England · Key Stage 2 · Ages 9–10

Year 5 maths:
the year the numbers
get big

A parent's guide to the Year 5 maths curriculum in England — every topic, what is genuinely new, the places children come unstuck, and why this is the year with the most room to fix a gap. Written by the people who teach it, one to one.

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The short answer

What does a child learn in Year 5 maths?

In Year 5, children in England work with numbers up to a million, finish the formal written methods for addition, subtraction and multiplication, and meet a run of ideas for the first time: percentages, square and cube numbers, prime numbers, mixed numbers, decimals to three places, and angles measured in degrees. Fractions go from something you shade in to something you calculate with.

Year 5 is the first year of upper key stage 2. The national curriculum says the focus of these two years is extending the number system to larger numbers and building the connections between multiplication, division, fractions, decimals, percentages and ratio — the equipment a child needs for Year 6, the SATs, and secondary school.

There is no national test in Year 5. That makes it the year with the most room: the times tables check was Year 4, the SATs are Year 6, and nothing in between is being measured. A gap found now can be fixed without anything else competing for the time.

The curriculum sets out the content, not the order. Schools sequence it themselves, often following a published scheme, and they are only required to have covered the Year 5 and Year 6 programmes of study by the end of key stage 2. If your child has not met percentages yet in the spring term, that is normal.

Source for everything below: the Year 5 programme of study in the national curriculum for England, published by the Department for Education.

The curriculum, area by area

Every topic in the Year 5 maths curriculum

What each area covers, the skill to hold on to, and the mistake we see most when we teach it.

Number and place value

Numbers to at least a million, and rounding to any place from the nearest 10 to the nearest 100,000.

  • Read, write, order and compare numbers to at least 1,000,000, and say what each digit is worth
  • Count forwards or backwards in steps of powers of 10 from any number
  • Interpret negative numbers in context and count through zero
  • Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 or 100,000
  • Read Roman numerals to 1,000 (M) and recognise years written in them
Example

Round 347,562 to the nearest 10,000.

350,000. The digit that decides it is the 7, not the 5 — children look at the wrong one.

Where it usually goes wrong Six-digit numbers read aloud with the groups muddled: "three hundred and forty-seven thousand, five hundred and sixty-two" needs the word thousand in the middle, and children who are not sure what the first group is worth leave it out.

Addition and subtraction

The column methods, now with numbers of more than four digits, and the habit of checking an answer by rounding.

  • Add and subtract whole numbers with more than 4 digits using columnar methods
  • Add and subtract mentally with increasingly large numbers
  • Use rounding to check answers and decide how accurate an answer needs to be
  • Solve multi-step problems, deciding which operations and methods to use and why
Example

A stadium holds 54,200. 37,865 tickets are sold. How many are left?

16,335 — and an estimate first (54,000 − 38,000 ≈ 16,000) tells you whether to trust it.

Where it usually goes wrong Exchanging across a zero. 54,200 − 37,865 needs a borrow through the two zeros, and that is where column subtraction most often falls over.

Multiplication and division

The biggest area in Year 5. Long multiplication arrives, along with factors, multiples, primes, squares and cubes.

  • Identify multiples and factors, including all the factor pairs of a number and common factors of two numbers
  • Know the words prime, prime factor and composite; tell whether a number up to 100 is prime; recall the primes up to 19
  • Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication
  • Divide numbers up to 4 digits by a one-digit number using short division, interpreting remainders for the context
  • Multiply and divide whole numbers and decimals by 10, 100 and 1,000
  • Recognise and use square and cube numbers and the notation ² and ³
  • Solve problems involving scaling by simple fractions and simple rates
Example

98 ÷ 4

The curriculum's own example: 24 r 2, or 24½, or 24.5, or about 25 — the context decides which is the answer.

Where it usually goes wrong Long multiplication done with the times tables looked up rather than known. The method is fine; every lookup is another chance to slip, and the whole thing takes far longer than it should.

