Structure scales up: proportional reasoning in Key Stage 3 (KS3)

The hugely anticipated Curriculum and Assessment Review (CAR) feels like a turning point for secondary maths education. By placing proportional reasoning at the heart of KS3, it offers a real chance to tackle one of the biggest barriers to success. 

Why proportional reasoning matters

Let’s start by clarifying what we mean by proportional reasoning. It isn’t just a set of tricks for working out ratios or percentages; it’s about understanding multiplicative relationships to make sense of the world – from scaling recipes to comparing exchange rates. Students who reason proportionally can flexibly compare quantities and choose strategies that fit the structure of a problem. This way of thinking underpins so much of maths - speed, percentages, best buys and more - and yet too often students fall back on additive shortcuts or memorised steps that collapse when the context changes.  

Consider the following questions:

What's the same and what's different?

At first glance, each question seems to cover a different topic, each needing a separate process. That’s how we often teach – isolated methods for isolated problems. And here lies the problem. Students with only surface-level knowledge will try to recall a different procedure for each question. But if we look deeper at the underlying structure, all of them can be solved using proportional reasoning.

Without making cross-topic links, students’ skills remain fragmented. If we help them see the connections, using proportional reasoning across multiple topics, we give them the key to unlock far more of the curriculum than they realise.

The CAR makes the stakes clear: students who cannot reason proportionally rarely achieve a grade 4 at GCSE.

What will make a difference?

The prospect of addressing this at KS3 is an exciting but daunting one. How do we ensure proportional reasoning lands as well as it should in classrooms? And how can teachers be supported to maximise this opportunity?

If we really want all students leaving school proficient in reasoning proportionally, we need to:

• Address the sequencing – connect proportional concepts across KS3, rather than teaching them in silos.

• Teach structures not tricks – so students can apply reasoning flexibly.

• Invest in teacher development – give teachers the confidence and tools to plan for understanding.

This won’t happen overnight, but with dedication to nationwide collaboration, we can shape students’ lives for the better.

What's next?

The ambition is clear, but the hard work lies in implementation. Non-specialist teachers, retention, and curriculum design all pose challenges. What we need now is practical guidance and shared examples that make this vision real in classrooms. If we can turn this ambition into action, proportional reasoning won’t just be a curriculum priority - it will become a powerful tool every student carries with them beyond school.

The second phase of Maths Horizons will focus on providing practical resources to support problem solving, including banks of problem-solving questions and worked examples to exemplify the different structures pupils need to know and how best to teach them.

Thank you Carys Hopkin and Chloë Adams from Ark Curriculum Plus for developing the Mathematics Mastery Secondary problems and ideas mentioned in this article.

Rachel Smedley is an expert on the Maths Horizons specialist team.  

Rachel has worked in various roles in the education sector for over 15 years, including coaching and mentoring teachers to improve their pedagogy and subject knowledge to ensure excellent outcomes for students. Rachel's passion for supporting improvement in Secondary Maths led her to Ark, where she worked as a Network Lead for 8 years before moving to the Ark Curriculum Plus team to focus more on supporting schools with curriculum and assessment.