Number Bonds

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What is a Number Bond?

A number bond is a simple addition method of two numbers that add up to give the sum. Using a number of bonds, we can instantly tell the answer without the need for the actual calculation.

In the example given we can see that when we see a number bond, we instantly know the answer, without doing the actual calculation.

Number bonds are also considered pictures that show the bond between parts and the whole.

A number bond consists of a minimum of three circles which is connected by lines. The “whole” number is written in the first circle and its “parts” are written in the adjoining circles. The "parts" when added together we will get the "whole".

Number bonds are the relationship between a number and its parts. They are the different pairs of numbers that add up to give the same number.

The following is the number bond that can be used to represent four number sentences.

3 + 2 = 5

2 + 3 = 5

5 − 3 = 2

5 − 2 = 3

It is very useful while learning addition and subtraction in arithmetic

For example:

Add 7 + 5

We know that 5 + 5 = 10 and 10 + 2 = 12

 The above expression can be represented as:

In the example above we broke the number 7 into two parts such that the value of the first part is 2 and the value of the second part is 5. And we are familiar with, 5 + 5 = 10.

It becomes easier to find the value of 10 + 2 = 12

From number bonds, we can understand that a whole number is made up of parts. These parts can be a combination of different numbers.

For example, a few of the number of bonds of 12 are: 

10 + 2 = 12

6 + 6 = 12

9 + 3 = 12

8 + 4 = 12

Number bonds are also helpful when we have to add many different numbers. In such cases, a grouping of similar numbers will make the addition easy.

Number Bonds to 10

Number bonds to 10 are the pairs of numbers that add together to make the sum of ten.

Number bond to 10 is the combination of pairs 

0, 10

1, 9

2, 8

3, 7

4, 6

5, 5

Following are the examples of a number bonds of 10.

Find the value of 2 + 7 + 4 + 6 + 8 + 3 = ?

In this case, if we know the number bonds of 10, we can easily combine the numbers that give 10 and make our calculations simpler and faster.

Given diagram below shows a different combination of 10.

So here, we have pairs of numbers that add up to 10.

2 + 8 = 10

7 + 3 = 10 

and 4 + 6 = 10.

So, we get the sum as adding all three pairs i.e 10 + 10 + 10 = 30

Subtraction Number Bonds

With the help of a number of bonds, we can also solve the problems of subtraction.

We will understand this with an example,

10 - ? = 8

In the above example, we know that 10 is the whole number and 8 is one of the numbers from the pair of number bonds.  The other number that combines with 8 to give 10 will be 2.

Hence, 10 – 2 = 8

How to Teach Number Bonds to Children?

We usually introduced the concept of number bonds to children through the Concrete, Pictorial, Abstract (CPA) approach. Here we have introduced one way to teach number bonds.

Concrete Step

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

After 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 in other ways to break numbers into two groups.

Pictorial Step

Now children understand the concept with hands-on objects and experience. They progress to write 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.

Abstract Step

With the concrete and pictorial steps, children progress to representing abstract problems using mathematical notation.

For example,Pictorial representation of  3 + 2 = 5 is shown below.

Advantages of Using Number Bonds:

  • Number bonds are used for additive relationships between 3 whole numbers. They are a useful tool in exploring the commutative property of addition.

  • Number bonds can be used to model number relationships and are useful representations for facilitating connections.

  • With the help of numbers, bonds learn to represent a mathematical situation with concrete materials.

  • It helps us to write equations for the easiest problem types (result from unknown / total unknown problems) after extensive teacher modelling.


The number bond is one of a number of coherent models that students regularly use in the story of units. It supports the number of senses that many adults are lacking. Seeing part-whole relationships and multiple solution paths is an important component of number sense. A student knows that 7 x 6 = 42, because 7 sixes = 5 sixes + 2 sixes, thus applying the earlier understanding method that 7 = 5 + 2. The number bond is a powerful model that supports students as it increases the ability to think flexibly, strategically, and creatively.

FAQ (Frequently Asked Questions)

1. Why do we Use Number Bonds?

Ans: We use number bonds because we can instantly tell the answer without the need for the actual calculation. In the given example when we see a number bond, we instantly know the answer, without calculating it.

2. What is a Number Bond to 10?

Ans: Number bonds to 10 are pairs of numbers that, when added together, give the number 10. They are also known as 'number pairs' or 'number partners'. Examples are 1 & 9, 7 & 3 and 5 & 5.

3. What is the Purpose of Number Bonds?

Ans: Number bonds helps students to split numbers in useful ways. They show how numbers join together, and also how they break down into component parts.