Teach Number Bonds Not Addition and Subtraction - The Singapore Math

If you asked people to tell you what they know about Singapore Math, many would say, Oh, that’s model drawing. And while that’s one part of it, it really starts much earlier than that with their incredible routines for building number sense. Enter number bonds, a cornerstone of Singapore Math.

In her book Why Before How: Singapore Math Computation Strategies, Jana Hazekamp explains number bonds this way:

'Number bonds help students see that numbers can be “broken” into pieces to make computation easier. With number bonds, students recognize the relationships between numbers through a written model that shows how the numbers are related.'

The way Mathematics is taught in Singapore schools has attracted a lot of global attention in recent years. This is because students in Singapore have outperformed their peers from many developed and developing countries in the subjects of Mathematics and Science according to Trends in International Mathematics and Science Study (TIMSS). TIMSS is a widely recognised achievement test by educators and governments globally. “Singapore Math” has also started catching on in American schools where tools like counting blocks and techniques like number bonds help to play an important part in building up the students’ foundation.

Singapore Math curriculum focuses more on the mastery of the various concepts rather than just equation solving. Students begin Primary 1 by learning basic skills and concepts, such as counting from one to 10, number bonds, addition and subtraction. Basic understanding of multiplication (in terms of repeated additions) and division concepts are also taught. All these helped to lay a good foundation for the students to pick up more advance level of the concepts later.

In recent years, Math has been taught more visually in Singapore schools. Using counting blocks and techniques like number bonds, students are able to see and learn Math with better understanding.

Number bonds are an essential component when teaching the Singapore method of maths for mastery. They foster number sense in students and are an important concept within the Singapore primary curriculum. However so-called ‘Singapore Number Bonds’ are not a specifically Singaporean method — the term has been around since the 1920s.

Number bonds have been regarded as one of the best ways to teach basic math concepts like addition and subtraction. A number bond diagram like the one below shows the relationship of 2 Parts (2,4) and 1 Whole (6).

Students will learn to see that the two Parts can be added up in any order to form the Whole. And when one of the Part is taken away from the Whole, they will just be left with the other part.

After a student understands the relationships of the 2 Parts and Whole, the concept can then be further extended to addition and subtraction as illustrated in the diagram below. Making it easier for the student to understand the concept of addition and subtraction.

Students will be practising the few scenarios below. Once they are familiar with number bonds, they will be able to recognize and complete it almost instantly.

Number bonds let students split numbers in useful ways. They show how numbers join, and how they break down into component parts. When used in Year 1, number bonds forge the number sense needed for early primary students to move to addition and subtraction. As students progress, number bonds become an essential mental problem-solving strategy.

Children are usually introduced to number bonds through the Concrete, Pictorial, Abstract (CPA) approach, games and apps. Here’s just one way to introduce and teach number bonds.

1. Concrete step

Children start out by counting familiar real-world objects that they can interact with. They then use counters to represent the real-world objects. From here, they progress to grouping counters into two groups.

By putting five counters into two groups, children learn the different ways that five can be made. For example, 3 and 2 as illustrated below. With further exploration, children work out other ways to break numbers into two groups.

2. Pictorial step

Now that they understand the concept with hands-on objects and experience, children progress to writing number bonds in workbooks or on whiteboards. Early number bond explorations might simply reflect the two groups of counters that they created during the concrete step, along with other combinations.

3. Abstract step

With the concrete and pictorial steps done and dusted, children progress to representing abstract problems using mathematical notation (for example, 3 + 2 = 5).

4. Apps and Games

Introducing “My Number Bond App” an editable, game-based and highly intuitive interactive desktop application that makes the learning of Math concepts come to life.

“My Number Bond App” has helped thousands of children excelled greatly in Mathematics by breaking down foundational concepts using the number bond approach. Need to help your children step up their math skills?

Number bonds also develop problem-solving strategies such as ‘making ten’ with ten frames, multilink or unfix cubes.

By mastering number bonds early on, pupils build the foundations needed for subsequent learning and are better equipped to develop mental strategies and mathematical fluency. By building a strong number sense, pupils can decide what action to take when trying to solve problems in their head.

This example shows how a pupil would develop their number sense, or mathematical fluency, by using number bonds to perform a mental calculation.

Would you be happy, if your child performed excellently in Math?

Most children don't do well in Mathematics because of the lack of a firm understanding of Math fundamental concepts.

Worry no more! My Number Bond App has helped thousands of children achieve excellence in math by helping them learn the basics in a fun and engaging way.

“My Number Bond App” is an editable, game-based and highly intuitive interactive desktop application that makes the learning of Math concepts come to life.

Number facts are basic addition, subtraction, multiplication and division calculations that children should learn to recall instantly with no working out (in other words, they need to learn them off by heart). Number facts are sometimes referred to as NUMBER BONDS (addition and subtraction) and times tables with related division facts (multiplication and division).

Download on Desktop or Laptop.

"My Number Bond App" will help your children build higher concepts of math fundamentals as shown below. It can be used by children of any age or level: