

In this activity, the teacher writes different numbers on the board like 27, 3, 64, 144, and so on. These numbers are the choices that students can choose to answer questions asked to them. Teachers may ask them questions that involve operations like multiplication or division or more complex calculations like factorization based on their level. 

For example, one student may be given  25 x 5 and another be asked to find the cube of 5, and yet another student may be asked to find half of 250, which will all be answered as 125. Students have to pick the correct answer from the board for the questions given to them. Therefore:  25 x 5 = 53 = 250 / 2  = 125

 2. Adding and Subtracting From Multiples of 10

You can use this activity for problems that students may find more taxing to solve in their heads. The process of computation starts with calculation with the multiples of ten and then adding/subtracting the required values to arrive at the answer. For instance, to add 999 to 82, students may choose to add 1000 to 82 and then subtract 1.

Therefore: 999 +82= 1000+(82-1)=1081

Similarly, You can also use this method to add and subtract the same question:

18 x 9= (18 x 10)- 18=162

3.  Finding Cubes of Numbers From 1 to 10

Do you find it hard to memorize cubes of different numbers from one to ten? Fortunately,  there is an easy way to remember these without having to use a rote learning method. You may notice that the last digit for the cubes of the numbers 1, 4, 5, 6, 9, and 10 are the same as the numbers themselves ( with 0 for 10), such as 1, 64, 125, 216, 729 and 1000 respectively. 

The other four digits, namely the pairs 2 and 8 and 3 and 7, have their last digits interchanged as in cube of 2 is 8 and cube of 8 is 512. Similarly, the cube of 3 is 27, and that of 7 is 343. 

 4. Sit and Stand Activity

The teacher may ask students to sit and stand based on the answers to the questions they are provided with. Adding this new layer involves them physically engaging with whatever they learn,  thus letting them learn effectively. 

Instructors may provide the students with a set of math problems and call out different answers after giving them time to solve those problems. If the answers are correct, the students may stand up, and if it is wrong, they may remain seated. This activity can help them increase their speed when calculating since they have to finish the computation before the teacher starts with the activity. 

 5. Math Facts

Write down any one number on the board each day. Assign students to develop different operations you can perform on the number or discuss other methods to arrive at that number. Also, ask them to find out if it is a prime or composite number and discuss different properties of the number. You can give numbers that may appear anywhere in the number system, from whole numbers to fractions, decimals, and more. Let us consider the number 2. Students may write down facts like two is the only even prime number and perform operations on the number such as division by two (half of a number) or squares and square roots of two being 4 and 1.414, respectively.

6.  Multiplying by 11

We can all multiply with ten very quickly, right? Well, how about 11? If you feel stuck here, learning this trick will make this process very simple to do in one’s mind. Let us take the number 53, to demonstrate. To multiply 53 with 11, we must first add the two digits in the number as 5+3, equal 8. Simply add this number between the other two digits to get your required answer, 583.

Now you may be wondering what happens if you get a two-digit number when you add the digits of the number you initially received. In that case, follow this procedure:

Let us take 39 and multiply it with 11 using this method. First, add 3+9=12. Now add the first digits of both the numbers as in 3 from 39 and 1 from 12, which gives 3+1=4. Now take the answer 4 and put it in the hundredth’s place, fill the tenth’s place with 2 from 12 and the one’s place with 9 from the original number 39. Your required answer will be 429.

7.  Finding Cube Roots

There is a simple method to calculate cube roots in your head. For this, you will have to have memorized the cubes of numbers from 1 to 10. Let us take the number 91,125 as an example and find its cube root using mental math. Let us take the last digit of the given number which, is 5, and put it aside.  Now we ignore the last three digits in the numbers 5, 2, and 1. Next, we find the closest cube without exceeding the remaining number of 91. In this case, the nearest cube is 64 without going over, giving us the number 4 as the cube root. So our required number will be 45. So the next time you want to find the exact cube root of a number, you don’t have to pull out a paper and pen.

  8. Calculate Percentages 

Using this strategy, students will be able to calculate percentages without resorting to any calculating device effortlessly.

For instance: To calculate percentages like 10%, you will need to move the decimal point over to the left, like 10% of 36 will be 3.6. If you want to calculate say 35% of a value, you can calculate the 10% of it and multiply it by three, then add half of the 10% value to it. For example, to find 35% of the number 12, we must first find the 10%, which is 1.2. Now multiply it with 3 to get 3.6. Add half of 1.2 which is 0.6, to get the required solution, which is 4.2. 

9. Word Problems

One sure way to engage your class into learning to solve math problems quickly in their mind is by breaking them down into manageable pieces. Making math fun is essential to help students not lose focus and study whole-heartedly. If your class, in general,  is into soccer or is interested in movies or games, it is necessary to make the word problems you present to them relevant to topics of their interest. Keeping things interesting can help them persevere through failures and gradually improve their mental math skills with constant practice and support. This method will help us motivate students with tailor-made questions.

10. Squaring Digits Ending in 5

To square digits that end with the number 5 like 15, 25, or 75, you can use this simple strategy that helps you solve the problem that would otherwise take a while to do in a matter of seconds.

Multiply the first digit with the number that comes after it that is 7 x 8 in the case of 75. The answer you will get is 56. Now all you will need to do is add 25 at the end of this number to get the required square of 75, 5625. This method will come in handy when you need to quickly find the square of a number ending with the digit 5.

Some other examples are:

Square of 105 that can be solved as (10 x 11) is 110, and add 25 to the end to get 11025.

Square of 125 can be found as (12 x 13), which gives 156 and 25 at the end to result in 15625.

Conclusion

Easy techniques and hints sometimes make computation effortless. These not only come in handy but also often save a lot of crucial time. We hope the above-handpicked activities and tricks will be insightful and assist your math learner in mastering mental math skills. Even if it may take a while, constant practice will ensure a better developmental outcome.[3]  The expedition can be engrossing with some activities and tricks to give them an upper hand. Evidently, these not only aid academics but also in daily routine computations too.

References

[1] Frontal lobe role in simple arithmetic calculations: an fNIR study: Hedva Meiri (2012, February 21)

[2] The Diagnosis and Management of Dyscalculia: Kaufmann L. (2012, November)

[3] Constant practice of Maths eliminates phobia – Prof. Opoku – Amankwa

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