England · Key Stage 2 · Ages 10–11

Year 6 maths:
what your child learns,
and where it gets hard

A parent's guide to the Year 6 maths curriculum in England — every topic, the KS2 SATs papers, and the places children most often come unstuck. Written by the people who teach it, one to one.

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The short answer

What does a child learn in Year 6 maths?

In Year 6, children in England work across ten areas of maths: number and place value, the four operations, fractions, decimals and percentages, ratio and proportion, algebra, measurement, geometry (shape, and position and direction) and statistics. Most of it is not brand new — it is earlier maths taken further, with the expectation that a child can now choose a method, work through several steps, and explain why the answer is sensible.

Three things genuinely arrive in Year 6: algebra, ratio and proportion, and long division. Everything else — fractions, decimals, percentages, area, coordinates, data — is a harder version of Year 5. That matters, because when a Year 6 child struggles it is usually not the Year 6 content that has failed. It is a Year 4 or Year 5 idea underneath it that never quite settled.

The programme of study itself groups these under nine headings — fractions, decimals and percentages sit together under one, and geometry is split into shape and into position and direction. We have separated them below because that is how parents look for them, not because the curriculum is written that way.

The national curriculum sets out the Year 6 content, but schools are only required to have taught the Year 5 and Year 6 programmes of study by the end of key stage 2 — not by the end of each year. It does not set out the order either: schools sequence the content themselves, often following a published scheme, so two children in the same year group at different schools can meet ratio in November and in March. If your child has not covered something yet, that is normal and not a sign of falling behind.

Source for everything below: the Year 6 programme of study in the national curriculum for England, published by the Department for Education. We have kept to what it actually requires rather than what tutoring sites tend to list.

The curriculum, area by area

Every topic in the Year 6 maths curriculum

What each area covers, one skill your child needs to hold on to, and the mistake we see most often when we teach it.

Number and place value

Numbers get bigger and negative numbers stop being a temperature curiosity and start being arithmetic.

  • Read, write, order and compare numbers up to 10,000,000, and say what each digit is worth
  • Round any whole number to a required degree of accuracy
  • Use negative numbers in context, and calculate intervals across zero
  • Solve number and practical problems using all of the above
Example

The temperature is −6°C at midnight and 4°C at noon. How much has it risen?

10°C. The zero has to be crossed, not jumped over.

Where it usually goes wrong Rounding "to a required degree of accuracy" is not one rule. A child who only ever rounds to the nearest 10 stalls the moment a question asks for the nearest 100,000.

The four operations

This is where the formal written methods are finished off, and where long division arrives.

  • Long multiplication: multiply numbers up to 4 digits by a 2-digit number
  • Long division and short division by a 2-digit number, interpreting remainders as a remainder, a fraction, or by rounding — whichever the question needs
  • Mental calculation, including mixed operations and large numbers
  • Common factors, common multiples and prime numbers
  • Order of operations: 2 + 1 × 3 = 5, but (2 + 1) × 3 = 9
  • Multi-step problems: decide which operation to use, and why
  • Estimation, to check whether an answer is even plausible
Example

148 children are going on a trip. Each minibus holds 18. How many minibuses are needed?

148 ÷ 18 = 8 remainder 4 — but the answer is 9 minibuses. The remainder decides it.

Where it usually goes wrong Remainders. A child who always writes "r 4" and stops has not been asked what the 4 stands for. Four leftover pencils can stay in the box; four leftover children need another minibus.

Fractions

Year 6 is the year fractions have to be secure, because ratio, percentages and probability all lean on them later.

  • Simplify fractions using common factors; use common multiples to give fractions the same denominator
  • Compare and order fractions, including fractions greater than 1
  • Add and subtract fractions with different denominators and mixed numbers
  • Multiply simple pairs of proper fractions, giving the answer in its simplest form
  • Divide a proper fraction by a whole number
  • Associate a fraction with division: 3 ÷ 8 = 0.375
Example

⅓ ÷ 2 = ⅙, and ¼ × ½ = ⅛

Dividing by 2 makes each piece smaller. Multiplying by a half does the same thing — which is exactly what confuses children.

