If you have kids in 1st grade (elementary school), you might heard them said they’re doing math number bonds in school. Or sometimes they started learning it in Kindergarten 2. They might told you about the *three circles* of number bond, or the *long rectangle block* thing, or the word “*whole*” and “*part*“. So what is number bond, in simple words?

### What is Number Bond in Math?

Number bond is a representation on **how numbers can join together to make a bigger number, or how a number can be broken down into smaller numbers**.

Number bond is usually presented by one circle having two adjoining lines connected to two more circles. The first circle will be called the “whole”, and will have the biggest number among the three. While the other two circles will be the “part”.

Sometimes, number bond can also be drawn as a long rectangle block, splitted into two, which each shorter block will be the “part”, and the whole block will be called, well, “whole”.

As you can see from the example above, you can then say “2 and 3 make 5” and “3 and 4 make 7”. What does that statement lead to? Yep. ADDITION. So, this is number bond.

### What is *Whole* and *Part* in Number Bond?

The basic concept; *a whole is made up from smaller parts*. Similarly, parts joined together will be a whole.

So the “whole” in number bond, would be the biggest number among the three numbers involved.

The other two smaller numbers will be the two “part”.

Sometimes they’ll write it as “W” for the whole, and “P” for the parts.

### What is this number bond for?

This helps children to understand how they can split a number into smaller “parts”.

When they join, i.e. add-up, all the parts, it becomes the bigger number.

When they break down a number and take away one part, i.e. substract, it will have the other part left.

In other words, this will lead to their addition & substraction concepts.

### How to practice number bond?

Usually it’s easier for the kids to learn first using **manipulatives/concrete objects.**

The main idea is, to introduce that some number of objects can be splitted into two groups.

Let me explain how with an example below.

First, get your child to take 5 objects and line them up on the table. You can use blocks, popsicle sticks, math cubes, math counters, or other small items.

Then ask him/her to split them into two groups. You can guide them by showing the first combination, say, “Let’s move two blocks up. Now can you count how many blocks left at the bottom?”

Now, ask them to count all the blocks again, from the top row to the bottom row. And teach them the sentence while pointing to each group of blocks, “Two and three make five.”

### Practice making different ways to split a number

Now, put all the five blocks on a row again. Then ask your child to split the blocks into different combinations.

Is there a different way to break down these five blocks?

Then practice to say the number bond statement again, “One and four make… FIVE!”

Now choose a different number. Ask them to find a few ways to split that number into smaller groups of blocks.

And ask them to practice saying out the number bond story, “_____ and _____ make ____ .”

For example you might get;

Number: 6

1 and 5 make 6.

2 and 4 make 6.

3 and 3 make 6.

6 and 0 make 6.

### Three circles of number bond

Once they’re comfortable in breaking down a number, subsequently they can learn the **pictorial** representation of number bond; the three connecting circles, with two “**part**” and one “**whole**“.

Let me bring the picture again.

At this step, after knowing how to break down a number, they need to know which one is the part and which one is the whole.

**Rule of thumb; the biggest number will be the WHOLE, while the other two smaller numbers are the PART.**

Practice: ask them to draw the number bond based on the different combinations of making-five as above.

### Number Bond Manipulatives – Learn Visually

What can you use to visualise a number bond?

You can use practically **anything small and countable, preferably in similar sizes.**

Here are some ideas:

1. I love to use our mathlink cubes (the ones you see from the previous images) to represent the number bond. This will simulate the blocks model of number bond. And with the actual action of assembling the blocks, I think it can represent better the idea of breaking down a number and joining numbers.

2. We also used three disposable plates (to represent the “whole” and two “parts”) and small objects. Here my daughter used her colorful counters.

3. You can also use popsicle sticks to represent the number, by lining them up vertically side by side.

This is also useful when your kids are taught to draw figure sticks at school to do their counting. Popsicle sticks is the closest real object to resemble the figure sticks.

### Next: Here comes the equation

By practising with the blocks or counters on how we can break down a number, these are the two points we want to emphasize to our kids:

1. Two numbers – the PARTs- can be joined together, to make a bigger number – the WHOLE.

2. A (bigger) number can be broken down into two smaller numbers – the PARTs.

With this concept in mind, we’ll learn how to write the addition equation based on the number bond.

The rule of thumb:

PART + PART = WHOLE

Let’s try some!

So, remember we already have some number bonds sentences previously?

2 and 3 make 5.

What is the WHOLE?

The biggest number from the sentence: 5.

What are the parts?

The two other smaller numbers: 2 and 3.

Ok slowly now… So the addition equation would be:

**PART + PART = WHOLE**

**2 + 3 = 5**

Pretty straight forward, right?

Now, go make the addition equations for the other number bonds!

What do you think? Is this number bond still a pain to explain (wow it rhymes!)?

I would love to hear from you! Comment below!