Fractions

Fractions stop being pictures and become numbers you can order, add, subtract and multiply.

  • Compare and order fractions whose denominators are all multiples of the same number
  • Identify, name and write equivalent fractions, including tenths and hundredths
  • Recognise mixed numbers and improper fractions and convert between them
  • Add and subtract fractions with the same denominator, and with denominators that are multiples of the same number
  • Multiply proper fractions and mixed numbers by whole numbers, supported by diagrams
  • Read and write decimals as fractions: 0.71 = 71/100
Example

2/5 + 4/5 = 6/5 = 1 1/5

The curriculum's example. Adding the fifths does not change the fifths — and an answer bigger than 1 is written as a mixed number.

Where it usually goes wrong Adding the denominators: 2/5 + 4/5 = 6/10. It looks plausible and it is smaller than one of the numbers being added, which is the tell.

Decimals and percentages

Thousandths arrive, decimals go to three places, and percentages appear for the first time.

  • Recognise and use thousandths and relate them to tenths, hundredths and decimals
  • Round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
  • Read, write, order and compare numbers with up to 3 decimal places
  • Recognise the % symbol and know that per cent means parts per 100
  • Write percentages as a fraction with denominator 100 and as a decimal
  • Know the percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25
Example

Which is bigger, 0.35 or 0.4?

0.4 — because 0.4 is 0.40. Children who see "35 is more than 4" have a place value gap, not a decimals gap.

Where it usually goes wrong Treating a decimal as two whole numbers either side of a dot. It survives until the numbers have different lengths, then it breaks in public.

Measurement

Converting between units, perimeter of composite shapes, area of rectangles, and the first look at volume.

  • Convert between metric units: km and m, cm and m, cm and mm, g and kg, l and ml
  • Know approximate equivalences between metric units and common imperial units such as inches, pounds and pints
  • Measure and calculate the perimeter of composite rectilinear shapes
  • Calculate and compare the area of rectangles in cm² and m², and estimate the area of irregular shapes
  • Estimate volume, for example with 1 cm³ blocks, and capacity
  • Solve problems converting between units of time, and money and measure problems using decimals
Example

A rectangle is 12 cm by 7 cm. Perimeter and area?

Perimeter 38 cm, area 84 cm². Different questions, different units — the units are the clue.

Where it usually goes wrong Converting the wrong way. 3.5 km is 3,500 m, but a child who "moves the point" without knowing why gets 35 m or 0.35 m and does not notice.

Geometry: shape, position and direction

Angles become numbers. Children measure and draw them in degrees, and use the facts about a full turn and a straight line.

  • Identify 3-D shapes, including cubes and cuboids, from 2-D representations
  • Know angles are measured in degrees; estimate and compare acute, obtuse and reflex angles
  • Draw given angles and measure them with a protractor
  • Angles at a point add to 360°; angles on a straight line add to 180°; other multiples of 90°
  • Use the properties of rectangles to find missing lengths and angles
  • Distinguish regular and irregular polygons by reasoning about equal sides and angles
  • Reflect and translate shapes, and know the shape itself has not changed
Example

Two angles on a straight line: one is 115°. What is the other?

65°. The fact is easy; the skill is spotting that "on a straight line" is the fact you need.

Where it usually goes wrong Reading the wrong scale on the protractor. A 65° angle comes out as 115° and the child does not see the problem because both numbers are on the tool.

Statistics

Short, and mostly about reading: line graphs, tables and timetables.

  • Solve comparison, sum and difference problems using information in a line graph
  • Complete, read and interpret information in tables, including timetables
Example

The 8:42 train arrives at 9:17. How long is the journey?

35 minutes. Timetable questions are time questions wearing a grid.

Where it usually goes wrong Reading a line graph at the label instead of between the labels. Most questions live between the gridlines.

Reasoning and problem solving

Not a topic in the curriculum, but the expectation behind every one of the topics above — and the thing Year 6 and the SATs will lean on hardest.

