What is Singapore Math?

The Singapore math method is a highly effective teaching approach originally developed by Singapore’s Ministry of Education in the 1980s for Singapore public schools. 

Singapore Math® programs instill conceptual depth and math mastery. We invite you to learn more about the unique strengths of the approach below.

Proven Results

Singapore consistently ranks at the top in international math testing.

Results indicate that students in Singapore not only score better on average than students in other countries, but have a very high percentage of students who demonstrate advanced knowledge of math. This is an indication of how the Singapore math method excels at teaching conceptual knowledge.

The Singapore math method is focused on mastery. It teaches students the how and why of math.
Intentional sequencing of concepts involves students returning to topics over the course of years, each time building complexity and depth.
Students are introduced to problem variation at an early stage. Instead of pushing through rote memorization, they are asked to think creatively and mathematically, relying on knowledge gained in previous lessons and trying new techniques.
Students explore many ways of solving the same type of problem. They develop a 360-degree understanding of topics.
An attitude that math is important and approachable is also essential. Students perform at a higher level when their potential for understanding and success is assumed.
In typical U.S. math programs, students get a worked example, then solve problems that very closely follow that example, repeating all the same steps with different numbers. In Singapore math, students must think through concepts and apply them in new ways from the very start. Since they can’t rely on simple replication, students are pushed to greater engagement and broader thinking. In U.S. math programs, concepts and skills are more compartmentalized within and across grade levels than in Singapore math, where a strong sense of connectivity to past learning is woven throughout.
Singapore math not only helps students become more successful problem solvers, it helps them gain a sense of confidence and resourcefulness because it insists on conceptual depth. This naturally prepares students to excel in more advanced math.
Some of the key features of the approach include the CPA (Concrete, Pictorial, Abstract) progression, number bonds, bar modeling, and mental math. See the details of those methods below.

Key Features

The Singapore math method is focused on mastery. It teaches students the how and why of math.
Intentional sequencing of concepts involves students returning to topics over the course of years, each time building complexity and depth.
Students are introduced to problem variation at an early stage. Instead of pushing through rote memorization, they are asked to think creatively and mathematically, relying on knowledge gained in previous lessons and trying new techniques.
Students explore many ways of solving the same type of problem. They develop a 360-degree understanding of topics.
An attitude that math is important and approachable is also essential. Students perform at a higher level when their potential for understanding and success is assumed.
In typical U.S. math programs, students get a worked example, then solve problems that very closely follow that example, repeating all the same steps with different numbers. In Singapore math, students must think through concepts and apply them in new ways from the very start. Since they can’t rely on simple replication, students are pushed to greater engagement and broader thinking. In U.S. math programs, concepts and skills are more compartmentalized within and across grade levels than in Singapore math, where a strong sense of connectivity to past learning is woven throughout.
Singapore math not only helps students become more successful problem solvers, it helps them gain a sense of confidence and resourcefulness because it insists on conceptual depth. This naturally prepares students to excel in more advanced math.
Some of the key features of the approach include the CPA (Concrete, Pictorial, Abstract) progression, number bonds, bar modeling, and mental math. See the details of those methods below.

The Framework

Mastery Spiral

CPA Approach

Concrete Pictorial Abstract Progression

Here's a step-by-step look at the Concrete Pictorial Abstract (CPA) approach.

This is a simple addition problem from Dimensions Math Textbook 1A.

CPA Approach

Concrete Stage: Interactive Activity and Manipulatives

In the introduction to the problem, students may do a full-class activity, representing birds and acting out the story problem. The interaction introduces students to the problem in a tangible way.

Students may also use linking cubes to model the problem in a concrete way.

CPA Approach

Pictorial Stage: Number Bonds

Students then turn to a visual representation of the problem by showing the two parts and the whole in the form of a number bond.

Pictorial representations vary and may include bar modeling or other visual methods.

CPA Approach

Abstract Stage: The Equation

Students move to the final stage of the sequence, an equation that represents the story problem. The numbers and equation now really mean something to them.

Number Bonds

Number bonds are a pictorial technique that show the part-whole relationship between numbers. Initially, the whole number is written in one circle, and the parts of the number are written in adjoining circles connected by lines to the first circle. This method helps early elementary students work towards addition and subtraction, and illustrates strategies to solve expressions mentally. Using number bonds fosters a solid number sense that serves students throughout their math education.

Bar Models

Bar models are a versatile and transferable tool that students can use to visualize a range of math concepts, such as fractions, ratios, percentages, and more. Drawing bar models for word problems allows students to determine the knowns and unknowns in a given situation. It extends the CPA approach, especially the pictorial phase, as it allows students to illustrate the mathematical information given in problems. It prepares them to understand more complex math on a conceptual level. This method is most effective when used frequently throughout the program.

Mental Math

The Singapore Math approach teaches techniques and skills to easily and accurately perform mental math. These strategies help students develop number sense and flexibility in thinking about numbers. Many mental math strategies involve factoring numbers into parts, then performing operations on them in a different order from the original expression. The thought processes involved in mental math are often illustrated by number bonds.

Some mental math strategies are taught as early as first grade. As students progress, they learn to apply new mental math strategies to specific types of problems and adapt ones they already know. Students are encouraged to develop their own strategies, and to use their discernment in deciding when and where to use them.

Why Us? Since 1998

we've believed that all students should have access to an excellent Singapore Math education. We saw the potential and value of this powerful pedagogy and were the first to bring it beyond Singapore's borders.

Our Singapore Math® programs maintain fidelity to the techniques, sequencing, and rigor that define the Singapore math approach. We've maintained our position as the most trusted source for Singapore math content by remaining committed to the highest standards and continually developing new material to better serve your needs.