How to build a maths curriculum that connects every stage

Most maths departments do not have a curriculum problem so much as a connection problem. The Year 7 unit on fractions is usually fine. The Year 10 unit on algebraic fractions is usually fine. What is often missing is the deliberate, traceable line between the two: The line that tells you exactly how a Year 7 idea grows into a Year 10 method and what work has to happen in Year 8 and Year 9 for that growth to land.

This guide is for heads of maths and second-in-departments who want to tighten that line. It draws on the NCETM's Curriculum Prioritisation materials, mastery principles, and the realities of teaching mixed classes inside a finite timetable. It is a way of thinking about how the years fit together, with worked examples and a checklist you can take into your next department meeting.

A common pattern in struggling maths departments is that every individual unit looks reasonable on paper. The topics are covered, the resources are present, the lessons are taught. And yet at the end of Year 9 a worrying share of students cannot fluently do the things they were said to have learned in Year 7.

The usual diagnosis is that the curriculum has been built as a sequence of standalone units rather than a connected progression. Each unit hits its end point, the next time the topic appears the previous learning has decayed, and the new unit has to rebuild it from scratch.

Mastery thinking is partly an answer to this. The point is not that every child masters every topic before moving on (that is a caricature) but that the curriculum is designed so key ideas keep showing up, in deliberately chosen ways, so they are revisited and refined rather than parked. The NCETM's Curriculum Prioritisation materials make this concrete for KS3 by identifying the core ideas that earn most of the return on investment.

A connected maths curriculum tends to be organised around a small number of core ideas that appear across the years at increasing depth. Different departments draw the lines differently, but the usual suspects look something like this: Number and place value, fractions, ratio and proportion, algebraic structure, geometric reasoning, statistical thinking, and the multiplicative relationships that knit them together.

Naming these explicitly matters because it changes how units are designed. A Year 8 unit titled 'percentages' is a unit. A Year 8 unit on percentages framed as 'continuing to build multiplicative reasoning, with percentages as the vehicle' is part of a curriculum. The same lessons might be taught, but the assessment, the language, and the connections to earlier and later work are deliberately different.

Five or six core ideas, sustained across five years, will usually beat a sprawling list of fifteen. If you cannot name your core ideas from memory, the list is probably too long to be operationally useful.

Once you have the core ideas, the highest-leverage piece of curriculum work is to map vertical progression for each one across all five years. This means writing down, in plain language, what students should be able to do with the idea at each stage and how each stage builds the next.

This is the kind of document that often does not exist anywhere. Schemes of work tell you what is taught when. Specifications tell you what is assessed at the end. The bit in the middle usually lives implicitly in the heads of experienced teachers. Making it explicit is what turns a sequence of units into a coherent curriculum.

The table below shows a worked example for fractions across KS3 and KS4. The principle scales: One idea, five years, each row building the next.

Two things tend to happen when a department does this exercise. The progression for some ideas turns out to be obvious and well-supported by the existing units. The progression for other ideas (ratio and proportion is a frequent culprit) reveals that the curriculum jumps a level somewhere, expecting fluency in Year 10 that the Year 8 and Year 9 units never built. That gap is the work to do next.

If your department is rebuilding the KS3 curriculum from scratch, or doing a serious review, the NCETM's Curriculum Prioritisation materials are the most useful single resource in the maths landscape. They identify priority topics for Years 7 to 9, structured around the multiplicative and algebraic ideas that earn the most return at GCSE.

The materials are not a curriculum you can lift wholesale. They are a structured argument about what to prioritise when time is tight, with example sequences, ready-to-use tasks, and notes on common misconceptions. The honest way to use them is to read the underlying rationale and adapt to your department's situation.

Departments that adopt them in full sometimes find the pace ambitious, particularly in schools with significant prior attainment gaps. The fix is usually to slow specific sections down and build in more retrieval. The framing still earns its keep even when the timing is adjusted.