Where it usually goes wrong Adding the tops and the bottoms. It gives 2/3 + 1/4 = 3/7, which is smaller than what you started with. Asking "is that answer bigger or smaller than 2/3?" catches it faster than any rule.

Decimals

Decimal place value extends to thousandths, and decimals start appearing inside division answers.

  • Identify the value of each digit in a number given to 3 decimal places
  • Multiply and divide by 10, 100 and 1,000, with answers up to 3 decimal places
  • Multiply one-digit numbers with up to 2 decimal places by whole numbers
  • Use written division where the answer has up to 2 decimal places
  • Round answers to a stated degree of accuracy
Example

0.4 × 2 = 0.8, and 3.75 ÷ 10 = 0.375

Digits move, the decimal point stays put — the version of the rule that survives contact with Year 7.

Where it usually goes wrong "Adding a zero" to multiply by 10. It works for whole numbers and quietly breaks the moment a decimal appears: 3.4 does not become 3.40.

Percentages

Percentages sit in two places in Year 6: knowing the equivalences, and using them to solve problems.

  • Recall and use equivalences between simple fractions, decimals and percentages, in different contexts
  • Solve problems involving the calculation of percentages — for example 15% of 360
  • Use percentages for comparison
Example

15% of 360

10% is 36, 5% is half of that (18), so 15% is 54. Reliable, and no calculator.

Where it usually goes wrong Percentage questions that are really comparison questions. "Which is the better deal, 25% off £40 or £12 off?" needs two calculations and then a judgement — children often do the first and stop.

Ratio and proportion

New in Year 6, and one of the topics parents most often tell us they cannot help with.

  • Problems where missing values are found using multiplication and division facts
  • Problems involving unequal sharing and grouping, using fractions and multiples
  • Problems involving similar shapes where the scale factor is known or can be found
  • Percentage comparison problems
Example

A recipe for 4 people uses 300 g of flour. How much for 10 people?

750 g. Find one portion first — the step children skip.

Where it usually goes wrong Reading a ratio as a fraction of the whole. In a 2:3 ratio, the first share is two fifths, not two thirds. Some schools introduce the notation a:b — the curriculum suggests it rather than requires it — but it is the thinking, not the colon, that is hard.

Algebra

Also new in Year 6, and much gentler than the word suggests — letters standing in for numbers your child already understands.

  • Use simple formulae
  • Generate and describe linear number sequences
  • Express missing number problems algebraically
  • Find pairs of numbers that satisfy an equation with two unknowns
  • Enumerate possibilities of combinations of two variables
Example

a + b = 10. List every pair of whole numbers that works.

Being systematic is the skill: 0 and 10, 1 and 9, 2 and 8… not guessing.

Where it usually goes wrong Year 6 algebra is not solving equations the way Year 8 does. If a child is being drilled on "change the side, change the sign", they are being taught the wrong year's method.

Measurement

Converting units, and the first proper area and volume formulae.

  • Convert between standard units of length, mass, volume and time, using up to 3 decimal places
  • Convert between miles and kilometres
  • Recognise that shapes with the same area can have different perimeters, and the other way round
  • Calculate the area of parallelograms and triangles
  • Calculate, estimate and compare the volume of cubes and cuboids, in cm³ and m³
  • Recognise when a formula can be used
Example

A triangle with base 8 cm and height 5 cm has area 20 cm².

Half of the rectangle it sits inside — worth seeing once, then it is never forgotten.

Where it usually goes wrong Area and perimeter swapped. The fix is not a mnemonic: ask what is being measured, the fence or the grass.

Geometry: shape, position and direction

Angle rules, parts of a circle, and coordinates in all four quadrants.

