Year 6 maths: what your child learns and how to help

What do Year 6 children learn in maths?

This is everything in the national curriculum for England for Year 6, 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 10,000,000, and say what each digit is worth.
• Round any whole number to a given accuracy, like the nearest 1,000 or the nearest 100,000.
• Use negative numbers in real situations, like temperatures, and work out the gap between a negative and a positive number.

Addition, subtraction, multiplication and division

• Multiply numbers with up to 4 digits by a two-digit number using long multiplication.
• Divide numbers with up to 4 digits by a two-digit number using long division, and short division (the bus stop method) where it works better.
• Decide what to do with a remainder: leave it as a remainder, write it as a fraction, or round, depending on the question.
• Do mental calculations with large numbers and with mixed operations.
• Find common factors, common multiples and prime numbers.
• Use the order of operations, including brackets: 2 + 1 × 3 is 5, but (2 + 1) × 3 is 9.
• Solve multi-step problems, choosing which operations and methods to use and why.
• Estimate to check answers, and decide how accurate an answer needs to be.

Fractions, decimals and percentages

• Simplify fractions using common factors, and use common multiples to give fractions the same denominator.
• Compare and order fractions, including fractions bigger than 1.
• Add and subtract fractions with different denominators, and mixed numbers, by finding equivalent fractions first.
• Multiply simple pairs of fractions, like a quarter times a half, and write the answer in its simplest form.
• Divide a fraction by a whole number, like a third divided by 2.
• See a fraction as a division, and work out its decimal: three eighths is 3 ÷ 8, which is 0.375.
• Know what each digit is worth in numbers with up to 3 decimal places, and multiply and divide by 10, 100 and 1,000.
• Multiply numbers with up to 2 decimal places by whole numbers, and use written division where the answer has up to 2 decimal places.
• Know the simple equivalences between fractions, decimals and percentages, like a quarter, 0.25 and 25%.

Ratio and proportion

• Solve problems that compare the sizes of two amounts, using multiplication and division facts.
• Work out percentages of amounts, like 15% of 360, and use percentages to compare.
• Solve problems with similar shapes, where one is an enlargement of the other by a scale factor.
• Solve problems about unequal sharing, like "for every egg you need three spoonfuls of flour".

Algebra

• Use simple formulae, written in words or with letters.
• Make and describe number sequences that go up or down in equal steps.
• Write missing number problems using letters for the unknowns.
• Find pairs of numbers that fit an equation with two unknowns, and list all the possible combinations.

Measurement

• Convert between units of length, mass, volume and time, using decimals with up to 3 decimal places.
• Convert between miles and kilometres.
• See that shapes with the same area can have different perimeters, and the other way round.
• Work out the area of parallelograms and triangles.
• Work out and compare the volume of cubes and cuboids in cubic centimetres (cm³) and cubic metres (m³).

Geometry: shapes

• Draw 2-D shapes with given lengths and angles.
• Recognise and build 3-D shapes, including making nets.
• Sort shapes by their properties, and find missing angles in triangles, quadrilaterals and regular polygons.
• Name the parts of a circle, and know that the diameter is twice the radius.
• Find missing angles where angles meet at a point, sit on a straight line, or are vertically opposite.

Geometry: position and direction

• Describe positions on the full coordinate grid, with all four quadrants.
• Draw and translate shapes on a coordinate grid, and reflect them in the axes.

Statistics

• Read and draw pie charts and line graphs, and use them to solve problems.
• Work out the mean of a set of data, and know what it tells you.

The multiplication tables don't stop in Year 6. The curriculum says children keep using all of them to stay fluent, because long multiplication, long division and fractions all lean on them. Our times tables pages have every table from 2 to 12 with free practice.

