Depth of understanding - exploring structure

When we talk about “depth of understanding” in primary maths, we often imagine tricky problems or unusual challenges. But real depth isn’t about making things harder. It’s about helping children see the structure of the maths in front of them so they can work with confidence, flexibility and independence.

Instead of treating methods as steps to memorise, we show how the maths itself can guide pupils toward efficient, meaningful strategies.

To show this in action, let’s look at a simple example:

34 + 49 = 83

You can see the image below, which I use in CPD and classroom modelling. It highlights three different approaches - all correct, all based on structure, and all helping children understand what is happening beneath the surface.

1. Partitioning

30 + 40 + 4 + 9

This is often the first structural approach pupils meet. We break numbers into tens and ones so the calculation becomes more manageable.

Partitioning isn’t just a method, it helps children see that numbers are composed and can be decomposed in flexible ways. That is the foundation of number sense.

2. Adjusting

34 + 50 – 1

Here we make use of the fact that 49 is very close to 50.Instead of counting-on in small steps, children learn that they can adjust a number to make the calculation more efficient - as long as they adjust back afterwards.

This builds relational thinking:

“What multiple of 10 is 49 close to?”

“Which adjustment makes the calculation easier?”

Adjusting helps pupils understand number operations as relationships rather than sequences of actions.

3. Redistributing

34 + 49 = 33 + 50 = 83

In this approach, we take 1 from the 34 (first addend) and give it to the 49 (the second addend). The total stays the same, but the calculation becomes friendlier.

This method encourages children to look for balance and equivalence. It teaches them that numbers can move around within a calculation without changing the result.

Redistributing is a powerful doorway into generalisation and algebraic thinking later on.

So What Is “Depth”?

Deep understanding emerges when children:

• recognise patterns

• notice relationships

• choose strategies with purpose

• understand why a method works

• can explain the structure to others

  
  

Depth is not an add‑on for “greater depth pupils” - it is part of every child’s maths journey. When we focus on structure, we make learning more equitable, more accessible

Why This Matters

When pupils see structure:

• arithmetic becomes more efficient

• misconceptions reduce

• confidence grows

• methods make sense

• and fluency develops naturally

  
  

The example of 34 + 49 is simple, but the principle holds across the curriculum. By drawing attention to the mathematics within the method, we allow every learner to develop a rich, connected understanding.

Now, how would you teach the structure of 230 + 390?