England · Key Stage 3 · Ages 11–12

Year 7 maths:
what changes when
secondary school starts

A parent's guide to Year 7 maths, the first year of key stage 3 — what your child will meet, why no two schools teach it in the same order, how sets and CATs actually work, and the places a good primary mathematician suddenly wobbles.

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The short answer

What does a child learn in Year 7 maths?

Year 7 is the first year of key stage 3. Most children spend it consolidating the number work from primary school — place value, negative numbers, fractions, decimals and percentages — while meeting three things properly for the first time: algebra with letters, ratio written as a:b, and probability. Geometry moves from finding angles to stating the reason, and statistics adds the median, the mode and the range to the mean.

There is an important difference from primary school. The national curriculum for England sets out maths year by year for key stages 1 and 2, but for key stage 3 it publishes one programme of study for Years 7, 8 and 9 together. There is no statutory Year 7 curriculum. The Department for Education has published a non-statutory sample framework that suggests a year-by-year order, but schools are not required to follow it: each secondary school decides what to teach in which year and publishes its own scheme, so one child can meet probability in October and another the following June. A website selling you "the Year 7 maths curriculum" is describing one scheme of work, not a national requirement.

That said, the key stage 3 programme of study is built on the assumption that key stage 2 is secure, and the DfE's sample framework, like most schemes we see, begins Year 7 with number, where Year 6 left off. What follows is the key stage 3 content, area by area, with a note on what tends to arrive in Year 7 — hedged, because your child's school will have its own order.

Source: the key stage 3 programme of study in the national curriculum for England, published by the Department for Education.

The curriculum, area by area

Every area of Year 7 maths and the rest of key stage 3

The six areas of the key stage 3 programme of study. "Usually early" means the schools we work with tend to start there in Year 7, and the DfE's sample framework does too; it is not a rule.

Number

Primary number, made rigorous. Negative numbers become arithmetic, fractions and decimals are used interchangeably, and powers and roots appear.

  • Place value for decimals, measures and integers of any size; ordering with the symbols =, ≠, <, >, ≤, ≥
  • Primes, factors, multiples, highest common factor, lowest common multiple and prime factorisation
  • The four operations with integers, decimals, fractions and mixed numbers — positive and negative
  • The priority of operations, including brackets, powers, roots and reciprocals
  • Integer powers and their roots; standard form; rounding to decimal places and significant figures
  • Percentages as fractions, decimals and multipliers, including percentage change and percentages over 100%
  • Using a calculator properly — taught and used routinely for the first time
Usually early

(−3) × (−4) = 12, and 7 − (−2) = 9

Negative numbers were an interval on a thermometer in Year 6. In Year 7 they are numbers you multiply.

Where it usually goes wrong Fractions. Every Year 7 topic quietly assumes them — ratio, percentages, algebra, probability — and a child who arrived without them finds out in all of those places at once.

Algebra

Year 6 used letters for missing numbers. Key stage 3 makes algebra a language of its own, and Year 7 usually starts with the grammar.

  • Notation: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b
  • Substituting numbers into expressions and formulae
  • Simplifying: collecting like terms, multiplying over a bracket, taking out common factors
  • Solving linear equations in one unknown, including ones that need rearranging
  • Coordinates in all four quadrants; graphs of linear functions and y = mx + c
  • Sequences: term-to-term rules, position-to-term rules, and the nth term
Usually early

Solve 3x + 5 = 20

x = 5. The method — undo the +5, then undo the ×3 — is the same one that solves everything up to GCSE.

Where it usually goes wrong Reading 3a as "three and a". A child who thinks 3a + 2b is 5ab has not been told that 3a means 3 × a, and will get every simplifying question wrong for a term.

Ratio, proportion and rates of change

Year 6 ratio was sharing sweets. Key stage 3 turns it into notation, scale, percentage change and speed.

