Year 5 maths: what your child learns and how to help

What do Year 5 children learn in maths?

This is everything in the national curriculum for England for Year 5, in plain words. Schools choose the order and the pace, so your child won't meet these in the order below.

Number and place value

• Read, write, order and compare numbers up to at least 1,000,000, and know what each digit is worth.
• Count forwards and backwards in steps of 10, 100, 1,000, 10,000 and 100,000 from any number.
• Use negative numbers in real situations, like temperatures, and count forwards and backwards 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 up to 1,000 (M), and read years written in Roman numerals.
• Spot the rule in a number sequence, including sequences with fractions and decimals, like "add a half".

Addition and subtraction

• Add and subtract numbers with more than 4 digits using column addition and column subtraction.
• Add and subtract bigger numbers in their head, like 12,462 − 2,300.
• Use rounding to check answers, and decide how accurate an answer needs to be.
• Solve problems with more than one step, choosing which operations and methods to use and why.

Multiplication and division

• Find multiples and factors, including all the factor pairs of a number and the common factors of two numbers.
• Know what prime numbers, prime factors and composite numbers are, say whether a number up to 100 is prime, and know the prime numbers up to 19.
• Multiply numbers with up to 4 digits by a one-digit or two-digit number with a written method, including long multiplication.
• Divide numbers with up to 4 digits by a one-digit number using short division, and decide what to do with a remainder.
• Multiply and divide in their head using facts they know.
• Multiply and divide whole numbers and decimals by 10, 100 and 1,000.
• Know square numbers and cube numbers, and how to write them: 5² for 5 squared and 2³ for 2 cubed.
• Understand that the equals sign means both sides are worth the same, as in 13 + 24 = 12 + 25.
• Solve problems with scaling by simple fractions and simple rates.

Fractions, decimals and percentages

• Compare and order fractions whose denominators are all multiples of the same number, like thirds, sixths and twelfths.
• Find equivalent fractions, including tenths and hundredths.
• Change mixed numbers to improper fractions and back again.
• Add and subtract fractions with the same denominator, or denominators that are multiples of the same number, including answers bigger than 1.
• Multiply fractions and mixed numbers by whole numbers, using diagrams to help.
• Write decimals as fractions: 0.71 is seventy-one hundredths.
• Use thousandths, and link them to tenths, hundredths and decimals.
• Round decimals with two decimal places to the nearest whole number and to one decimal place.
• Read, write, order and compare numbers with up to three decimal places.
• Know that per cent means "out of 100", and write a percentage as a fraction out of 100 and as a decimal.
• Know the percentage and decimal for a half, a quarter, a fifth, two fifths and four fifths, and for fractions out of 10 or 25.

Measurement

• Convert between metric units, like kilometres and metres, centimetres and millimetres, grams and kilograms, and litres and millilitres.
• Know rough equivalents between metric units and imperial units such as inches, pounds and pints.
• Measure and work out the perimeter of shapes made from rectangles, in centimetres and metres.
• Work out and compare the area of rectangles in square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes.
• Estimate volume, for example by building cuboids from centimetre cubes, and capacity, for example with water.
• Solve problems that involve converting units of time.
• Use all four operations to solve measure and money problems with decimals.

Geometry: shapes

• Recognise 3-D shapes, including cubes and other cuboids, from 2-D drawings.
• Know that angles are measured in degrees, and estimate and compare acute, obtuse and reflex angles.
• Draw angles and measure them with a protractor.
• Know that angles around a point make 360°, angles on a straight line make 180°, and other multiples of 90°.
• Use what they know about rectangles to find missing lengths and angles.
• Tell regular and irregular polygons apart by their sides and angles.

Geometry: position and direction

• Describe where a shape ends up after a reflection or a translation, and know the shape itself hasn't changed.

Statistics

• Answer questions that compare, add or find the difference using a line graph.
• Complete, read and use tables, including timetables.

Long multiplication and short division in Year 5

Year 5 is when written methods for multiplying and dividing grow. Children have used the column method to multiply by a one-digit number since Year 4. In Year 5 they use it for numbers with up to 4 digits, start long multiplication for multiplying by a two-digit number, and learn short division.

Short multiplication. For 236 × 3, work from the ones: 6 × 3 = 18, so write 8 and carry 1 ten. Then 3 tens × 3 is 9 tens, plus the 1 carried makes 10 tens: write 0 and carry 1 hundred. Then 2 hundreds × 3 is 6 hundreds, plus the 1 carried makes 7 hundreds. The answer is 708.

Long multiplication. To multiply by a two-digit number, split it into tens and ones and multiply by each part on its own row. For 23 × 14: first 23 × 4 = 92, then 23 × 10 = 230, and finally add the two rows: 92 + 230 = 322.

Short division (the bus stop method). For 852 ÷ 4, divide each digit from the left. 8 hundreds divided by 4 is 2 hundreds. 4 goes into 5 tens once, with 1 ten left over, so that ten is exchanged for 10 ones and joins the 2 ones to make 12. Then 12 ÷ 4 = 3. The answer is 213.