  • Draw 2-D shapes from given dimensions and angles
  • Recognise, describe and build simple 3-D shapes, including making nets
  • Compare and classify shapes by their properties and sizes, and find unknown angles in triangles, quadrilaterals and regular polygons
  • Name parts of a circle — radius, diameter, circumference — and know the diameter is twice the radius
  • Find missing angles at a point, on a straight line, and vertically opposite
  • Describe positions on the full coordinate grid, all four quadrants
  • Translate and reflect simple shapes on the coordinate plane
Example

Two angles in a triangle are 47° and 68°. The third is 180 − (47 + 68) = 65°.

The same relationship written as a = 180 − (b + c) is where geometry and algebra meet.

Where it usually goes wrong Negative coordinates. Reflecting (3, 2) in the y-axis gives (−3, 2), and children who learned coordinates in one quadrant often move the wrong number.

Statistics

A short area with two requirements, both of which turn up in the reasoning papers.

  • Interpret and construct pie charts and line graphs, and use them to solve problems
  • Calculate and interpret the mean as an average
Example

Four scores: 7, 9, 6, 10. The mean is 32 ÷ 4 = 8.

Then the harder version: three scores have a mean of 8, two of them are 7 and 9 — what is the third?

Where it usually goes wrong Pie charts are a percentage question wearing a circle. A quarter of the circle is 90° and 25% — children who have not connected those three things read the chart but cannot answer the question.

Reasoning and problem solving

Not a separate topic in the curriculum, but the thing the whole of Year 6 is aiming at — and the difference between the arithmetic paper and the two reasoning papers.

  • Choosing which operation a worded problem needs, and in what order
  • Working through several steps without losing the thread
  • Explaining a method, not just producing an answer
  • Checking whether an answer is sensible before moving on
Example

"Explain why Ali's answer cannot be correct."

Worth marks in the KS2 papers, and impossible to bluff — it needs the reasoning said out loud, regularly.

Where it usually goes wrong A child who is fluent in arithmetic but freezes on word problems does not have a maths problem. They have a translation problem, and it is fixable.

Statutory content taken from the national curriculum programme of study for Year 6 (Department for Education). Examples and the "where it goes wrong" notes are ours, from teaching the year group.

Year 5 to Year 6

What is actually new this year

Useful to know before you panic about a topic. Most of Year 6 is Year 5 taken further — only a few things start from nothing.

TopicStatus in Year 6What that means for your child
Ratio and proportionNewNo Year 5 foundation to fall back on. Expect it to feel hard for a few weeks; that is not a warning sign.
AlgebraNewLetters for unknowns, simple formulae, sequences. Gentler than it sounds, and it does not include solving equations by rearranging — that is Key Stage 3.
Long divisionNewShort division was Year 5. Long division by a 2-digit number is the Year 6 step, and it needs times tables to be automatic.
FractionsExtendedDifferent denominators, multiplying pairs of fractions, dividing by a whole number. Year 5 gaps show up here first.
PercentagesExtendedFrom recognising them to calculating with them and comparing with them.
Area and volumeExtendedRectangles were earlier. Triangles, parallelograms and the volume of cuboids are Year 6.
CoordinatesExtendedOne quadrant becomes four, so negative numbers arrive in geometry.
StatisticsExtendedPie charts and the mean are new; reading line graphs and tables is not.

Square and cube numbers, and multiplying a fraction by a whole number, are Year 5 content that Year 6 assumes and revisits — they are not new Year 6 requirements.

The tests

What are the Year 6 SATs, and how does the maths work?

At the end of Year 6, children in England sit the national curriculum tests at the end of key stage 2 — what almost everyone calls SATs. There are tests in English grammar, punctuation and spelling, English reading, and mathematics. Writing and science are teacher-assessed instead of tested. Maths is three papers: one arithmetic and two reasoning, 110 marks in total.

The tests are sat in one week in mid-May, Monday to Thursday, with maths on the last two days. Results reach schools in early July, and you should have them before the end of the summer term. Each year's exact dates are published by the Standards and Testing Agency on GOV.UK.

Results come as a scaled score between 80 and 120, not a raw mark. GOV.UK puts it plainly: 100 or more means your child is working at, or above, the expected standard for the key stage, and below 100 means they may need more support to reach it. What the score does and does not mean is set out in full on our SATs maths page.

