Rethinking “Greater Depth” Through the Lens of the KS2 Maths SATs
Each year, the KS2 Maths SATs offer a moment to pause and reflect—not just on what pupils know, but how they think. This year, we were really interested in the question below. Try it for yourself:
Source: 2025 Key Stage 2 Mathematics Paper 3: Reasoning, question 17. Available at: UK Government Education Website
At first glance, this looks like a straightforward two-step problem involving multiplication and division. However, we argue that there is a lot more opportunity for depth, elegance and exploration here.
In many classrooms, pupils working at “greater depth” is often outcome-based, with pupils achieving a certain score on either internal or external summative assessments. Yet, when we looked closely at how pupils tackled this SATs question—even those who will be labelled as working at “greater depth”—we saw a heavy reliance on standard written algorithms. Most multiplied 35 by 48 using long multiplication, then divided the result by 56 using long division. How long did that take?
Such an approach might get the correct answer, but it raises a question: is this what greater depth should look like?
Understanding mathematical depth requires us as teachers to move beyond simply counting correct answers and also focus on how pupils see mathematics and apply it with flexibility.
In this question, for example, the structure is key. Pupils need to find the total number of crisp packets (35 × 48), then divide this by 56 to determine how many days it will take to sell them. While many correctly followed the steps, we noticed an opportunity to go further—not by adding complexity, but by applying mathematical reasoning and structure.
We were reminded of the phrase:
“Don’t just do something, sit there.”
When we pause and represent the problem in different ways, we begin to see alternative paths—often more efficient and more elegant.
A Closer Look: Structure and Simplification
One way to approach this questions is as a missing number problem:
35 × 48 = ? × 56
This frames the question as a proportional relationship. Noticing common factors between the numbers (like the shared 7 and 8 in 35, 48, and 56), we can simplify both sides of the equation:
5 × 7 × 8 × 6 = ? × 7 × 8
Cancel the common factors (7 and 8) on both sides:
5 × 7 × 8 × 6 = ? × 7 × 8
Which gives us:
5 × 6 = 30 days
Alternatively, consider using fractions and multiplicative reasoning:
35 × 48 ÷ 56
We can rewrite the division as a fraction:
35 × (48⁄56)
Since both 48 and 56 are multiples of 8, this simplifies to:
35 × (6⁄7)
Now we’re finding six-sevenths of 35, which is again:
30 days
Both strategies highlight not just correct working, but thoughtful, connected mathematical reasoning.
The strategies above aren’t just quicker—they demonstrate a deep, flexible understanding of number, structure, and equivalence. These are the kinds of behaviours we want to nurture in all pupils, not just those at the top end.
This brings us back to the term “greater depth.” If it’s meant to capture rich, connected thinking, we have to ask: how many pupils actually approach problems in this way? And how often do our assessments reward this kind of reasoning?
Maybe it’s time to reconsider what “greater depth” means in practice. Perhaps it’s less about complex procedures or polished algorithms, and more about the ability to represent, notice, and reason—hallmarks of true mathematical fluency.
Rather than reserving these types of insights for a select few, we can use them to shape how we teach and assess all pupils. If we focus on securing key concepts and encouraging flexible thinking, we create the conditions where elegant solutions can flourish.
As we reflect on the KS2 SATs and how pupils responded to them, let’s shift our focus away from labels like “greater depth” and toward developing the habits of mind that lead to genuine mathematical understanding.
Because in the end, the goal isn’t just to solve the problem—it’s to understand the mathematics within it.
Thanks for reading,
Joe and Adam
