Introducing Place Value: Hands On Maths and Living Maths

There is a difference between doing maths… and truly understanding it. This week we began by Introducing Place Value  in our homeschool using a far more hands on maths approach than I had before. The girls confidently insisted they understood. And to be fair, they can usually complete long addition, subtraction and multiplication correctly.

But every so often, everything seemed to vanish.

That told me something important: they may understand the method, but they hadn’t internalised the concept.

And that is where living maths changed everything for us.

Introducing Place Value: When Understanding Isn’t Internalised

In An Elephant in the Classroom, the author explains how a child can appear to understand a concept at the point of instruction. They can replicate the method shown. They can arrive at the correct answer.

The teacher moves on.

Later, the same child cannot solve a similar, but slightly different, problem.

Why?

Because they were never given time to play with the concept. To discuss it. To wrestle with it. And to view it from different angles.

That was exactly what I was seeing.

So instead of pushing ahead, I decided we would slow down and truly explore place value through hands on maths and living ideas.

It took time.

And it was completely worth it.

Introducing Place Value – Book One: Solid, But Not Transformational

The first book I used covered place value clearly and competently. It reinforced what the girls already knew.

But it didn’t deepen their understanding.

To be fair, it was likely written for slightly younger children. Still, I was left wanting more. I didn’t want them to simply repeat that our number system works in tens, I wanted them to understand what that means.

So it was back to the drawing board.

Introducing Place Value: The Book That Changed Everything

Completely by chance, I stumbled upon How to Count Like a Martian.

Go and beg, steal, or borrow it. You won’t regret it.

This book is essentially about place value, but it takes readers on a journey through number systems across ancient and modern civilisations, asking:

• Does this system use place value?
• What base is it written in?
• Why might that base have been chosen?

It explores, among others:

• The Babylon base 60 system
• The Maya civilization base 20 system

And here is my confession: I have advanced level maths, and I did not truly understand what “base 10” meant.

I knew we used a decimal system. I knew it works in tens. And I knew I could operate within it fluently.

But I didn’t deeply understand it.

A bit like using a computer without knowing how it works internally.

This book changed that.

Discovering the Abacus Within Our Own System

One of the most eye-opening moments for the children came when the book introduced the abacus method of counting.

C10 struggled enormously at this point. But that struggle was valuable.

Because without realising it, we use an “abacus-like” place value structure in our own number system. Each digit’s position determines its value.

When the penny dropped, I could actually see the confusion lift from their faces.

That is internalisation.

Not memorising.
Not replicating.
But understanding structure.

This is why I love living maths, I am learning right alongside them.

Making Maths Musical

The writing style of How to Count Like a Martian reminded me of the 80s hit Walk Like an Egyptian.

Much to my children’s amusement, I kept bursting into song, wildly out of tune, singing about “counting like an Egyptian.”

We all agreed the perfect assignment would be to rewrite the song using:

• Base 10
• Base 20
• Base 60
• Roman numerals
• Any system we encountered

Off they went to compose their own mathematical songs.

My plan? To collate the best lines from each and create one final version we can use as a memory tool.

This is hands on maths at its most joyful.

Asking the Big Question

One major shift I’m making in our homeschool is this:

Less telling.
More questioning.

Instead of:

“Here is how place value works.”

I now ask:

“What is a number?”

That one big question opens everything up.

• Is a number just a symbol?
• Is it a quantity?
• Does it exist without a system?
• Would aliens count the same way we do?

Suddenly, place value is no longer a worksheet topic. It becomes philosophical, historical, and creative.

That is living maths.

Why Exploring Base Systems Deepens Place Value

When children explore:

• Babylonian base 60
• Mayan base 20
• Roman numerals (non-place value)
• Our base 10

They begin to see:

• Place value is not universal.
• Base systems are human constructs.
• Our decimal system is efficient but not inevitable.

Understanding this makes their grasp of base 10 far more secure.

They are no longer just following steps.
They understand the framework beneath the steps.

Reflection Questions for Your Homeschool

Use these to deepen your own exploration of place value:

1. What is a number?
2. Why do we use base 10?
3. What might happen if we had eight fingers instead of ten?
4. Why is place value more efficient than Roman numerals?
5. Could you invent a number system that doesn’t use place value?
6. What makes a number system practical?
7. How does understanding other bases help you understand base 10?

Encourage discussion, debate, and disagreement. Internalisation happens through thinking.

Hands On Maths Activities to Internalise Place Value

Here are some practical, living maths ideas you can try:

🔢 1. Build Numbers with Physical Objects

Use:

• Lego bricks
• Bundled straws (groups of ten)
• Beads on skewers

Physically create:

• Units
• Tens
• Hundreds

Then regroup them.

Let them see carrying and borrowing happen.

🌍 2. Invent a New Number System

Challenge your child to:

• Choose a base (5? 8? 12?)
• Create symbols
• Write numbers
• Teach it to a sibling

Teaching solidifies understanding.

🧮 3. Create a Human Abacus

Assign children:

• Ones
• Tens
• Hundreds

Have them physically move positions as numbers change.

Movement makes abstraction concrete.

🎵 4. Write a Maths Song

Choose a familiar tune (we borrowed from Walk Like an Egyptian).

Write lyrics explaining:

• Base 10
• Place value
• Regrouping
• Different civilisations’ systems

Music is a powerful memory tool.

📜 5. Explore Ancient Civilisations Through Maths

When studying:

• Babylon
• Maya civilization

Don’t skip their number systems.

Draw them.
Count with them.
Compare them.

This integrates history and maths beautifully.

The Joy of Learning Together

One of my greatest delights in this journey has been learning alongside my children.

When we struggled to understand the Mayan system, we worked through it together.

When confusion turned into clarity, it felt earned.

That is the beauty of hands on maths.
That is the power of living maths.
And that is how place value finally moved from procedure to understanding in our home.

Next week? The children design their own number systems.

And I cannot wait to see what they create.

For all of my living hands-on maths posts, click here