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Understanding Singapore Math

Posted by Thej Academy on 14th March 2019

Questioning Children is an Excellent Way to Develop their Thinking

Singapore math is a teaching method based on the National Mathematics Curriculum used from Kindergarten till sixth grade in Singapore. It is an interesting way of teaching math, in which even the struggling learners excel enough to progress to the next stage. In Singapore math system, students solve mathematical problems in an abstract way by using numbers and symbols. It intrigues the child’s way of thinking and questioning attitude, towards math.

The worthwhile benefit of practicing Singapore Math is that, the average learners would be able to perform in a better level. The advanced learners abilities are challenged.Singapore Math is beingincorporated these days in schools to increase the level of proficiency of children.This is because they have professional development materials embedded in textbooks for easy understanding.


In the 1980’s, the Ministry of Education, Singapore decided to change their textbooks. The present-day mathematics textbooks are from the series developed in 1982 called primary mathematics. By 1992, based on International research, it seemed that problem solving became the focus of school mathematics. This marked the introduction of Singapore math in Singaporean schools. Following this, in 1997, the Thinking Schools Learning Nation Initiative altered and structured all the subject curriculums on the basis of development of thinking.

Soon Singapore math attracted international interest, as

  • The textbook had unique ways to teach mathematics, which enhances the curiosity towards the subject.
  • The concrete materials helped the students to grasp and understand mathematics in an easier way.
  • This method has shown effectively that many children can learn mathematics very well, with slight changes in the mentoring methods. The findings in INTERNATIONAL studies widely support the same.

In 2009 World math fest, the proportion of two 15 year olds who managed to reach the highest proficiency levels are way above the international levels – reason being the Singapore Math


In the Singapore math curriculum, mathematics is defined as an acute and excellent vehicle for the development and improvement of a person’s intellectual competency. As metaphoric as it sounds, the destination of a problem, i.e. the solution is the focus. This is done by Problem-solving, using the 21st century competencies. Thus, Singapore math tends to be the mode of attaining intellect through inculcating the above qualities, by augmenting innovation levels in children’s minds.

Innovation Distinguishes Between a Leader and a Follower

Steve Jobs

Purpose of Singapore Math

Understanding Singapore Math - Purpose of Singapore Math

Singapore math was designed with the sole purpose of improving the students critical thinking and mathematical mastery. It has a 5-point concrete approach to attain the same. The math lessons will be explained through scaffolding. Students are expected to persevere through the problem- solving process, which eventually stimulates the critical thinking attribute in the student’s brain.

In Singapore Math, the main task for students is to build meaning to learn concepts and skills, as opposed to rote memorization of rules and formulas.

To attain the same, we at Thej Academy,

  • Encourage algebraic thinking, even among early learners
  • Help the students to reduce complexity in mathematical problems
  • Promote a deeper understanding of essential math concepts
  • Enhance the students’problem solving skills

Singapore Math Program

Example Problems of Singapore Math CPA Approach

Any math lesson including addition, subtraction, multiplication, has a basic CPA approach, i.e with Concrete actors, Pictorial illustrations and Abstracts.

Students will bedivided into 3 groups, to illustrate the same for easy understanding.

Once the math problem is given, the teacher says READY- SET- ACTION!!

The question is, say, 5×2 = ? The acting kids quickly spread into 5 groups of 2 each into each circle arranged by narrating kids. This is the concrete level part. These kids illustrate the problem in a practical way by spreading themselves accordingly as per the problem.

The abstract level is, writing numbers. This part is, using symbols and numbers to work out the problem. The kids in the abstract group note down their inferences and understandings from the enact of the concrete actors.

Pictorial Representation of the Math Problem

The basics of this part of Singapore math is understanding the Number bond – i.e., understanding the numbers as part and whole. This is done to speed up the students understanding of fractions and rational numbers. This also helps them to develop a strong command over the same. There are 2 basic concepts that drive Singapore math, that we teach at Thej academy.

  • Whole-part concept
  • Thinking block concept

Number bond helps to understand the compensation and decomposition of numbers.

So, when a problem says 8 + 5, a student with a good understanding of the number bond, perceives it as 8+(2+3), breaking 5 into 2 and 3 in order to add convert to the nearest whole number, 10. This way, the entire calculation becomes easier and simpler. The answer 13 can bedetermined in less than 2 seconds.

Subtraction in Singapore math

Compensation method is used to subtract values.
Here’s an example: 6 – 4 = ?

The two ways to solve this simple problem are

  • Compensation by adding the values
  • Compensation by subtracting the values

In compensation by addition, 6 being the minuend and 4 being the subtrahend, convert any one of these values to a whole number by adding a new value.

i.e., 6 + 4 = 10 (the nearest whole number, easier to manipulate)

Add the same value to the subtrahend.

i.e., 4+4 = 8

Now manipulate the numbers to find the difference.

10 – 8 = 2.

There we go!!!

This is the simplest strategy followed in Singapore math to help children solve faster.Similarly, in compensation by subtracting or deducting values, the same value should be deducted from both the minuend and subtrahend to find the difference.

OH WAIT!! I hear you..!!
Stating examples like plain rice and expecting you to solve Biriyanis???

Haha, I feel you!

Here is an example of Singapore math subtraction with complex numbers, solved using the compensation method.

Problem: 5000 – 3267 = ?

Method to solve: Applying the method of compensation by subtraction.

Strategy Applied: 5000 being a whole number, it is better to deduct values from it, to simplify the subtraction process.

5,000 – 1 = 4,999
3267 – 1 = 3,266
Difference 1,733
Understanding Singapore Math - Singapore Math Program

Doesn’t this method sound crisp and easier? It sure does, right? Singapore Math has totally revolutionized the history of complex mathematics by introducing such smart strategies to make math fun, effortless and unchallenging!