Maths misconceptions are remarkably consistent. Most teachers, given a list of ten misconceptions students will have about negative numbers, could name eight. Yet very few departments formally write the misconceptions down anywhere in the curriculum. They live in individual teachers' heads, which means new colleagues and ECTs have to rediscover them from scratch.

A curriculum that names misconceptions explicitly, by topic and by year, tends to outperform one that does not. The document does not need to be elaborate: A page per unit, listing the three or four misconceptions students typically arrive with, the diagnostic question that exposes each, and the teaching approach that addresses it. Over a couple of years this becomes one of the most useful documents in the department.

A few examples that show up almost everywhere: Students treating fractions as two separate whole numbers ('a half plus a third is two fifths'), applying additive thinking to multiplicative contexts ('the recipe serves 4, we want it to serve 6, so I add 2 to everything'), and treating algebraic letters as labels rather than variables ('3a means 3 apples'). Each has a known fix. Building the fixes into the curriculum, not just into individual lessons, is what raises the floor.

The cognitive science on spacing and retrieval is best applied at curriculum scale rather than left to individual teachers. The Education Endowment Foundation's guidance on cognitive science in the classroom highlights both, and both work better when they are baked into the structure than when they depend on improvisation.

At curriculum scale, spacing means deliberately revisiting earlier topics in later units. A Year 9 unit on simultaneous equations should not be the last time students see linear equations; that work should reappear in Year 10 and Year 11 so it is retrieved and refined over years rather than parked after a single block. Many departments now build this in with a weekly low-stakes quiz that rolls back through past topics on a deliberate schedule.

A shared department approach to the numeracy starter, with content drawn from a rolling pool of past topics, produces compound effects across the years that no individual teacher's effort can match. The upfront cost is real, but the payoff is years of steadier retention. Tools that automate the scheduling, including Cognito, can take some of the manual load off and give you cohort-level data on what is and is not sticking.

End-of-unit tests are useful but rarely tell you what you most want to know. They confirm whether the unit's specific content was learned. They are less good at telling you whether the core ideas of the curriculum are building over time, which is the bigger question for a HoD.

A stronger assessment architecture has three layers. Low-stakes retrieval embedded in lessons does the day-to-day memory work. End-of-unit assessments confirm the unit's end points. Synoptic assessments (one per year, ideally) test progression against the core ideas, using questions that pull across multiple topics. The synoptic pieces are what give you a real read on whether the curriculum is doing its job.

The most useful kind of assessment data is not the headline percentage. It is the pattern of strengths and weaknesses across the cohort, mapped to your progression maps. If Year 10 students are still struggling with the multiplicative reasoning the Year 8 map said they had reached, the fix sits in Year 8 or 9 rather than in catch-up sessions later.

A maths curriculum that only works when delivered by the most experienced teachers is not really a curriculum. It is a personal scheme of work. A genuine departmental curriculum has to be teachable by the whole team, including ECTs, trainees and the non-specialist who covers your half-timetable when someone is off.

In practice this means investing in shared resources: Worked example decks, knowledge organisers, misconception documents, model written solutions, and end-of-unit assessments with mark schemes. Fully scripted curricula often suffocate; thin outlines often produce inconsistent delivery. The middle path (a clear core, with deliberate room for adaptation) is where strong maths departments tend to land.

It also means aligning department CPD to upcoming content. If Year 9 includes a tricky unit on functions, the team should have a CPD session on the misconceptions and pedagogy a few weeks before, not generic training disconnected from the timetable.

A maths curriculum is a living document. The first version is rarely the keeper, and even mature curricula benefit from annual review. The risk is the opposite extreme: Tinkering so often that no version is taught twice in the same form and no useful data accumulates.

A workable cadence is to lock the curriculum for the year, run it as designed, and review formally at the end with the assessment data and the team's experience in hand. Identify two or three changes for the following year, document the reasoning, and run again. Over three or four cycles, the curriculum will mature into something that genuinely reflects the department's collective expertise.