  • Ratio notation a:b, and reducing a ratio to its simplest form
  • Dividing a quantity in a given ratio, part:part and part:whole
  • Scale factors, scale diagrams and maps
  • Percentage increase and decrease, and finding the original value
  • Direct and inverse proportion
  • Compound units: speed, unit pricing, density
Usually early

Share £60 in the ratio 2:3

£24 and £36. Five parts, £12 a part. The step children skip is finding one part.

Where it usually goes wrong Treating a 2:3 ratio as 2/3. The first share is two fifths of the whole, and a child who does not see the five parts will keep getting fractions-of answers to ratio questions.

Geometry and measures

From measuring to reasoning: angle rules that have to be stated, constructions with compasses, and formulae for circles, trapezia and prisms on top of the ones from Year 6.

  • Perimeter and area of triangles, parallelograms and trapezia; volume of cuboids and other prisms
  • Circumference and area of circles
  • Angles at a point, on a straight line, vertically opposite; alternate and corresponding angles on parallel lines
  • Angle sums of triangles and polygons, and the properties of quadrilaterals
  • Ruler and compass constructions: perpendicular bisector, angle bisector
  • Translations, rotations, reflections and enlargements
  • Pythagoras' theorem and, later in the key stage, trigonometry in right-angled triangles
Usually early

Two angles in a triangle are 52° and 71°. Find the third, and give the reason.

57°, because angles in a triangle sum to 180°. The reason is now part of the answer, and part of the marks.

Where it usually goes wrong "Because it looks like it." Secondary geometry stops accepting the diagram as evidence, and a child used to measuring finds that a strange rule.

Probability

Entirely new at key stage 3 — nothing in the primary curriculum covers it. Usually short, and usually enjoyed.

  • The language of chance and the 0 to 1 probability scale
  • Probabilities of all outcomes summing to 1
  • Listing outcomes systematically, with tables, grids and Venn diagrams
  • Sample spaces for single and combined events, and theoretical probability
Usually later in Year 7

Two coins are flipped. What is the probability of two heads?

¼. Listing HH, HT, TH, TT is the whole skill — and it is why fractions matter here too.

Where it usually goes wrong Writing a probability as a ratio (1:4) or a percentage ("25") when the question asked for a fraction. Notation counts in a way it did not in primary.

Statistics

The mean was Year 6. Key stage 3 adds the other averages and the idea of spread, and starts asking what a chart can and cannot tell you.

  • Mean, median, mode and range, and choosing between them
  • Frequency tables, bar charts, pie charts, and vertical line charts for grouped data
  • Scatter graphs and relationships between two variables
  • Describing and comparing distributions
Usually early

Scores: 3, 7, 7, 9, 14. Mean 8, median 7, mode 7, range 11.

Four different numbers describing the same five, and a question about which one is fair.

Where it usually goes wrong Median found without sorting first. The data is always given unsorted, on purpose.

Content taken from the key stage 3 programme of study (Department for Education), which covers Years 7 to 9 together. The "usually early" notes are our observation of how schools commonly sequence it, not a curriculum requirement. Your child's school publishes its own year-by-year scheme.

Year 6 to Year 7

What actually changes at secondary school

The content overlaps more than parents expect. What changes is the rigour, the pace, and what counts as an answer.

AreaEnd of Year 6Key stage 3
AlgebraMissing numbers, simple formulae, pairs that satisfy an equationNotation, simplifying, solving equations that need rearranging, straight-line graphs
RatioSharing problems, similar shapes, percentages of amountsa:b notation, simplest form, dividing in a ratio, percentage change, proportion, speed
Negative numbersCounting across zero, intervalsAdding, subtracting, multiplying and dividing with them
ProbabilityNot in the curriculumNew: the probability scale, sample spaces, combined events
StatisticsThe mean; pie charts and line graphsMean, median, mode, range; grouped data; scatter graphs
GeometryAngle facts used to find missing anglesAngle facts stated as reasons; parallel lines; constructions; formulae for circles and prisms
CalculatorsNot allowed in any KS2 testTaught and used, alongside non-calculator work
What counts as an answerMostly the right number, with method marks on some longer questionsThe number, the method and the reason, with marks for each

The curriculum rows are from the national curriculum programmes of study; the last two rows are ours. Which key stage 3 items your child meets in Year 7 rather than Year 8 depends on the school.

