21 New Math Teaching Methods [Updated 2021]| MentalMathWorksheets

new math techniques
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Are you wondering about how can you improve your child’s math skills? Do you want to familiarize yourself with new math teaching methods and techniques used today? Do you want to help your child become successful in math? Then, you have come to the right place, you can depend on us to help you out.

Math has always been evolving and today math is no longer the same as it was when today’s parents today were in school. Many parents have come across strange and unfamiliar techniques for solving math problems in their children’s textbooks. This often leaves them confused and wondering about how to help the child with math. There has been a great shift in how math is taught today from a decade ago. Math today relies more on intuition and reasoning, rather than just memorizing facts or countless formulas. Students are encouraged to use different approaches to solve math problems and understand relationships rather than following one traditional method. 

With advancements in the education field, many new math methods have been adopted BY schools to encourage math learning in children. Children often get discouraged with complex math problems. But, with these new math techniques, the complex problems can easily be broken down into simple arithmetic and solved with great ease. With this new math techniques, the kids begin to see and explore relationships between various numbers and processes. It improves number sense, critical thinking, and logical skills. It also reduces the time taken to solve math problems. These new techniques make use of ample visual aids, math tricks, and shortcuts that will change the way your kids look at the math. It also encourages mental math abilities and reduces the need for a calculator. With these methods, math no longer has to be a boring subject.

In this article, we have shortlisted 21 new math teaching methods that are used widely today. With these methods, you can help your kids gain a better understanding of math.

1. Ten-frame 

This new math method is perfect for teaching numerical math skills to kindergarten level children. It will also help the students understand how to compose or decompose numbers, and improve their number sense. The Ten-frame method is a wonderful way to reinforce fluency in counting and math facts up to 10. 

In this method, the students will simply draw 2 tables of 5 rows and 2 columns and put dots or objects inside the boxes for counting, addition, or subtraction. This method teaches kids how different combinations of numbers can be used to get 10. It also helps perform additions and subtractions up to 10 with ease. Later on, the children will be able to apply the same logic with complex numbers.

2. Number Bonds 

Number bonds are a great way to teach math to elementary level students and develop an understanding of basic math facts. It effectively shows the relationship between numbers like how numbers can join together to form a new number or how a number can be broken down into various smaller numbers. This new math technique improves number sense and is ideal for helping kids understand basic addition and subtraction.

Creating number bonds are super easy. Number bonds are just a circle connected by two lines to 2 adjoining circles. The whole number is written in the first circle, while the components are written in the adjoining two circles. 

For example: 

6 can be written in the first circle and 2 and 4 in the adjoining circles. This way the child can understand that 6 can be broken down into 2 and 4 or understand that 2+4 =6 and 4+2=6 or 6-4=2 or 6-2=4. You can also leave one circle blank so the students can fill the missing number by understanding the relationship between the two other numbers.

3. Base Ten

In Base Ten method, the students will make use of tables and divide it into place values: ones, tens, hundreds, thousands, and so on. The students will then place each number in the table according to their place value. This will help kids understand more about the place value of numbers. For example: The number 3254 is made up of 3 thousands, 2 hundreds, 5 tens and 4 ones). 

It is also a useful tool for performing arithmetic related to addition and subtraction. This new math teaching methods will help the students see clearly how the number is carried in addition and burrowed in subtraction. Moreover, it can be modified for older students. It can be used to denote decimal numbers by adding a column for decimal point followed by columns of tenths, hundredths, thousandths and so on.

4. Addition by Decomposing

Decomposing is a helpful method for solving math problems related to arithmetic. This new math addition method makes use of the expansion of numbers to simplify the arithmetic calculation. In the decomposing method, the first step is to break the number down into its digit values. By doing this, the student will make calculations much easier, simpler, and faster. It is also a helpful strategy for metal math calculation. Through this method, the student will also develop an understanding of number relationships.

For example: 

If the question asks to add 49 and 36, the student will first decompose the numbers individually as (49 is 40 and 9) and (36 is 30 and 6). 

The next step will be to add the digit values. The student will add the first component numbers from both numbers (40 + 30) which is 70. They will repeat with second decomposed numbers (9 + 6) which is 15. 