There is a fuller guide to the papers, the scores and a term-by-term revision plan on our Year 6 SATs maths page. It is worth being clear about what the tests are for. GOV.UK gives four purposes: measuring attainment against the standards in the national curriculum, helping teachers and parents see where a pupil may need extra support, reporting publicly on school performance, and producing national and regional statistics. Your child's individual result is not published. Some secondary schools use SATs results as one input when grouping pupils, and many run their own assessments in the first term of Year 7 as well. A single week in May does not decide how a child's secondary maths goes.

The maths papers

Three papers, 110 marks

70 of the 110 marks are in the two reasoning papers, which is why practising arithmetic alone is not enough preparation.

Paper 1
Arithmetic
30 minutes, 40 marks. Calculations only, no words — fluency with the written methods, fractions and decimals.
Paper 2
Reasoning
40 minutes, 35 marks. Word problems, multi-step questions and "explain your answer" questions across the whole curriculum.
Paper 3
Reasoning
40 minutes, 35 marks. Same format as Paper 2, sat the following day.

Paper structure, timings and marks as set out in the key stage 2 mathematics test framework and the published test materials (Standards and Testing Agency). Past papers from previous years are published free on GOV.UK — you do not need to buy them.

Where children get stuck

The Year 6 maths difficulties we see most

Not every child struggles with these, and a wobble in one topic is not a problem. What to look for, one thing you can try at home, and when it is worth getting help.

Multi-step word problems

The place we most often see marks lost in the reasoning papers. The arithmetic is usually within reach; the difficulty is working out what the question is asking and in what order.

Try this at home

Before your child calculates anything, ask: "What are you being asked to find? What do you need first?"

Two questions, thirty seconds, and no maths from you.

Where it usually goes wrong If your child can do the same sums correctly when they are written as bare calculations but not when they are wrapped in a sentence, that is a reasoning gap, and talking it through is usually the thing that shifts it.

Fractions with different denominators

Adding and subtracting fractions with unlike denominators is where we most often see an earlier gap in equivalent fractions surface.

Try this at home

Cut something into halves and quarters. Ask which is bigger, 2/3 or 3/4, and how they know.

If the answer is "the one with the bigger number", the gap is in Year 4 equivalence, not Year 6 addition.

Where it usually goes wrong Worth support when a child can follow a worked example but cannot start one alone. That gap does not close with more worksheets of the same kind.

Long division

It is one of the most procedurally demanding things in the primary curriculum: several steps, each depending on the last, with a times table lookup inside every one.

Try this at home

Check the times tables first. If 7 × 8 takes more than two seconds, long division will be exhausting.

Fluency underneath makes the method feel manageable rather than impossible.

Where it usually goes wrong Errors scattered randomly through the steps usually mean recall, not method. Errors in the same place every time mean the method — and a method error is usually far quicker to put right than a fluency one.

Ratio, proportion and percentages

New content, no earlier scaffolding, and it arrives in the same year as SATs. Parents often tell us this is where they stop being able to help.

Try this at home

Use a recipe. Double it, then make it for 6 people when it serves 4.

That second question is a proportion problem, and it is the one children find hard.

Where it usually goes wrong If ratio was covered in a fortnight and moved on from, a child can look fine on the practice questions and be lost by the test. It is a topic that rewards going back to.

Confidence, and speed

Some children in Year 6 can do the maths and still do badly, because they have decided they are bad at it, or because they have learned that finishing first is what counts.

Try this at home

Praise the method, not the speed: "how did you work that out?" rather than "well done, that was quick".

It sounds small. Over a term it changes what a child thinks maths is.

Where it usually goes wrong A child who says "I'm just not a maths person" in Year 6 can carry that into Year 7. This is the one we would act on early, before the content gets harder.

Pressure around the tests

Year 6 children pick up more about SATs than adults expect — from school, from each other, and from us.

Try this at home

Be accurate rather than reassuring: the tests check what has been learned, and they help their next school know how to help.

Children handle a true explanation better than a vague one.