Word Problems Solved Using Singapore Maths

Apart from numerical problems, kids these days have a tougher time with the word problems. Ability to read and understand the context in the word problem, process it into numbers and then solving the problem is a tad bit difficult for average students. Singapore Math has a simple yet effective plan for this as well.

The Thinking Blocks Method

Understanding Singapore Math - The Thinking Blocks Method

The thinking block method is an innovative tool to help students understand the word problems using block models. It is indeed a non-traditional way of teaching math, that is followed at Thej Academy. In the thinking blocks method, kids are trained in such a way that they are able to develop strong visual sense. This, in turn helps them to enhance their kinesthetic aspect of manipulating blocks, mentally. Thinking blocks method could be taught using both whiteboard method or by drill practice.

At Thej Academy, clear explanations and guidance are provided to the students in the above methods, to demonstrate the same. This is a practice at Thej, to make sure that they understand the underlying math concepts.

Example 1

Understanding Singapore Math - The Thinking Blocks Method Example 1

Ragu wants to buy a notebook that costs Rs.63. He has saved Rs.38 so far. How much more money does Ragu need?

Create a block with 63 written on it, which represents the cost of the book. Draw one more block to half of its length, representing the money Ragu has saved. Another empty block occupies rest of the space where the final value is to be entered.By manipulating 63 – 38, the difference is calculated and filled on the empty box as 25.

Cost of the notebook
Money Raghu has saved
Money Raghu needs

By this way of breakingthe problem, kids develop a better understanding of the question and will be able to process the answer, with practical understanding.

Example 2

Understanding Singapore Math - The Thinking Blocks Method Example 2

Shiva is riding in a bike-a–thon. He rode 49 miles in the morning, stopped for a lunch break, then rode another 37 miles in the afternoon. Shiva was then only 62 miles from the finish line. How long was Shiva’s bike ride?

Solution: Sketch a block with 49 written on it, indicating Shiva’s morning ride distance. Another block is sketched along with it, in order to indicate his afternoon ride. Apparently, Shiva has 62 miles left to complete his bike-a-thon, a block is drawn with 62 written on it.

Morning ride
Noon ride
Distance from the finish line
Total distance of the ride

It is clear that the total distance is calculated by adding all 3 values. The sum is 148 miles. So, Shiva’s bike ride is 148 miles long. And we’re done!

Multiplication by Singapore Math

The thinking blocks method is highly versatile that any kind of manipulation could be crushed in seconds, using it. In multiplication, The applications of Singapore mathare as follows.

Problem: Jay has 7 books. Jen has 4 times the number of books Jay has. How many boos does Jen have?


Jay’s Book


Jen’s Books

7 7 7 7

The single block represents Jay’s books. The other 4 blocks in the next line represents Jen’s books, as given in the question.

We know that 1 block = 7 books and 4 blocks = 7 x 4 = 28 books

By manipulating 7 x 4, we get the answer as 28, which is the number of books Jen has.

Similar way, complex multiplications could be cracked using a combination of blocks. Check out for highly intriguing Singapore math problem solving strategies.

Singapore math versus common core

Common core is widely accused as the “Fuzzy math“. Unlike Singapore math, they create greater perplexity in students with overly complex explanations, that confuses pedagogy with the concept. Common core convinces the students to follow multiple approaches while tackling arithmetic problems, which eventually leaves the students baffled. In the simplest of terms, in Common core, finding answers to the math problems is the “goal”. To the absolute contrast, in Singapore Math, arriving at solutions are made as “clear cut ends” with a coherent understanding of the logic behind. Therefore, it is needless to say that students reach a higher level of math proficiency, by practicing the Singapore math.

Focus on mastering

At Thej Academy, Singapore Math is taught with focus on assisting the kids to master in math concepts and not just prepare them for a test. Attributes in math manipulations are given a deep dive, so that the students don’t just learn the equations to figure out the answer. They learn how the equation works. The abstract representation of the mathematical problem stimulates their concrete thinking, thus making them thrive better in the future.

  • Visual learners are thriving the best: This visual approach is the secret behind Singapore Math’s success. The LAYERED STRATEGY of making the students understand the logic behind the problems rather than rushing them towards the answer, undoubtedly inflates the kid’s skillsets.
  • Singapore students are Math leaders: Singapore being the top in terms of math achievers, It is not surprising that the common core replicates most of the Singapore math approach. From including the narrower focus and greater depth in terms, the common core tries to upgrade itself to reach Singapore math standards, constantly.

Applications of Singapore Maths

Understanding Singapore Math - Applications of Singapore Math

With the advent of technology progressing beyond bounds, mobile applications to learn Singapore math had been introduced. Singapore Math by Math games is an app that aims at teaching the kids the following:

  • Count and trace numbers – younger kids learn their numbers and how to write them
  • Foundational numeracy skills – know what the numbers mean
  • Math operations – add, subtract, multiply, and divide
  • Geometric shapes – basic figures and features
  • Patterns and sequencing – understand the relationship between multiple items and identify patterns

This app is a must download for kids struggling with math.


Elementary math forms the basis of so much in a child’s later years of education and adult life. It is mandatory to make sure that the foundation is solid. At Thej Academy, with Singapore Math, a strong foundation is accorded to the kids. With simple textbooks and concise graphics, math is made simple and interesting. While several types of research suggest that Singapore math is superior to the U.S textbooks, consider giving it a try. Because, it is important to perceive math more than just a subject- as a logical tool that is handy for a lifetime.

Learning and Creativity are contagious, Pass it on!!

Albert Einstein