Teaching Number bonds

One of the greatest gifts homeschool maths gives us is time. Time to slow down, notice misunderstandings, and truly respond to the child in front of us. This lesson on teaching number bonds reminded me just how powerful living maths can be when understanding, not speed, is the goal.

Click here to read our first post about Living maths and Number Bonds

Teaching Number Bonds in our Homeschool

What Are Number Bonds, Really?

I began the lesson by asking the girls to explain number bonds in their own words. While it was clear that Charlotte understood them, she struggled to articulate that understanding. I was hoping to hear language that included ideas like picture, relationship, whole, and parts.

Lillie, who typically finds maths very challenging, surprised us both by explaining number bonds clearly and confidently. For a ten-year-old this might seem like a simple concept, but for a child who struggles with maths, this moment was a breakthrough. We were both delighted.

Seeing the Relationship: Whole and Parts

In this lesson, I wanted to deepen the idea that the whole is made up of parts, and that all three numbers in a number bond are related.

I reminded the girls that the whole-and-parts diagram shows the relationship between any number and the parts that make it up. This visual representation is such a powerful tool in hands on maths, especially for children who struggle to hold abstract ideas in their heads.

Playing With Words: Living Maths in Everyday Life

To make things more playful, we explored the idea that everything in life is a sum of its parts.

I used Lillie as an example, explaining that she is made up of many parts such as legs, arms, head, and body. I asked her what she would be without her legs.

“Legless!” she replied.

“A legless what?” I asked.

Giggling, she answered, “A legless Lillie!”

She then eagerly gave her own examples: a table made of a tabletop and four legs, objects breaking down into their components. These simple conversations allowed both girls to pictorially see how the whole-and-parts diagram applied far beyond numbers.

This is the heart of living maths, connecting ideas to real life so they make sense.

Transferring Understanding to Blocks

Next, I brought out the blocks and revisited number bonds to ten. The girls experimented freely, removing pieces and figuring out what was missing. They practised this with many combinations.

Then I introduced a larger challenge:

• A hundred block labelled c
• Three tens and a four (34) labelled a
• One unknown space labelled b

They worked out b quickly and accurately and, crucially, without counting on fingers. For Lillie, this was a huge improvement.

This activity introduced the idea of an unknown, something that had always baffled her before. I realised she hadn’t struggled with unknowns because of the numbers themselves, but because she didn’t yet understand the relationship within number bonds.

We practised with blocks until her confidence was secure.

Moving from Concrete to Numbers

Abstract numbers have always been difficult for Lillie. She can solve maths problems when they are connected to something tangible (cooking, measuring, building) but struggles when numbers stand alone.

We began with simple two-digit problems, and she did very well. Then I introduced this equation:

x – 96 = 57

Immediately, she placed 96 in the “whole” section of the diagram, not realising that x was the whole. I guided her, but she couldn’t quite see it.

So I simplified:

x – 8 = 2

She instantly replied, “x = 10,” and recognised that 10 must be greater than 8. With this understanding in place, she easily returned to the original problem.

Then I gave her a much harder one:

x – 3214 = 1111

Tears welled up immediately. She was convinced she couldn’t do it.

My purpose wasn’t to challenge her arithmetic, it was to show her that maths follows the same rules no matter how large the numbers are. If you understand the relationship, you can always find the solution.

I asked her not to think about the entire sum, but simply to use the diagram and fill in what she knew. Reluctantly, she did and then she was off…!

The pride on her face was unforgettable.

Tools for Confidence, Not Panic

It’s possible she could have done the calculation mentally. My other children certainly could. But that wasn’t the point.

The goal was to give Lillie a tool she could rely on when anxiety set in. The whole-and-parts diagram became her anchor.

Up to this point, I had given the girls one main tool: the diagram. The next step was introducing a second, equally important tool : do what you can before panicking about the whole problem!

This simple mindset shift is invaluable in homeschool maths, especially for children who experience maths anxiety.

Hands-On Maths Activities to Try at Home

Here are some practical ideas to reinforce number bonds using hands on maths:

1. Build-and-Break Blocks
   Use blocks or LEGO to build a number, remove pieces, and identify the missing part.
2. Whole and Parts Drawing
   Draw large circles for the whole and smaller ones for parts. Let your child fill in what they know.
3. Everyday Objects
   Take household items apart conceptually, furniture, recipes, toys, and identify their “number bonds.”
4. Unknown Mystery Bag
   Put objects in a bag, reveal some, and have your child calculate how many are hidden.
5. Equation Swap
   Take a known number bond and rewrite it in different equation forms (addition and subtraction).

Reflection Questions for Parents and Children on Teaching Number Bonds

• Can my child explain number bonds using their own words?
• Do they understand the relationship between the whole and the parts?
• What tools help my child feel calm when maths feels overwhelming?
• Where can I slow down and allow understanding to grow?
• How can I connect this concept to everyday life?

Final Thoughts on Teaching Number Bonds

This lesson reminded me that progress in homeschool learning is not always loud or obvious. Sometimes it looks like a quiet moment of understanding, a tear turned into a smile, or a child realising, “I can do this.”

When foundations are firmly laid, children can approach even the hardest problems with confidence, and that is the true goal of living maths.

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