Where it usually goes wrong Regular tears, stomach aches on test-practice days, or refusal to try are worth raising with the class teacher first — before anyone books tutoring.

At home

How to help with Year 6 maths without teaching it

You do not need to remember long division to be useful. Most of what helps is conversation, not instruction.

How we help

How ClassArc supports a Year 6 student

Live one-to-one classes, taught to the England national curriculum, with the same teacher every week.

We find the gap first

A Year 6 child struggling with fractions is usually missing something from Year 4 or 5. The first classes go looking for that, because teaching Year 6 content on top of a hole does not hold.

The same teacher, every week

One teacher who knows your child has already seen which topics get quietly avoided. Nobody spends the first ten minutes working out what happened last week.

Lessons follow the national curriculum

We teach the Year 6 programme of study for England, and we work with what your child's school is covering rather than running a separate syllabus alongside it.

Reasoning, not just answers

Two of the three maths papers are reasoning papers. In class your child is asked to explain the method out loud, every time — which is also how we spot a misunderstanding early.

Our own classroom, not a video call

A shared worksheet you both write on, a shared whiteboard, and answers that sync live. The teacher sees the working, so a wrong step gets caught before it becomes a wrong habit.

Preparation that is not just past papers

Practice questions in the KS2 style, worked properly, with the mark scheme open so a child learns where the working earns credit. The published papers are free to anyone on GOV.UK.

Inside a class

What a Year 6 ClassArc class looks like

Fifty-five minutes, one teacher, one child, in the same shape each week so nothing about the class is a surprise.

“

A gap in Year 6 fractions does not stay in Year 6. It turns up again in Year 8 algebra, wearing a different hat.

Why we go backwards first
i
🔍

Pick up where you left off

Last week's work and marked homework are already open. The teacher checks what stuck before adding anything new.

ii
✏️

Teach it properly

The concept, worked together on the shared worksheet — your child writing, the teacher watching each step rather than the final answer.

iii
🧩

Then they try it

Independent questions, then a reasoning question: explain it, or say why an answer cannot be right. This is where SATs marks are won.

iv
📌

Close the loop

What was solid, what needs another go, and homework aimed at exactly that. Reviewed at the start of the next class.

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Year 6 to Year 7

How Year 6 maths prepares a child for secondary school

Secondary maths does not restart. Year 7 assumes the Year 6 content is in place and moves quickly — algebra becomes solving equations, ratio becomes proportional reasoning and scale, fractions turn up inside almost everything, and negative numbers stop being a special case.

The areas that carry forward hardest are the ones that were new this year: ratio and proportion, algebra, and secure fractions, decimals and percentages. A child who leaves Year 6 shaky on those is not behind on day one of Year 7, but they are working uphill by Christmas — which is why the summer between the two years is a good time to close a gap, with no homework and no tests competing for the attention.

Secondary schools often group pupils for maths at some point in Year 7. SATs results may be one of the things they look at, and schools commonly run their own assessments in the first term as well. Arriving able to explain a method is worth more than arriving with a number.

ClassArc teaches the same child through both years, with the same teacher — Key Stage 2 into Key Stage 3 and on to GCSE. Nothing has to be handed over. What Year 7 actually looks like, and how sets are decided, is on our Year 7 maths page; if the gap is earlier, the Year 5 page shows what Year 6 assumes was already secure.

Next

Where to go from here

Three things parents usually want after this page.

Year 6 SATs maths

The three papers, what each one tests, where to download the real papers free, and a term-by-term revision plan.

Read the SATs guide

Year 7 maths

What changes at secondary school, why there is no statutory Year 7 curriculum, and how sets and CATs work.

What comes next

Key Stage 2 maths, Years 3 to 6

The whole key stage in one place: what each year adds, the two national checks, and the thread that runs through all four years.

The KS2 overview

UK pricing in pounds

Every plan, per class and in total, with no joining fee and no materials fee. The first class is free.