Sets and CATs

Sets, CATs, and the first term of Year 7

The large majority of English secondary schools put pupils into sets for maths at some point — the Education Endowment Foundation's evidence summary on setting says so — and Year 7 is where it usually starts. How they decide varies. Some use the key stage 2 SATs results the primary school passes on. Some run a baseline maths test in the first weeks. Many use a cognitive abilities test such as CAT4, which its publisher GL Assessment says is used by over half of UK secondary schools; it is a reasoning test rather than a maths test, taken early in the autumn term. Schools that use more than one of these cross-reference them, and GL's own case study describes a school giving the KS2 result more weight where the two disagree.

Two things are worth knowing. Sets move. A first-term placement is a starting point, and most schools review sets during the year — ask when yours does. And CATs are explicitly designed to be taken without preparation — the publishers say so — so tutoring "for the CAT" is not a thing worth buying. What is worth having, before September, is secure fractions, place value and negative numbers, because those are what a baseline maths test checks and what every Year 7 topic assumes.

Research from UCL's Institute of Education (Connolly and colleagues, British Educational Research Journal, 2019) looked at over 9,000 Year 7 pupils in 46 English schools and found nearly a third sitting in a different maths set from the one a ranking on key stage 2 scores alone would have put them in. That is not the same as saying the placements were wrong — schools use more than the SATs, and the study's method was later debated in the same journal — but it does show that set placement is an estimate. If your child's feels wrong, ask the school what it was based on and when it is reviewed.

Where children wobble

The Year 7 maths difficulties we see most

A child who was fine in Year 6 can wobble in Year 7 without anything being wrong. What to look for, one thing to try, and when to get help.

Algebra notation

The single most common Year 7 confusion: what 3a, ab and a² actually mean. Everything in algebra sits on top of it.

Try this at home

Ask: "If a is 5, what is 3a? What is a²? What is 2a + a?"

15, 25 and 15. If any of those needs a long pause, the notation has not landed yet.

Where it usually goes wrong Worth fixing straight away. A child who reaches the equations unit with shaky notation will find every method looks like magic.

Negative numbers

Year 6 crossed zero on a number line. Year 7 subtracts a negative and multiplies two of them, and the rules feel arbitrary until they are understood.

Try this at home

Use money: "You have £7 and owe £3. Someone cancels the debt. What are you worth now?"

£10 — and that is 7 − (−3) = 10 in a sentence.

Where it usually goes wrong "Two minuses make a plus" recited without understanding. It works for multiplying and fails for adding, and a child using it as a rule will get −3 + (−4) wrong.

Fractions coming back everywhere

A Year 6 fractions gap that was survivable in primary school shows up in Year 7 inside ratio, percentages, probability and algebra all at once.

Try this at home

"What is 3/4 of 60? What is 3/4 as a decimal and a percentage?"

45, 0.75, 75%. Moving between the three forms is the Year 7 skill, and most of KS3 leans on it.

Where it usually goes wrong If equivalent fractions are the problem, go back to them rather than pressing on. In a one-to-one class it is a short, bounded job, and it unlocks four topics at once.

Reasons, not just answers

Secondary maths starts giving marks for the method and the justification. A child used to being right is now asked to say why, in writing, in the right words.

Try this at home

When homework has a geometry question, ask them to say the angle fact out loud before writing anything.

"Angles on a straight line add to 180 degrees" is worth a mark on its own.

Where it usually goes wrong Full marks at primary school, half marks at secondary for the same understanding. It is usually a habit, not a maths problem.