The total of both these numbers will give the answer (70 + 15) = 85, which is the correct answer for the question (49 + 36). 

5. Subtraction by Decomposing

The decomposing technique can also be effectively used for subtraction and is similar to addition. In the decomposing new math technique, the first step is to break the number down into its digit values. By doing this, the calculation will be much simpler and will also encourage mental calculation . 

For example: 

If the question asks to find the difference between 49 and 36, the student will first decompose the numbers individually (49 is 40 and 9) and (36 is 30 and 6). 

The next step will be to subtract the digit values. The student will subtract the first component numbers from both numbers (40 – 30) which is 10. They will then subtract the second component numbers (9 – 6) which is 3. 

The total of both these numbers will give the answer (10 + 3) = 13, which is the correct answer for (49 – 36). 

6. Addition by Rounding off

In this new math addition method, the student will need to analyze the number and round off the number to the nearest larger number, so the numbers are easier to work with. This method will also improve your child’s reasoning and make calculations easier.

For example: 

If the question asks for a sum of 494 and 97, the student will round off the first number 494 to the nearest larger number 500, which can be done by adding 6 to 494 (494 + 6 = 500). 500 is much easier to work with. 

The student must also subtract the same digit i.e. 6 from the second number (97 – 6 = 91). 

Now, the student will simply add the two numbers 500 and 91 together. So, the answer will be (500 + 91) = 591, which is the correct answer for (494 + 97). 

7. Subtraction by Rounding off

In this new math technique, the student will need to analyze the number and modify it to make it easier to work with. To achieve this, the larger numbers are rounded off to the nearest smaller number. This method will make subtraction a lot easier and the student can avoid the process of burrowing numbers. It also helps increase reasoning in math.

For example: 

If the question asks for the difference of 494 and 97. The student will round off 494 to 400. This can be done by subtracting 94 from 494 (494 -94= 400). 400 will be much easy to work with. 

The student must also subtract the same digit i.e. 94 from the second number (97 – 94 = 3). 

Now, the student will simply subtract the two numbers 400 and 3. So, the answer will be (400 – 3) = 397, which is the correct answer for (994 – 97). 

8. Subtraction for numbers with the power of 10

This is an easy method to subtract any number from a number with a power of 10 starting from 100 (100, 1,000, 10,000, 100,000, and so on). In this new math method, the student will just need to subtract the digits of the given number except for the last digit from 9. The last digit will be subtracted from 10. The final answer will be the difference written in sequential order. 

For example: 

If the question asks to subtract 1837 from 10,000, the student will subtract the first 3 digits from 9 and the last digit from 10. 

So for 1837, the first three digits is subtracted from 9 (9-1=8, 9-8=1 and 9-3=7) giving 817 and the last digit is subtracted from 10 (10-7=3). 

Now, the student will just put the numbers together as 8173, which is the correct answer for (10,000 – 1837)

9. Open Number Line 

Open number lines are a very versatile tool in math that can use used to solve a variety of math problems in many different ways. This new math teaching method is perfect for elementary grade students. An open number line has no number written on it and the student can use any number as the starting number depending on the math problem. 

It is a great way to demonstrate various math strategies the student is learning and allows them to add or subtract visually. The number line will also help improve a student’s understanding of place value, decomposition, and the relationship between numbers. It is also a helpful aid in breaking down and solving word problems.

10. Bar Diagram

This is another great visual aid to solve arithmetic word problems. It is based on Singapore’s new math method which has been found to be very effective as a math teaching tool. In this method, the students will draw bars to represent numbers and the length of the bar can be drawn proportional to the number. 

By organizing information visually, the student will simplify the math problem and will be able to solve it easily. This method will help the students gain an insight into number relationships, and understand known and unknown quantities. Bar diagrams can be used to solve addition, subtraction as well as multiplication problems.

11. Arrays & Area Model for simple multiplication

Using Area model & Arrays for multiplication is a way to perform basic multiplication in a visual way. In this new math teaching methods, the student will make use of a rectangular or square diagram to perform and show multiplication. The number of rows and columns in the table will be proportional to the numbers to be multiplied. 

For example: 

If a student has to show multiplication of 3 and 5, they can draw a rectangular diagram with 3 rows and 5 columns, which means 12 boxes. 