Remainders. When a division doesn't come out exactly, Year 5 children decide what the answer should look like. 98 ÷ 4 is 24 remainder 2, which can also be written as 24 and a half, or 24.5, or rounded to about 25. If 98 children are going on a trip in cars that take 4 each, you need 25 cars, not 24.

Mental maths in Year 5. Written methods don't replace mental maths. Children still work things out in their head when it's quicker, like 12,462 − 2,300, and use facts they know with place value: 3 × 4 = 12, so 0.3 × 4 = 1.2. They estimate first by rounding, so they can tell whether a written answer makes sense.

What should a Year 5 child know by the summer?

The curriculum describes what children are taught across the year, and every child moves through it at their own pace. Government guidance for teachers picks out the ideas that Year 6 builds on most:

• that 10 tenths make 1, 100 hundredths make 1, and 10 hundredths make one tenth
• what each digit in a number with up to 2 decimal places is worth, where it sits on a number line, and rounding it to the nearest whole number or tenth
• converting between units of measure, like centimetres and metres
• all the times tables and division facts, secure enough to use without thinking in written methods
• multiplying and dividing by 10 and 100, as making a number 10 or 100 times the size, or a tenth or a hundredth of the size
• factors and multiples, including common factors and common multiples
• multiplying a number with up to 4 digits by a one-digit number with a written method
• dividing a number with up to 4 digits by a one-digit number with short division, and deciding what to do with the remainder
• finding fractions of amounts, like three fifths of 40, and finding equivalent fractions
• the decimals for a half (0.5), a quarter (0.25), a fifth (0.2) and a tenth (0.1)
• measuring and drawing angles in degrees, and working out the area of rectangles

Are there Year 5 maths tests?

There's no national maths test in Year 5. Many schools use their own tests during the year to see what to teach next, and your child's teacher can tell you how these are used and what they show.

The next national maths tests are the key stage 2 SATs in May of Year 6. For children in Year 5 in 2026 to 2027, they're timetabled from Monday 8 May to Thursday 11 May 2028. Our KS2 maths SATs guide explains what the tests cover.

Maths words for Year 5

Factor and multiple

Factors are numbers that multiply together to make another number. 4 and 6 are factors of 24, and 24 is a multiple of both.

Common factor

A number that is a factor of two numbers. 4 is a common factor of 12 and 20.

Prime number

A number with exactly two factors, 1 and itself. 2, 3, 5, 7, 11, 13, 17 and 19 are the prime numbers up to 19.

Composite number

A whole number bigger than 1 that isn't prime, like 12.

Prime factor

A factor that is also a prime number. The prime factors of 12 are 2 and 3.

Square number

A number made by multiplying a number by itself. 5 squared, written 5², is 25.

Cube number

A number made by multiplying a number by itself and then by itself again. 2 cubed, written 2³, is 8.

Long multiplication

The written method for multiplying by a number with two or more digits, one row at a time.

Short division

The written method for dividing by a one-digit number, also called the bus stop method.

Remainder

What is left over when a number doesn't divide exactly.

Mixed number

A whole number and a fraction together, like two and a half.

Improper fraction

A fraction where the numerator is bigger than the denominator, like seven thirds.

Thousandth

One part when something is split into 1,000 equal parts. 0.001 is one thousandth.

Per cent

Out of 100. 25% means 25 out of every 100.

Degrees

The unit for measuring angles. A right angle is 90° and a whole turn is 360°.

Reflex angle

An angle bigger than a straight line (180°) but smaller than a whole turn.

Protractor

A see-through ruler, shaped like a half circle, for measuring angles.

Regular polygon

A flat shape whose sides are all the same length and whose angles are all the same size, like a square.

Reflection

Flipping a shape over a mirror line.

Year 5 maths questions to try

These are our own practice questions for Year 5, not a test from school, so there's no score to worry about. Try a few together, then open the answers to check.

1. 2,436 × 7
2. 23 × 14
3. 1,456 ÷ 4
4. Round 3.47 to one decimal place.
5. Write seventeen fifths as a mixed number.
6. Which of these is a prime number: 21, 23, 25 or 27?

Answers

1. 17,052
2. 322
3. 364
4. 3.5
5. Three and two fifths
6. 23

How to help with Year 5 maths at home

• Keep the times tables fresh. Long multiplication and short division lean on them at every step. The times tables test mixes up every table, and the multiplication grid is handy to print.
• Ask how they worked it out. Explaining a method out loud helps it stick, and shows you which method your child's school uses. It's worth sticking to that method rather than teaching a different one.
• Estimate first. Before a calculation, ask for a rough answer by rounding. It's how children spot when a written method has gone wrong.
• Spot percentages in shops. "25% off" and "half price" are good for linking fractions, decimals and percentages.
• Cook and measure. Recipes are full of grams and kilograms, and millilitres and litres, and doubling or halving a recipe is scaling.
• Read timetables together. Working out how long a bus or train journey takes uses time, tables and subtraction all at once.