Pace, and the homework platform

Topics change weekly, homework is often online and self-marking, and a child who fell behind in week three can be quietly lost by half term without anyone noticing.

Try this at home

Ask what this week's topic is called, in the school's own words, and whether the homework felt like the lesson.

If the answers are "don't know" and "no", that is the signal, not the homework score.

Where it usually goes wrong Homework that is finished but not understood. Where a platform allows unlimited retries, a completed task proves persistence rather than learning.

The confidence dip

Top of the class in a primary school of 30 and middle of a secondary year of 200 feels like falling, even when nothing has changed.

Try this at home

Talk about the set as a starting point, not a verdict, and ask the school when it is reviewed.

Children hear "set 3" as a permanent description of themselves. It is neither.

Where it usually goes wrong "I used to be good at maths." Said in Year 7, it is worth acting on in Year 7, because Year 8 adds content on top and the story hardens.

At home

How to help with Year 7 maths without knowing it yourself

The maths is harder to help with than it was. The support is not.

How we help

How ClassArc supports a Year 7 student

Weekly one-to-one classes taught to the England national curriculum, with the same teacher from the first class.

We follow the school's order

Since nothing is set year by year at key stage 3, we ask the school what it is teaching and when, and slot in alongside it.

The transition gap, closed first

Fractions, place value, negative numbers, times tables. If any of those arrived from Year 6 unsteady, the first classes fix them, because every Year 7 topic assumes them.

The same teacher from Year 6

Wherever we can, a child who was with us in primary keeps the same teacher through the transition, so nothing about the way they learn has to be discovered again by someone new.

Reasons, written down

Every answer in class comes with its method and its reason, in the form secondary marking expects. It is a habit, and habits are built weekly.

No promises about sets

Set movement is not something we can promise. What we can give you, every term, is a clear account of what your child can and cannot yet do.

It runs through to GCSE

Key stage 3 is the foundation of GCSE, and the same teacher can carry on into Years 9, 10 and 11 wherever we can arrange it.

Inside a class

What a Year 7 ClassArc class looks like

One teacher, one child, 55 minutes, built around what school did that week.

“

A method half understood in Year 7 becomes a lost mark in Year 11. We close the loop the same week.

Why the loop matters
i
🔍

What did school do this week?

The class starts from the school's current topic and the marked homework, so what we teach lands on what they are hearing in lessons.

ii
✏️

Teach the idea, not the trick

Built up on the shared worksheet, with the reason asked for before the answer and every line visible as it is written.

iii
🧩

Practice with reasons

Questions alone, each with the method and the reason written the way secondary marking wants them.

iv
📌

Next week set up

A record of what landed and what did not, with homework aimed squarely at the second, marked before you next meet.

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Year 7 to GCSE

Where Year 7 maths leads

Key stage 3 is not a separate subject from GCSE. Key stage 3 and key stage 4 are two halves of one syllabus — the key stage 3 page sets out how they fit together — and much of the foundation-tier content is first taught between Year 7 and Year 9. The algebra started in Year 7 is the algebra of the GCSE papers; the ratio is the same ratio.

This is why Year 7 gaps are worth taking seriously without panicking about them. A child who leaves Year 7 fluent in fractions, secure in algebraic notation and used to giving reasons has most of what Years 8 and 9 will build on. A child who leaves it having learned to survive each unit and forget it will meet all of it again in Year 10, with less time.

When your child reaches Year 9 the choice of tier and exam board starts to matter; our GCSE maths page explains how that works and what changes.

Next

Where to go from here

Useful next steps for a Year 7 parent.

Year 6 maths curriculum

What your child was meant to arrive with. Useful for spotting which foundation is the shaky one.

What Year 6 covered

Year 8 maths

Equations, percentages as multipliers and circles — and the year gaps most easily go unnoticed.

