Tricks To Help Improve Mental Math Ability

5 Tricks To Help Improve Your Students’ Mental Math Ability

As students progress in their academics, their ability to mentally calculate math sums and solve problems improves. From calculating simple addition and subtraction to remembering the square root of integers, mental math comprises of specific learning techniques that help students solve math problems quickly.

Research from The Department Of Education, UK shows that learning key math facts ‘by heart’ enables children to concentrate on the calculation which in turn helps them to develop calculation strategies. Using and applying these strategies to practical use helps them work out answers and remember more facts. (source: The National Strategies; Teaching Children To Calculate Mentally, 2010)

School curriculums often include topics that develop and strengthen students’ mental math calculations throughout the year. Apart from that, teachers also use efficient strategies to build students’ mental math skills and raise their awareness and understanding of the range of mental math methods that they can work on. This also helps in developing their confidence and fluency by practising math problems using these strategies.

To help students improve their mental math proficiency and progressively solve difficult math problems in less time, teachers can implement a range of suitable classroom resources and tricks.

Here are the 5 math tricks to help improve the mental math ability of your students:

 

1. Make It Easy

Students can sometimes find it challenging to multiply or add big denominations. A good strategy is to help them simplify the problem by temporarily shifting the values around. 

For example, if the problem is to calculate 791 + 540, it is easier to add 9 to 800 which becomes more manageable to calculate. Now calculate 800 + 540 which is 1340, and take away the additional 9 to get the correct answer 1331. 

You can teach students to apply this strategy with multiplication also. For example, if the problem is to calculate 59 x 7, calculate 60 x 7 instead, and then subtract that additional 7, so 420-7 = 413

Calculating with multiples of 10 becomes much easier for students, so always remind them to round off numbers during calculations.

 

2. Subtract By Adding

This is a very important principle, based on the connection between addition and subtraction. Once this strategy is understood properly, students don’t need to memorise subtraction facts.

For example, if the problem is to find the difference between 14 and 8, instead of subtracting, think “8 plus what makes 14?”  In other words, think of the missing number that has to be added; 8 + ___ = 14. The answer to that is also the answer to 14 − 8.

This principle comes in especially handy with subtractions such as 13 − 7, 17 − 8, 16 − 9, and other basic subtraction facts where the minuend is between 10 and 20. But you can also use it in multitudes of other situations. For example, 72 − 55 is easier to solve by thinking of addition: 55 + 17  makes 72, so the answer to 72 − 55 is 17.

 

3. Tough Multiplications Made Simple

Multiplying large numbers can be challenging for students. So, the most logical thing to teach is how to simplify the numbers and then multiply them. Some cool multiplication tips have been given below that your students can follow:

• The easiest multiplication trick to remember is when multiplying any number by 10 just add a zero to the end of the number. For example, 62 x 10 = 620.
• If one of the numbers is even, you can divide the first number in half, and then double the second number. For example, 20 x 120 can also be solved by dividing 20 by 2 which is 10 and doubling 120 which is 240. Then multiply the two answers; the answer is 10 x 240 = 2400.
• There is also an easy trick to multiply any two-digit number by 11. All you need to do is add the two digits of the multiplicand and insert the answer in the center. For example, to multiply 35 by 11, add the numbers 3 and 5 which is 8 and add it in between the two-digit multiplicand; the answer is 385.

 

4. Division Tricks To Remember

To uncomplicate division problems for your students, you can give them a quick list of key facts they can remember to perform division easily. Here’s a quick way to know when a number can be evenly divided by these certain numbers:

•  A number can be divided by 10 if the number ends in 0
•  A number can be divided by 9 when the digits are added together and the total is evenly divisible by 9
•  A number can be divided by 8 if the last three digits are evenly divisible by 8 or are 000
•  A number can be divided by 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
•  A number can be divided by 5 if it ends in a 0 or 5
•  A number can be divided by 4 if it ends in 00 or a two-digit number that is evenly divisible by 4

 

5. Solving Percentage Problems

As students progress in class, topics like finding the percentage of a number become somewhat tricky but using the right math strategies and tricks can help them tackle these problems with ease.