  • Choosing the operation, and being able to say why
  • Multi-step problems that need two or three ideas at once
  • Using the equals sign properly: 13 + 24 = 12 + 25 is a statement about balance, not an instruction to add
  • Checking whether an answer is sensible before moving on
Example

33 = 5 × ? Explain how you know.

The curriculum's own missing-number example. There is no whole-number answer, and saying why is the point.

Where it usually goes wrong "I just know" as an explanation. It is fine in Year 3. By Year 5 the words are part of the maths.

Statutory content taken from the national curriculum programme of study for Year 5 (Department for Education). Examples marked as the curriculum's own are from its non-statutory guidance; the rest, and the "where it goes wrong" notes, are ours, from teaching the year group.

Year 4 to Year 5

What is actually new this year

A lot of Year 5 is Year 4 with bigger numbers. These are the things that start from nothing, or nearly.

TopicStatus in Year 5What that means for your child
PercentagesNewOnly the meaning and the simple equivalents this year. Calculating with them is Year 6.
Square and cube numbersNew5² = 25 and 2³ = 8, and the notation. Small, but it comes back in Year 6 and Year 7.
Prime numbersNewThe vocabulary, whether a number up to 100 is prime, and recalling the primes up to 19.
Long multiplicationNewYear 4 multiplied by a one-digit number. Multiplying by a two-digit number is the Year 5 step, and it needs the tables to be automatic.
Mixed numbersNewConverting between 6/5 and 1 1/5, and writing answers bigger than 1 as mixed numbers.
Angles in degreesNewYear 4 compared angles. Year 5 measures and draws them with a protractor.
DecimalsExtendedFrom 2 decimal places to 3, and thousandths as a place.
FractionsExtendedSame-denominator adding was Year 4. Related denominators, and multiplying by a whole number, are Year 5.
NumbersExtendedFrom 4-digit numbers to a million, and rounding to any place.

Ratio, algebra, long division and calculating percentages of amounts are all Year 6. If a tutor or a workbook has your Year 5 child doing them, that is ahead of the curriculum, not part of it.

Why this year matters

Why Year 5 is the year to fix a gap

The Year 6 tests cover the whole of key stage 2, not just Year 6. A child who reaches Year 6 with shaky times tables, a fuzzy idea of place value in decimals, or fractions they can draw but not calculate with will be taught Year 6 content on top of that gap — and Year 6 has ratio, algebra and long division of its own to fit in. Year 5 is the year with the most room to go back.

There is also a practical reason. Nothing is being tested. The multiplication tables check was Year 4; the SATs are Year 6. In Year 5 a teacher, or a parent, can spend six weeks on decimals without a deadline moving.

One more thing, for families in areas with grammar schools: the 11+ is usually sat in September or early October of Year 6, depending on the area, so any preparation for it happens in Year 5. GL Assessment, which writes many of the tests, says the maths papers are based mainly on content reached in the early part of Year 6, and many areas test reasoning more than maths — so check your local authority's familiarisation materials before buying anything. It is a separate decision from tutoring for the curriculum, and worth going into with clear eyes about what is being asked of a nine-year-old.

Where children get stuck

The Year 5 maths difficulties we see most

Some children sail through Year 5 and some hit one of these. The signs, something to try, and the point at which help is worth it.

Times tables that are not automatic

Year 5 assumes them. Long multiplication, short division, factors, equivalent fractions and simplifying all run on tables recall, and a child who is still working them out pays for it in every one.

Try this at home

Ask a few mixed facts out of order, in the car. 7 × 8, 6 × 9, 48 ÷ 6.

If the answers come in a beat, move on. If there is counting on fingers, this is the thing to fix first.

Where it usually goes wrong Worth support when a child avoids any question that needs a table fact. Five minutes a day, kept up for a term, is where we would start, and it pays off in every later topic.

Decimal place value

Decimals with different numbers of digits expose whether a child understands what the digits mean or is pattern-matching.

