Year 8 maths: the big strands of key stage 3

What do children learn in Year 8 maths?

In Year 8 maths, children carry on with the key stage 3 programme of study they started in Year 7. The curriculum sets out what children should learn by the end of Year 9, not what belongs in each year, so your child's school decides which topics come in Year 8. If you'd like to know exactly what's planned, ask the school for its maths scheme of work or curriculum map.

There are no national tests in Years 7, 8 or 9. Your child's school will check progress in its own way and report it to you at the end of the year.

The middle of key stage 3: three ways of working

The KS3 curriculum asks for more than knowing methods. Alongside the topics, it describes three ways of working that children use in every strand:

• Fluency. Using facts and methods quickly and accurately, and moving between different ways of showing the same idea, like a fraction and a decimal, or an equation and its graph.
• Reasoning. Spotting patterns, making a guess about why they happen, and then testing it or proving it. The curriculum says children should begin to reason step by step in geometry, number and algebra.
• Problem solving. Breaking a problem into simpler steps, and choosing which maths to use, including for money problems.

One idea runs through the middle of KS3 in particular: the curriculum asks children to tell when a problem needs adding, when it needs multiplying, and when it needs proportional thinking. For example, if 3 pens cost £1.20, then 6 pens cost £2.40: the number of pens has doubled, so the cost doubles too.

The big strands of Year 8 maths

These are the main strands of the KS3 curriculum, each with a worked example. Your child might meet some of them in Year 8 and some in Year 7 or Year 9, depending on the school.

Algebra: expressions and equations

Children simplify expressions by collecting like terms, multiply out brackets, and take out common factors. They solve linear equations by doing the same thing to both sides, using inverse operations. Solving equations has more on this.

Worked example: solve 3x + 5 = 20.

1. Take 5 from both sides: 3x = 15.
2. Divide both sides by 3: x = 5.
3. Check: 3 × 5 = 15, and 15 + 5 = 20.

Algebra: sequences and graphs

Children find rules for sequences, including the nth term of a sequence that goes up in equal steps. They plot straight-line graphs from equations like y = 2x + 1, and learn what the gradient (the steepness) and the intercept (where the line crosses the y-axis) tell you.

Worked example: the sequence 4, 7, 10, 13 goes up by 3 each time, so the nth term starts with 3n. The first term is 4, which is 1 more than 3 × 1 = 3, so the nth term is 3n + 1. Check the 4th term: 3 × 4 = 12, and 12 + 1 = 13.

Ratio, proportion and rates of change

Children share amounts in a ratio, solve problems with direct and inverse proportion, and work out percentage change. They also use compound units, like speed in kilometres per hour or the price per gram.

Worked example: a coat costs £80 and the price goes up by 15%. 10% of £80 is £8, and 5% is £4, so 15% is £12. The new price is £92. Children also learn to do this in one step, by multiplying by 1.15: 80 × 1.15 = 92.

Geometry and measures

Children work out the area of trapezia and circles and the volume of prisms, use angle facts (including the angles made where a line crosses two parallel lines), and draw constructions with a ruler and compasses.

Worked example: two angles in a triangle are 48° and 67°. Angles in a triangle add up to 180°. 48 + 67 = 115, and 180 − 115 = 65, so the third angle is 65°.

Probability

Children use the 0 to 1 probability scale, list all the possible outcomes in a table or grid, and use Venn diagrams to sort outcomes.

Worked example: the chance of rain tomorrow is 0.3. The probabilities of all the outcomes add up to 1, so the chance of no rain is 1 − 0.3 = 0.7.

Statistics

Children compare sets of data using an average (the mean, median or mode) and the range, and draw charts for grouped data. They use scatter graphs to see whether two things are linked, like height and arm span.

Worked example: one class scored 4, 6, 6, 7 and 12 in a quiz. The mean is 35 ÷ 5 = 7, the median is 6 and the range is 12 − 4 = 8.

Maths words for Year 8

Coefficient

The number in front of a letter. In 3x + 5, the coefficient of x is 3.

Expand

To multiply out brackets. 3(x + 4) expands to 3x + 12.

Factorise

The reverse of expanding: putting brackets back in by taking out a common factor. 6x + 9 factorises to 3(2x + 3).

Formula

A rule linking two or more quantities, like speed = distance ÷ time.

Linear equation

An equation with no powers of the unknown, like 3x + 5 = 20. Its graph is a straight line.

Sequence

A list of numbers that follow a rule.

nth term

A rule that gives any term of a sequence from its position. For 4, 7, 10, 13 it's 3n + 1.

Gradient

How steep a straight-line graph is: how far it goes up for every 1 across.

Direct proportion

Two amounts that grow at the same rate. Double one and the other doubles.

Inverse proportion

When one amount is multiplied by a number, the other is divided by it. Twice as many workers take half the time.

Compound unit

A unit made of two others, like kilometres per hour or grams per cubic centimetre.

Prism

A 3-D shape with the same cross-section all the way along, like a cuboid or a cylinder.

Alternate and corresponding angles

The equal angles made where a straight line crosses two parallel lines.

Construction

An accurate drawing made with a ruler and compasses, like cutting an angle exactly in half.

Sample space

A list or table of every possible outcome.

Scatter graph

A graph of points that shows whether two sets of data are linked.

End of year 8 maths tests

There's no national maths test in Year 8. GOV.UK's guide to the national curriculum lists national assessments for the primary years and GCSEs in key stage 4, but none for Years 7, 8 and 9. If your child's school sets an end-of-year maths test or exam, the school writes it and decides what it covers, so ask your child's maths teacher which topics will come up and how the results are used. The school's curriculum map shows what's been taught so far, which is a good guide to what to revise.

For a bit of practice at home, try the Year 8 maths questions below.

Year 8 maths questions to try

These are our own practice questions, not a test from school. They cover a few of the KS3 strands above.

1. Solve 2x + 7 = 19.
2. Expand 3(x + 4).
3. Find the nth term of 5, 8, 11, 14.
4. Increase £80 by 25%.
5. A car travels 150 km in 2 hours. What is its average speed?
6. Two angles in a triangle are 50° and 65°. What is the third angle?
7. A bag has 3 red counters and 5 blue counters. What is the probability of picking a red one?

Answers

1. x = 6
2. 3x + 12
3. 3n + 2
4. £100
5. 75 km per hour
6. 65°
7. ³⁄₈

How to help with Year 8 maths at home

• Ask "how do you know?" Reasoning is a big part of KS3. Asking your child to explain why an answer is right is as useful as checking that it is.
• Spot proportion in real life. Recipes, best-value offers in the supermarket, exchange rates and journey times are all ratio, proportion and rates.
• Encourage written working. In algebra especially, setting out each step on a new line makes mistakes easier to find.
• Keep number facts quick. Times tables and negative numbers come up in almost every algebra question. The times tables test is a quick way to keep the tables fresh.
• Ask the school for its curriculum map. It shows which strands come up this term, so you can talk about them at home.

Our Year 7 maths guide covers the move from primary school, and the Year 9 maths guide looks ahead to GCSE.