See UK pricing

Year 6 maths questions

What topics are covered in Year 6 maths?
Number and place value to 10,000,000; the four operations including long multiplication and long division; fractions, decimals and percentages; ratio and proportion; algebra; measurement including area and volume; geometry, angles and coordinates in four quadrants; and statistics, meaning pie charts, line graphs and the mean. Every one of these is set out in the national curriculum programme of study for Year 6 in England.
Is Year 6 maths difficult?
It is a step up, but a manageable one for most children. Ratio, algebra and long division are genuinely new, and the rest is Year 5 content taken further. The part children find hardest is not any single topic — it is multi-step problems that need several ideas at once, which is exactly what the reasoning papers test.
What should my child know by the end of Year 6?
By July a child working at the expected standard can use the formal written methods for all four operations, work confidently with fractions, decimals and percentages, solve ratio and proportion problems, use simple formulae, calculate area and volume, find missing angles, plot coordinates in four quadrants, and read a pie chart or line graph — and can explain how they got an answer, not only produce one.
Does Year 6 maths include algebra?
Yes. Year 6 algebra covers using simple formulae, generating and describing linear number sequences, expressing missing number problems algebraically, finding pairs of numbers that satisfy an equation with two unknowns, and listing combinations of two variables. It does not include solving equations by rearranging — that is Key Stage 3.
Does Year 6 maths include ratio?
Yes, and it is new this year. Children solve problems involving the relative sizes of two quantities, unequal sharing and grouping, similar shapes with a scale factor, and percentage comparison. The notation a:b is suggested rather than required at this stage, and the reasoning matters more than the notation.
Does Year 6 cover fractions, decimals and percentages?
All three, and they are treated as connected rather than separate. Children add and subtract fractions with different denominators, multiply pairs of proper fractions, divide a fraction by a whole number, work with decimals to three places, and recall equivalences between simple fractions, decimals and percentages — then use those equivalences to solve problems such as finding 15% of 360.
When are the Year 6 SATs?
In one week in mid-May of Year 6, Monday to Thursday, with the three maths papers on the last two days. Results reach schools in early July and parents receive them before the end of the summer term. The exact dates for each year are on GOV.UK.
How is the SATs maths score reported?
As a scaled score between 80 and 120. A score of 100 or more means your child is working at or above the expected standard; below 100 means they may need more support to reach it. The number of raw marks needed for a scaled score of 100 changes slightly each year, because the papers vary in difficulty.
Do Year 6 SATs decide which set my child is in at secondary school?
Not on their own. The secondary school can see the results and uses them to plan support, and some schools consider them when grouping pupils. Many also run their own assessments during the first term of Year 7. The tests are a snapshot of where a child is in May, not a decision about the next five years.
How can I help my child with Year 6 maths at home?
Ask them to explain their method rather than checking answers; use shopping and cooking for percentages, ratio and proportion; estimate before calculating; and go back to the earlier year when something will not stick, because a Year 6 problem is usually a Year 4 or 5 gap. Short sessions work better than long ones, particularly in the run-up to the tests in May.
Do you cover SATs preparation?
Yes, as part of teaching the Year 6 curriculum properly rather than as a separate crammer. We work on the topics that carry the most marks, practise reasoning questions in the KS2 style, and if your child's school sends past papers home we go through them in class. The papers themselves, what each one tests, and a term-by-term revision plan are on our Year 6 SATs maths page.
How can a tutor help a Year 6 child?
One to one, a teacher can find the specific earlier gap causing the current problem — something a full class cannot easily do — and can ask your child to explain their thinking every few minutes. That matters in Year 6 because two of the three maths papers are reasoning papers, and because the year ends with a transition into secondary maths that assumes all of this is secure.
Is my child too far behind for tutoring to help before May?
It depends what the gap is, and we would rather say so honestly after a class than promise a result. The free first class is 55 minutes of actual teaching, and at the end we will tell you what we found and whether weekly classes are the right answer. Sometimes the honest answer is that school support plus a specific fix at home is enough.
What does ClassArc cost for a Year 6 student?
Year 6 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, and classes you have paid for but not used are refunded. Full details are on the UK pricing page.
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