Try this at home

Put 0.5, 0.45, 0.405 and 0.6 in order.

The order is 0.405, 0.45, 0.5, 0.6. A child who puts 0.405 last is reading the digits as a whole number.

Where it usually goes wrong Left alone, it turns up again in Year 6 money, measures and percentages. A place value chart fixes it quickly; more worksheets do not.

Fractions as numbers

Children who are fine shading three quarters of a shape can still have no sense that 3/4 is a number that sits between 0 and 1.

Try this at home

Ask where 3/4, 1/2 and 5/4 go on a number line from 0 to 2.

If 5/4 is a mystery, the mixed numbers work in Year 5 has nothing to hang on.

Where it usually goes wrong If equivalent fractions are also shaky, stop and fix those. Everything in Year 6 fractions — different denominators, simplifying, comparing — depends on equivalence.

Long multiplication

Several steps, a zero to remember, and a tables fact inside each step. The method is usually taught well; it goes wrong on recall, layout and the placeholder.

Try this at home

Ask your child to talk you through 24 × 16, not just do it.

If the explanation includes "then you put a zero" without knowing why, that is the bit that will be forgotten under pressure.

Where it usually goes wrong Errors in the same place every time are the method; errors scattered everywhere are the tables. They need different fixes.

Word problems

The maths in a Year 5 word problem is rarely the hard part. Working out which maths it wants is.

Try this at home

Before any working, get the question said back in their own words.

No maths from you, and it is the habit the reasoning papers reward in Year 6.

Where it usually goes wrong A child who can do the sum when you say it aloud but not when it is written in a sentence has a reading-the-maths problem, and it is very teachable.

Deciding they are bad at maths

Year 5 is often when a child who has been quietly coping stops coping quietly. The content jumps, the class moves on, and the story they tell themselves changes.

Try this at home

Notice the working, not the speed: "show me how you got there".

Small, and cumulative. By the summer it changes what the child thinks maths is for.

Where it usually goes wrong This is the one we would act on early. A gap in decimals is a bounded job. A child who has decided they cannot do maths is a longer job, and easier the sooner it starts.

At home

How to help with Year 5 maths without teaching it

Most of what helps is conversation and routine, not instruction.

How we help

How ClassArc supports a Year 5 student

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

We look underneath first

A Year 5 problem with decimals is usually a Year 3 or 4 problem with place value. The first classes find it and fix it there, rather than teaching Year 5 content on top of it.

Tables until they are automatic

A few minutes of out-of-order practice inside every class until recall is instant. Unglamorous, and the thing we would do first with any Year 5 child.

The same teacher, every week

One teacher who remembers last week without being told, and knows which topics your child steers around.

Lessons follow the national curriculum

We teach the Year 5 programme of study and work alongside what your child's school is covering, rather than running a separate syllabus.

Explaining out loud

Every few minutes a child is asked why, not only what. It is how reasoning is built and how a misunderstanding is caught before it sets.

Into Year 6 without a handover

Wherever we can, the same teacher carries on into Year 6 and the SATs year, so what is learned now is not re-explained by someone new next September.

Inside a class

What a Year 5 ClassArc class looks like

One teacher, one child, 55 minutes, and a rhythm that is the same every week so nothing about the class is a surprise.

“

Every Year 6 topic stands on a Year 5 one. Fix the floor before you build the room.

Why we start where the gap is
i
🔍

Check what stuck

Last week's work and marked homework are open before the class starts. A two-minute look at what held and what slipped.

ii
✏️

Teach it properly

A single idea, built up on the shared worksheet with the teacher watching the working as it happens, not the answer afterwards.

iii
🧩

Then they try it

Questions alone, then a harder one that needs an explanation. The teacher listens for the reasoning, not just the answer.

iv
📌

Set the next step

A short note of what held and what did not, and homework aimed at the second, marked before the next class.

