What are Number Bonds (and Why They Help Kids Understand Math)

If you've seen circles connected by lines in your child's math homework, you've encountered number bonds. You might be wondering what they are, why teachers use them, and how they help your child learn math. This post will walk you through everything you need to know about number bonds and how they support your child's mathematical thinking.

What are number bonds?

A number bond is a visual diagram that shows the relationship between a number and its parts (aka how numbers break apart and come back together). It typically consists of three circles connected by lines, forming a triangle-like shape. The total number sits in one circle, and the two parts that make up that total sit in the other two circles.

For example, a number bond for 8 might show 8 in the top circle, with 5 and 3 in the bottom circles. This simple diagram shows that 8 can be broken into 5 and 3, or that 5 and 3 combine to make 8.

Number bonds help children see the part-part-total relationship that exists within numbers. This relationship is fundamental to understanding both addition and subtraction.

Why teachers use number bonds

Teachers use number bonds because they make abstract number relationships visible and concrete. When children see a number bond, they're not just looking at isolated numbers, they're seeing how those numbers relate to each other.

Number bonds help children understand that numbers are flexible. Eight isn't just "eight." It's also 5 and 3, or 6 and 2, or 4 and 4. This flexible thinking about numbers is at the heart of number sense.

Children who understand number bonds can see that addition and subtraction are connected operations. If they know that 5 and 3 make 8, that helps them  know that 8 minus 5 equals 3, and that 8 minus 3 equals 5. This understanding helps children move beyond memorizing isolated math facts to truly understanding how numbers work together.

How number bonds support addition and subtraction

Number bonds provide a powerful foundation for both addition and subtraction. When children understand the part-part-total structure of numbers, they can approach problems with flexibility and reasoning.

For addition, number bonds help children see that they're combining two parts to make a total. When solving 6 + 4, a child who understands number bonds recognizes they're finding the total that's made up of parts 6 and 4.

For subtraction, number bonds reveal that subtraction is really about finding a missing part. When solving 10 − 6, a child can think "10 is the total, 6 is one part, what's the other part?" This transforms subtraction from a mysterious "take away" operation into a logical question about parts and totals.

Simple ways to use number bonds at home

You don't need special materials to help your child practice with number bonds. Here are some easy ways to start:

Start with small numbers. Use physical objects like blocks, coins, or snacks. Show your child 6 items, then split them into two groups. Ask "How many are in each group? How many do we have altogether?" This helps them see the part-part-total relationship in action.

Draw simple number bonds together. Draw three circles connected by lines, or download our number bonds worksheet. Put a number in the top circle and ask your child to find different ways to break it apart. For example, with 7 in the top circle, they might put 4 and 3, or 5 and 2, or 6 and 1.

Connect to addition and subtraction. When your child is working on addition or subtraction, help them see the number bond. For 8 + 5, you might draw a number bond showing the parts (8 and 5) and ask them to find the total. For 13 − 8, show 13 as the total and 8 as one part, then ask them to find the missing part.

Use everyday situations. "We have 10 crackers. If we give 4 to your friend, how many will we have left?" Help your child see that 10 is the total, 4 is one part, and they're finding the other part.

Ask questions that encourage flexible thinking. "What are some different ways we can make 12?" or "If 7 and 5 make 12, what else does that tell us?" These questions help children explore the relationships within numbers.

Number bonds vs. fact families

You might have grown up working with “fact families,” which are related to number bonds. A fact family shows all the addition and subtraction facts that can be made from three numbers. For example, the fact family for 5, 3, and 8 includes: 5 + 3 = 8, 3 + 5 = 8, 8 − 3 = 5, and 8 − 5 = 3.

Number bonds and fact families are closely connected. A number bond shows the part-part-total relationship visually, while a fact family shows the same relationship through four related equations. Both tools help children see how addition and subtraction connect.

Number bonds often come first because the visual representation helps children understand the underlying relationship before they work with the symbolic equations in a fact family.

When children struggle with number bonds

If your child finds number bonds confusing, start with concrete experiences before moving to the diagram. Use physical objects to show how a group can be split apart and put back together. Let them physically separate and combine objects many times before trying to represent this with a number bond diagram.

Some children struggle to see that the same total can be broken into many different pairs of parts. Give them lots of practice with one number, finding all the different ways to break it apart. Use objects they can move and rearrange so they can see the possibilities physically. Connecting cubes like the ones below or legos work great for this, but you can really use anything from blueberries to pencils. 

If your child has trouble connecting number bonds to addition and subtraction, spend time making those connections explicit. Each time you work with a number bond, say all four related facts out loud together: "5 and 3 make 8. 3 and 5 make 8. 8 take-away 5 is 3. 8 take-away 3 is 5." You can also write about the addition and subtraction equations if you think it would be beneficial for your child.

The long-term benefits of understanding number bonds 

Understanding number bonds builds a foundation that supports all future math learning. Children who grasp part-part-total relationships find addition and subtraction more logical and connected. They develop mental math strategies because they can flexibly break numbers apart and recombine them.

As children move into more complex math, number bonds continue to be useful. The same part-part-total thinking helps with multiplication and division, fractions, algebra, and beyond. When children understand that numbers can be decomposed and recomposed, they're prepared to think flexibly about mathematical relationships throughout their education.

Most importantly, number bonds help children see math as something that makes sense. Rather than memorizing disconnected facts, they understand the logic behind the numbers. This understanding builds confidence and helps children see themselves as capable mathematical thinkers.

The takeaway

Number bonds are simple visual tools that reveal the part-part-total structure of numbers. They help children understand how numbers relate to each other and see the connection between addition and subtraction. This understanding builds number sense and creates a foundation for all future math learning. You can support your child's work with number bonds at home through simple conversations, hands-on activities with everyday objects, and questions that encourage flexible thinking. You got this!