What should a Year 6 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 secondary school maths builds on most:

• multiplying and dividing by 10, 100 and 1,000, and how the place values from hundredths up to 10 million connect
• what each digit is worth in numbers up to 10 million, including decimals, and splitting numbers up in different ways
• where any number sits on a number line, and rounding it sensibly
• reading scales and number lines split into 2, 4, 5 or 10 equal parts
• using one calculation to work out a related one, like using 24 × 3 = 72 to see that 2.4 × 3 = 7.2
• solving ratio problems, and problems with two unknowns
• simplifying fractions using common factors, and comparing fractions with different denominators
• drawing and making shapes from given lengths, angles and areas

The Year 6 SATs in May

In May of Year 6, children in England take the key stage 2 national curriculum tests, often called SATs. In 2027 the three maths papers (one arithmetic paper and two reasoning papers) are on Wednesday 12 and Thursday 13 May, and results come as a scaled score from 80 to 120. Our guide to the KS2 maths SATs explains what's in each paper, how the scores work, where to find the official papers from previous years on GOV.UK, and how to help your child prepare calmly. To practise paper 1, try our free SATs arithmetic practice paper.

Maths words for Year 6

Long multiplication

The written method for multiplying by a two-digit number, where you multiply by the ones and the tens separately and then add the two rows.

Long division

The written method for dividing by a two-digit number, where you write out each subtraction step under the number.

Short division

The written method often called the bus stop method, where you divide one digit at a time and move any remainder on to the next digit.

Common factor

A number that divides into two or more numbers exactly. 4 is a common factor of 8 and 12.

Common multiple

A number that is in the times tables of two or more numbers. 12 is a common multiple of 3 and 4.

Prime number

A number with exactly two factors, 1 and itself, like 2, 3, 5, 7 and 11.

Order of operations

The rule for which part of a calculation to do first: brackets, then multiplying and dividing, then adding and subtracting.

Simplest form

A fraction that can't be simplified any more. Six eighths in its simplest form is three quarters.

Mixed number and improper fraction

A mixed number has a whole number and a fraction, like 1 and a half. An improper fraction has a numerator bigger than its denominator, like three halves.

Percentage

A number of parts out of 100. 25% means 25 out of every 100.

Ratio

A way of comparing two amounts. If there are 2 red beads for every 3 blue beads, the ratio of red to blue is 2 to 3.

Scale factor

How many times bigger one shape is than a similar shape.

Formula

A rule for working something out, written in words or letters. The area of a rectangle is length times width.

Volume

The amount of space a 3-D shape takes up, measured in cubes, like cubic centimetres.

Net

A flat shape that folds up to make a 3-D shape.

Radius and diameter

The radius is the distance from the centre of a circle to its edge. The diameter goes all the way across through the centre, so it is twice the radius.

Circumference

The distance all the way around a circle.

Vertically opposite angles

The angles opposite each other where two straight lines cross. They are always equal.

Quadrant

One of the four parts of a coordinate grid, made by the two axes crossing at zero.

Mean

A kind of average: add up all the values and divide by how many there are.

Year 6 maths questions: a quick test to try at home

These Year 6 maths questions are our own, written to match the curriculum above. Try them as a quick test at home: most are calculations, like the ones on the arithmetic paper, and the last one is a reasoning question, where your child has to decide what to do. It doesn't matter if some are tricky; talking through how they got an answer is the useful part.

1. 34 × 26
2. Round 4,382,519 to the nearest 100,000.
3. What is 15% of 360?
4. Write three eighths as a decimal.
5. What is 2 + 6 × 4?
6. What is the mean of 4, 7, 9 and 12?
7. A recipe uses 3 spoonfuls of flour for every egg. How many spoonfuls of flour are needed for 5 eggs?

Answers

1. 884
2. 4,400,000
3. 54
4. 0.375
5. 26 (multiply first, then add)
6. 8
7. 15

How to help with Year 6 maths at home

• Keep the times tables fresh. A few minutes most days keeps them quick, which makes long multiplication, long division and fractions much easier. Our guide on how to learn times tables has a 10 minute routine, and the times table 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.
• Use percentages when you shop. Sale signs like "20% off" are good practice for percentages of amounts.
• Cook with ratio. Doubling or halving a recipe, or working out how much flour goes with 3 eggs, is ratio in real life.
• Read charts together. Weather forecasts, sports results and news graphics are full of line graphs and pie charts.
• Keep it calm around the SATs. Short, regular practice does more than long sessions, and your child's teacher is the best person to ask about what to focus on.

If you'd like to look back at what came before, our Year 5 maths guide and Year 4 maths guide cover the earlier years.