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Year 5 to Year 6

How Year 5 maths sets up Year 6

Year 6 adds three things that are genuinely new — ratio and proportion, algebra, and long division — and then tests the whole of key stage 2 in May. Everything else in Year 6 is Year 5 content taken further: fractions with different denominators, percentages of amounts, decimals inside division answers, area of triangles instead of rectangles.

So the Year 5 skills that carry forward hardest are the foundations: automatic times tables, secure decimal place value, fractions understood as numbers, and the written methods done fluently rather than laboriously. A child who has those finds Year 6 a step. A child who does not finds it a wall, and the wall arrives in the same year as the tests.

If you want to see what is coming, our Year 6 maths page sets out every topic, and the SATs maths page explains the papers themselves.

Next

Where to go from here

Useful next steps for a Year 5 parent.

Year 4 maths

All the times tables, the check in June, and the first decimals — what Year 5 assumes is there.

The year before

Year 6 maths curriculum

Every topic in the year that follows, what is new, and where children get stuck.

See what comes next

Key Stage 2 maths

Years 3 to 6 on one page: what each year adds, the two national checks, and the ideas that carry through.

The KS2 overview

Year 5 maths questions

What topics are covered in Year 5 maths?
Place value to at least a million; column addition and subtraction with large numbers; multiplication and division including long multiplication, short division, factors, multiples, primes, squares and cubes; fractions including mixed numbers and adding with related denominators; decimals to three places; the first work on percentages; measurement including unit conversion, perimeter, area of rectangles and volume; angles in degrees, reflection and translation; and statistics using line graphs and tables. All set out in the national curriculum programme of study for Year 5 in England.
What should a Year 5 child know in maths by the end of the year?
Read, write and round numbers to a million; add, subtract and multiply with the formal written methods, including long multiplication; divide with short division; know all the times tables automatically; convert between mixed numbers and improper fractions; add and subtract fractions with related denominators; compare and order decimals to three places; know what a percentage is and the simple equivalents; measure and draw angles; and explain a method in words.
Is Year 5 maths hard?
It is a noticeable step up from Year 4. The numbers get much bigger, several ideas appear for the first time — percentages, primes, squares and cubes, mixed numbers, angles in degrees — and fractions become something to calculate with. In our experience children manage it well when the Year 3 and 4 foundations are secure; the difficulty usually comes from an earlier gap, not the new content.
Does Year 5 maths include percentages?
Yes, for the first time, but only the meaning and the simple equivalents: the % symbol, per cent as parts per 100, writing a percentage as a fraction over 100 and as a decimal, and knowing the percentage equivalents of halves, quarters, fifths and fractions with denominators that are multiples of 10 or 25. Calculating a percentage of an amount is Year 6.
Does Year 5 include long division or ratio?
No. Year 5 uses short division by a one-digit number. Long division by a two-digit number, ratio and proportion, and algebra are all Year 6 content.
Is there a test in Year 5?
No national test. The multiplication tables check is in Year 4 and the key stage 2 tests (SATs) are in Year 6. Some schools run their own end-of-year assessments, which are for the school's use, not reported nationally.
Should my Year 5 child be preparing for the 11+?
Only if you are in an area with grammar schools and intend to apply. The tests are usually sat early in the autumn of Year 6, so preparation falls in Year 5, and the maths in them can reach into early Year 6 content that school has not yet taught. It is a separate decision from supporting the curriculum, and we would rather talk it through honestly than sell it.
How can I help my child with Year 5 maths at home?
Make the times tables automatic with a few minutes a day; use money and measures for decimals; ask your child to explain their method rather than checking answers; and fix earlier gaps rather than pushing ahead. Short sessions, little and often.
How can a tutor help a Year 5 child?
One to one, a teacher can find the earlier gap causing the current difficulty and fix it before Year 6 piles new content on top, while building the reasoning habits the Year 6 tests reward. Year 5 has no test of its own, which makes it the year with the most room to do this properly.
What does ClassArc cost for a Year 5 student?
Year 5 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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