KS3 maths: a parent's guide to Years 7 to 9

What is KS3 maths?

KS3 maths is key stage 3 of the national curriculum for maths in England, which covers Years 7, 8 and 9. The programme of study treats the three years as one stage. It lists everything children should know, apply and understand by the end of Year 9, but it doesn't say which year each topic belongs to.

The curriculum asks children to build on what they learned in KS2 maths rather than start again. Its first aim is that children consolidate their number skills from primary school and extend them to decimals, fractions, powers and roots. It also says calculators shouldn't replace good written and mental arithmetic, so the written methods from primary school, like long multiplication and long division, still matter.

Alongside the content, the curriculum describes three ways of working that run through every topic:

• Fluency: knowing facts and methods well enough to use them quickly and accurately.
• Reasoning: spotting patterns, explaining why something works, and testing ideas with examples.
• Problem solving: breaking a problem into simpler steps and choosing which maths to use.

The KS3 maths curriculum: six areas

The KS3 maths curriculum is split into six areas. This table gives a short version of each, and the year guides go through them in more detail.

Area	Some of the main ideas
Number	Place value for numbers of any size, negative numbers, prime factors, highest common factor and lowest common multiple, powers and roots, standard form, rounding to significant figures
Algebra	Algebraic notation, expanding brackets, factorising, solving equations, inequalities, sequences and the nth term, straight-line graphs
Ratio, proportion and rates of change	Ratio notation and sharing in a ratio, direct and inverse proportion, percentage change, speed and unit pricing
Geometry and measures	Area of trapezia and circles, volume of prisms, angle facts with parallel lines, constructions with a ruler and compasses, Pythagoras' theorem, trigonometric ratios
Probability	The 0 to 1 probability scale, outcomes that add up to 1, Venn diagrams, listing every possible outcome
Statistics	Mean, median, mode and range, charts for grouped data, scatter graphs

Probability isn't in the primary curriculum at all, so it's the one area that starts fresh at secondary school. Everything else grows out of something children met in primary school.

Which year is each KS3 maths topic taught in?

The national curriculum doesn't say. Schools decide the order and pace across Years 7, 8 and 9, so one school might teach Pythagoras' theorem in Year 8 and another in Year 9. The curriculum also says decisions about moving on should depend on how secure a child's understanding is, not on a date.

If you'd like to know what's coming up, ask your child's school for its maths scheme of work or curriculum map. It's the most reliable guide to what your child will meet each term. Our year guides describe the KS3 content from three different angles: Year 7 on the move from primary school, Year 8 on the big strands in the middle of key stage 3, and Year 9 on finishing KS3 and getting ready for GCSE.

KS3 maths levels and tests

National curriculum levels, like "level 4" or "level 6", are no longer used. The Department for Education removed the levels system for grading children, and schools now choose their own ways of assessing progress. So if you hear about "levels 4 to 6" for Year 7, or come across old KS3 maths test papers marked in levels, they come from the old system.

There's no national KS3 maths test either. Children take national tests at the end of Year 6 and GCSEs at the end of Year 11, but nothing national in Years 7 to 9. Instead, your child's school checks progress in its own way, and by the end of each summer term it must write you a report on your child's progress and talk it through with you. The school can tell you how its own KS3 maths tests work and what the results mean.

From KS3 maths to GCSE

KS3 maths leads straight into GCSE maths, which children study in Years 10 and 11 (key stage 4). Most children take their GCSEs in Year 11. The key stage 4 programme of study says that the KS3 and KS4 content together covers everything in GCSE maths. The GCSE subject content also says that GCSE builds on maths typically taught at key stage 3, and that schools don't need to teach it again if children have learned it well.

GCSE maths is taken at one of two tiers, foundation or higher. Our Year 9 maths guide explains how KS3 topics carry on into GCSE.

KS3 maths questions to try

1. What is 2⁵?
2. Simplify 4a + 3b + 2a − b.
3. Share £60 in the ratio 2:3.
4. Find the mean, median, mode and range of 3, 7, 7, 9 and 14.
5. What is 3 − (−5)?
6. Write 0.375 as a fraction.

Answers

1. 32 (2 × 2 × 2 × 2 × 2)
2. 6a + 2b
3. £24 and £36 (5 parts, so each part is £12)
4. Mean 8, median 7, mode 7, range 11
5. 8 (taking away a negative is the same as adding)
6. ³⁄₈

How to help with KS3 maths at home

• Keep number skills sharp. Times tables, fractions, decimals and percentages are used in almost every KS3 topic. If the times tables are shaky, our times tables test mixes up all of them, and the times table grid is handy to print.
• Ask them to explain. Asking "how did you get that?" helps a method stick, and shows you which method the school uses. It's best to stick with that method rather than teach a different one.
• Revise little and often. For maths revision in KS3, a short go at a few questions most days does more than a long session before a test. Getting a question wrong and then fixing it is good practice, not a failure.
• Check the working, not just the answer. At secondary school, writing out the steps matters more and more, especially in algebra.
• Use maths in real life. Sale prices, recipes, travel times and bills are all percentages, ratio and speed.
• Talk to the school. Your child's maths teacher knows what they're working on and what would help most.

See all our maths guides, from Year 1 to GCSE