The student will then simply count the number of boxes to get the answer which is 12. 

It can also be a fun math activity for younger children. Instead of drawing tables, the student can also use arrays of objects in which they will arrange various objects into rows and columns to perform multiplication calculations.

12. Area Model for multiplication of large numbers

The Area model can be used as an important strategy for multiplying large numbers. It also helps students understand how addition is related to multiplication. In this new math technique for multiplication, numbers are first broken down into its digits values. 

For example: 

If the student has to multiply 23 and 44, the student will first decompose 23 and 44 individually like this (23 is 20 and 3) and (44 is 40 and 4). 

The student will then multiply each component of the first number by each component of the second number. In this case, it will be (20 x 40), (20 x 4), (3 x 40) and (3 x 4). 

After this step, the students will simply add up all the multiplication answers together to get the final answer (800 + 80 + 120 + 12) = 1012, which is the correct answer for (23 x 44). 

This method can be simplified and demonstrated visually by drawing an area model diagram which is a table with rows and columns proportional to the number of digits to be multiplied. The decomposed components are written beside the boxes, and the product of the numbers is written inside the boxes.

13. Multiplication using Lines and Intersections

This is a lesser-known and uncommon new math method of performing multiplication. However, it is highly effective and can be a great strategy to have up your sleeve. 

For example. 

If a student has to multiply 12 and 13, the student will take the first number 12 and draw two sets of vertical lines corresponding to the number. For 12, the left set will have 1 line and the right set will have 2 lines. 

The student will then take the second number 13 and draw 2 sets of horizontal lines across the vertical lines in the same way. For 13, the upper set will have 1 line and the bottom set will have 3 lines. 

By doing so, there will be 4 sets of intersection points. The student will then simply count the number of intersections in each set diagonally. In this case, it will be 1 intersection, (3+2 = 5 intersections) and 6 intersections. 

The student will just arrange the number sequentially as 156, which is the correct answer for 12 x 13.

14. Multiplying even numbers by 5

This math short-cut method works perfectly for any digit even number being multiplied by 5. In this method, you just need to know basic division. 

For example: 

If the question asks to multiply 5 and 12. The student just needs to half the number that is being multiplied by 5, and then add a zero at the end. 

In this case, the student will first half 12 (12 /2) which is 6, and then add zero to this. 

So, the answer is 60, which is the correct answer for (5 x 12)

15. Multiplying odd numbers by 5

This new math technique can be used for multiplying any digit odd number by 5. In this case, the student has to subtract 1 from the number that is being multiplied by 5 so that it becomes an even number. Then divide the even number by 2, and add 5 at the end. 

For example: 

If the question asks to multiply 5 and 45, the student will first subtract 1 from 45, so that it becomes an even number (45 -1) = 44. 

The student will then get half of 44 by dividing it by 2 which is 22 and then add 5 at the end. 

So the answer is 225, which is the correct answer for (5 x 45).

16. Multiplication for numbers with Power of 2

This new math teaching method is perfect for multiplying any number that can be broken down into the power of 2. This technique requires a thorough understanding of the 2 times table and exponents. Even if the student is not proficient, using this method will help them improve their knowledge of exponents. This method is a bit longer but it will help students develop a deeper understanding of number relationships. 

For example: 

If the question requires multiplication of 7 and 32, the student will first need to analyze the question and check if any of the numbers can be broken down into power of 2. In this case, 32 can be broken down into a power of 2. 

Then, they need to find the power of 2 for 32 (2,4, 8, 16, 32) which is 5.  So, 7 x 32 can also be written as 7 x 25. 

To get the answer the student will double the other number 7 for 5 times while reducing the power by 1 in each step as shown below.  

7 x 25

14 x 24

28 x 23

 56 x 22

112 x 2

The answer will be the last step (112 x 2) = 224, which is the correct answer for (7 x 32).

17. Multiplication by halving and doubling

This new math method is similar to the above method but it can be used for performing multiplication of any 2 digit numbers provided at least one of the numbers is an even number. In this method, the student will just half the even number and then double the other number. This process will be continued till the number cannot be halved any more or when the equation has been simplified. 

For example:

If the question is to multiply 21 by 12, the student will first take the even number 12 and will halve it to 6. The next step will be to double 21 to 42. 