What comes next

Key Stage 3 maths

Years 7 to 9 in one place, why every school's order differs, and how it leads into GCSE.

The KS3 overview

GCSE maths tutor

Where key stage 3 leads: tiers, exam boards, and how we teach Years 10 and 11.

GCSE tutoring

Year 7 maths questions

What topics are covered in Year 7 maths?
It depends on the school, because the national curriculum sets one programme of study for the whole of key stage 3 rather than a Year 7 list. Schools commonly begin Year 7 with number (place value, negative numbers, fractions, decimals, percentages), the basics of algebra (notation, simplifying, solving simple equations), ratio, angles and area, averages, and often a first unit on probability. The full key stage 3 content covers number, algebra, ratio and proportion, geometry and measures, probability and statistics.
Is there an official Year 7 maths curriculum?
Not a statutory one. The national curriculum for England is set out year by year for key stages 1 and 2 only; for key stage 3 there is a single programme of study covering Years 7, 8 and 9. The Department for Education has published a non-statutory sample framework that suggests a year-by-year order, but each school decides its own and publishes its own scheme. Websites that offer a "Year 7 curriculum" are describing one scheme, not a national requirement.
Is Year 7 maths harder than Year 6?
The content overlaps more than parents expect — much of Year 7 revisits primary number. What changes is the rigour: algebra with letters, negative-number arithmetic, ratio notation, and marks for methods and reasons rather than only answers. The pace is faster and the homework is more independent. In our experience the adjustment is harder than the maths.
What is new in Year 7 maths?
Probability is entirely new; nothing in the primary curriculum covers it. Algebra becomes a language rather than missing-number puzzles. Ratio gets its notation. Negative numbers become arithmetic. Statistics adds the median, mode and range. And a calculator is taught and used routinely for the first time.
How are Year 7 maths sets decided?
It varies by school. Some use the key stage 2 SATs results, some run their own baseline test in September, and many use a cognitive abilities test such as CAT4, often cross-referenced with the KS2 result. Most schools review sets during the year and children move. Ask the school what its placement was based on and when it is next reviewed.
What are CATs, and should my child prepare for them?
Cognitive abilities tests, most commonly CAT4, are reasoning tests some secondary schools give in the first weeks of Year 7 to help with setting and to spot pupils whose scores do not match their SATs. The publishers say they are designed to be taken without preparation. Secure maths foundations help far more than practising the test.
Does Year 7 maths use a calculator?
Yes. Calculators are not allowed in any key stage 2 test, and the national curriculum says they should only be introduced near the end of key stage 2 once written and mental arithmetic are secure; the key stage 3 programme of study then includes using a calculator and other technology accurately and interpreting the results. Schools teach both calculator and non-calculator methods, as GCSE has both kinds of paper.
My child was good at maths in primary school and is struggling in Year 7. Why?
Usually one of three things: a fractions or place-value gap that primary school could work around and secondary cannot; algebra notation that has not landed, so every algebra lesson looks like magic; or the transition itself — a bigger year group, a set placement that feels like a verdict, and homework that is done but not understood. All three are fixable, and the sooner the better.
How can I help with Year 7 maths if I cannot do it myself?
You do not need to. Ask what the week's topic is called, ask your child to explain one homework question to you, ask "how do you know?" when they give an answer, and keep the fractions and times tables sharp. Find out how sets work at the school so a placement does not feel permanent.
How can a tutor help a Year 7 child?
One to one, a teacher can find the primary-school gap that secondary maths is exposing and close it while the school moves on, then work alongside the school's own scheme so the tutoring lands on what your child is hearing in lessons. Year 7 is also when the habit of giving reasons is built, and that habit is worth marks all the way to GCSE.
What does ClassArc cost for a Year 7 student?
Year 7 sits in our Years 1–8 band, from £11 per 55-minute one-to-one class on the largest plan. Nothing is charged for joining or for materials. Full details are on the UK pricing page.
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