For example, finding the percentage of 5 for any number can be done within seconds. Follow this method to find what is 5% of 235:

Step 1: Move the decimal point over by one place, 235 becomes 23.5
Step 2: Divide 23.5 by 2 and the answer is 11.75. That is also the answer to the original equation.

10 Tricks for faster calculations

10 tricks for doing fast math

Here are 10 fast math strategies students (and adults!) can use to do math in their heads. Once these strategies are mastered, students should be able to accurately and confidently solve math problems that they once feared solving.

1. Adding large numbers

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example:

644 + 238

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240.

Now, add 650 and 240 together. The total is 890. To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.

650 – 644 = 6 and 240 – 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

890 – 8 = 882

So the answer to 644 +238 is 882.

2. Subtracting from 1,000

Here’s a basic rule to subtract a large number from 1,000: Subtract every number except the last from 9 and subtract the final number from 10

For example:

1,000 – 556

Step 1: Subtract 5 from 9 = 4

Step 2: Subtract 5 from 9 = 4

Step 3: Subtract 6 from 10 = 4

The answer is 444.

3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

• Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
• Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

5 x 4 = 20

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

• Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
• Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

5 x 3 = 15

4. Division tricks

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

• 10 if the number ends in 0
• 9 when the digits are added together and the total is evenly divisible by 9
• 8 if the last three digits are evenly divisible by 8 or are 000
• 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
• 5 if it ends in a 0 or 5
• 4 if it ends in 00 or a two digit number that is evenly divisible by 4
• 3 when the digits are added together and the result is evenly divisible by the number 3
• 2 if it ends in 0, 2, 4, 6, or 8

5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let’s use the example of 9 x 3.

Step 1: Subtract 1 from the number that is being multiplied by 9.

3 – 1 = 2

The number 2 is the first number in the answer to the equation.

Step 2: Subtract that number from the number 9.

9 – 2 = 7

The number 7 is the second number in the answer to the equation.

So, 9 x 3 = 27

6. 10 and 11 times tricks

The trick to multiplying any number by 10 is to add a zero to the end of the number. For example, 62 x 10 = 620.

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

11 x 25

Take the original two-digit number and put a space between the digits. In this example, that number is 25.

2_5

Now add those two numbers together and put the result in the center:

2_(2 + 5)_5

2_7_5

The answer to 11 x 25 is 275.

If the numbers in the center add up to a number with two digits, insert the second number and add 1 to the first one. Here is an example for the equation 11 x 88

8_(8 +8)_8

(8 + 1)_6_8

9_6_8

There is the answer to 11 x 88: 968

7. Percentage

Finding a percentage of a number can be somewhat tricky, but thinking about it in the right terms makes it much easier to understand. For instance, to find out what 5% of 235 is, follow this method:

• Step 1: Move the decimal point over by one place, 235 becomes 23.5.
• Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

8. Quickly square a two-digit number that ends in 5

Let’s use the number 35 as an example.

• Step 1: Multiply the first digit by itself plus 1.
• Step 2: Put a 25 at the end.

35 squared = [3 x (3 + 1)] & 25

[3 x (3 + 1)] = 12

12 & 25 = 1225

35 squared = 1225

9. Tough multiplication

When multiplying large numbers, if one of the numbers is even, divide the first number in half, and then double the second number. This method will solve the problem quickly. For instance, consider

20 x 120

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

10 x 240 = 2400

The answer to 20 x 120 is 2,400.

10. Multiplying numbers that end in zero

Multiplying numbers that end in zero is actually quite simple. It involves multiplying the other numbers together and then adding the zeros at the end. For instance, consider:

200 x 400

Step 1: Multiply the 2 times the 4

2 x 4 = 8

Step 2: Put all four of the zeros after the 8

80,000

200 x 400= 80,000

Practicing these fast math tricks can help both students and teachers improve their math skills and become secure in their knowledge of mathematics—and unafraid to work with numbers in the future.