# What are number bonds?

## Number bonds. Yes, they’re important, but what exactly are they and why do children have to learn about them?

If you’re a parent with a child of school age, you may well have heard of the term ‘number bonds‘.

Children begin exploring number bonds in math as early as in kindergarten.

Why? Because they help show the relationship between numbers, they’re crucial for building number sense, and they lay the foundation for more complex areas of math like addition, subtraction and mental math.

And if that’s not enough, you may also be interested to know that number bonds are a key component of the math curriculum in Singapore (‘Singapore Math’) – a country with some of the highest levels of math attainment in the world.

If you’re not entirely sure what number bonds are, or indeed why they feature quite so prominently in your child’s math curriculum, then panic not. Read on and all will (hopefully) become clear.

## Number bonds – what exactly are they?

Quite simply, number bonds are pairs of numbers that add together to make another number.

Number bonds can be shown in the form of a diagram, like this:

This diagram shows that 3 and 2 can be added together to make 5.

Or, looking at it another way, it also shows us that 5 (the whole) can be broken down (or ‘decomposed’) into two smaller parts (the 3 and 2).

Of course, this example shows just one number bond to 5 (3 and 2). 5 can also be broken down in other ways.

For example, into 4 and 1:

Or 5 and 0:

Related post: How to add numbers using a number line

## Number bonds to 10

Number bonds to 10 are pairs of numbers that add together to make 10, such as 6 and 4, or 9 and 1.

Special attention gets paid to these, and quite rightly so.

Ours is a base ten number system, so being able to recall pairs of numbers that total 10 is really important (and extremely helpful).

In kindergarten, children should get lots of opportunities to explore how the number 10 can be broken down into different pairs of numbers by doing hands-on work with math manipulatives .

For example, they may work with Lego bricks or unifix cubes to explore different ways that a stick of 10 bricks can be divided into two parts. Or they may work with small objects like counting bears and explore how a group of 10 can be divided into two different piles.

Children will revisit number bonds to 10 often, with the aim being that can quickly recall them from memory, without having to work them out each time.

## Why are number bonds important?

Exploring number bonds is important for lots of reasons. Here are just a few:

### 1) They make all sorts of math calculations and problems a lot easier to solve!

Yes, it’s true, a good knowledge of number bonds and how numbers can be decomposed is incredibly helpful when doing all kinds of math calculations – think mental math for a start.

For example, let’s think about the sum 16 + 8.

If you don’t know the answer to this from memory, if you know your number bonds, it’ll be much easier for you to work out the answer. Let me explain:

If you know all the pairs of numbers that total 20, you’ll know that 16 + 4 makes 20. If you also recognize that 8 can be broken down into two 4s, you’ll see that you can add one 4 to 16 to make 20 and then the remaining 4 to 20 to give the answer 24.

If I were to jot this down in note form, it would look something like this:

So, as you can see from just one example, having a knowledge of how numbers can be joined together and broken apart is really helpful. It allows you to work flexibly with numbers and do calculations more easily and quickly, both on paper and in your head.

### 2)Number bonds show how addition and subtraction are connected

By looking at number bonds and seeing how a number can be broken down into two smaller ones, we are paving the way for basic addition and subtraction and showing how they are connected.

In fact, by looking at just one number bond, you can derive four related addition and subtraction number sentences.

Let’s take this number bond, which shows 7 as the sum of 3 and 4:

From this one number bond, we can come up with the following four related facts:

A set of four related number sentences, derived from one number bond like this, is often called a fact family. ( I really like this name as it emphasises that all four number sentences are related.)

### 3)Simple number bonds can be applied to bigger numbers

Once you know simple number bonds, you can use these to help you out when working with bigger numbers.

For example, if you know that 8 + 2 = 10, it’s not too much of a stretch to see that 80 + 20 = 100.

Likewise, if you know that 10 can be decomposed into 5 and 5, you can work out that 100 – 50 must equal 50.

Knowing all the number pairs that equal 10 will also help enormously when it comes to learning number bonds to 20. After all, if you know that 3 + 7 = 10, then it’s not such a leap to learn that 13 + 7 equals 20.

While the concept of number bonds is pretty simple, it is definitely worth taking some time to explore them with your child. Help your child learn their bonds to 5, 10, and (when they’re ready) to 20. Understanding the concept of number bonds and being able to recall simple facts easily, will be so helpful for them going forward.