The subsequent steps will be: 42 x 6 and 84 x 3. 

Now, in the last equation, 3 can no longer be halved to an even number. 

To get the answer, the student will simply solve the equation in the last step (84 x 3)= 252, which is the correct answer for (21 x 12)

18. Multiplying numbers with a pattern of 9

This new math method is excellent for multiplying any number by numbers following number patterns like 9, 99, 999, 9999 and so on. 

In this method, firstly the student will round up the numbers in the pattern (9, 99, 999, 9999 and so on) to the pattern (10, 100, 1,000, 10,000 and so on). After this, the student will multiply this rounded off number with the other number. Finally, they will just subtract the other number itself from the product between the other number and rounded off number to get the answer. 

For example: 

If the question is to multiply (58 x 99). The student will first round up 99 to 100. 

Then multiply 58 by 100, which is 5800. 

After this, the student will reduce the original number 58 from this number (5800-58) = 5,742, which is the correct answer for (58 x 99).

19. Multiplying 2 digit number by 11

Using this new math technique makes multiplying any 2 digit number by 11 super easy. It just makes use of simple addition. 

For example: 

If the question is to multiply (45 x 11). The student will write the number that is to be multiplied by 11 and put a blank space between them. In this case, it is 45, so 4_5. 

Then, the student just needs to add the two digits together (4+5=9) and put it in the blank space (495). 

So, the answer for (45 x 11) is 495. 

If the sum is greater than 9

In this case, the student will simply put 2nd digit in the space and add 1 to the number left of the space. 

For example: 

If the question is to multiply (11 x 87).  The student will write 87 as 8_7. 

But, the sum of 8 and 7 is 15. So, the student will write 5 in the space and add 1 to 8. 

So the answer is (8+1) 5 7 that is 957.

20. Finding Percentages

Calculating percentages can be tricky and often confusing for students. However, this simple new math teaching methods will make calculating percentages easy and fast. 

For example: 

If the question asks for 25% of 11. The student can simply multiply the numbers first (25 * 11) = 275, and then move the decimal point two digits to the left in the answer. So the answer is 2.75. This method is so easy.

21. Forming equations by identifying Key Words

Many students have trouble solving word math problems especially when the problems are complex in nature. Formulating a correct equation is the first step towards solving word problems but this is also the most difficult stage. 

The key to solving word problems quickly and efficiently is to break them down first and then observe the relationships between them. The student can start by looking for the main keywords that explain the problem. For example: Words like increase in, the total of, the sum of, more than, etc. will denote that there is addition (+) involved, or words like ratio, out of, per, etc. will denote that there is division (/) involved. 

Next, the students can focus on the question and find out what components the word problem already has and what components are missing, and what component they will need to find. Hence, by decomposing the word problems into smaller components and identifying the main keywords, the student will be able to understand the word problem easily and formulate a suitable equation to get the required answer.

Learn more about how to improve word problem-solving skills.

Math is important in everyday life and learning math is necessary. But, many children find math to be difficult and boring. This is also because children think they need to memorize one method or formula to solve the problem. However, this is not true at all. Math is more like an art and it is actually not necessary to use just one method of doing math. It is possible to reach the same solution and solve the problems using a multitude of methods. 

These new math teaching methods have been formulated to make learning math engaging for students. These methods not only improve your child’s mathematical knowledge but also promotes learning math and logical skills in children. These methods are also useful tools to have when it comes to difficult problems and can boost the student’s problem-solving abilities and confidence in math.

Approaching math this way is beneficial as sheds math in a new light. Your child will begin to really understand math as they observe the various relationships, patterns, and concepts of math. Math is a dynamic subject and it only makes sense that the methods you use to solve problems are also dynamic. These new methods will definitely spark up your child’s curiosity and interest in math. Moreover, these methods are great tools to make complex math problems easier, improve mental math abilities, and enhance abstract thinking.

With these helpful new math methods for teaching, your child will be solving complex problems like a pro in no time.

Help your child master math and have fun with math!

There are plenty of methods you can use to make math fun for your kids. We have a ton of resources on playful and engaging math activities for kids that are also great tools for learning math. Click on the links below to learn more.

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