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Before you revise a single number, read this: there is no national PGCE numeracy test any more. The national literacy and numeracy skills tests for teacher training were abolished in 2019 — the Department for Education announced the change on 16 July 2019, and from October 2019 training providers have been responsible for assuring that trainees meet the fundamental literacy and numeracy requirements by the end of their training. There is no national test, no national format and no national pass mark.
That matters, because many websites still sell "PGCE numeracy test" preparation for a test that no longer exists. What your provider will actually check is your maths subject knowledge — whether you can do the primary curriculum maths fluently, explain it clearly, and spot children's errors. That is what this article revises: the maths itself, the common errors, and a 10-question self-test to find your weak spots.
What your provider expects you to know
To train as a primary teacher in England you need a bachelor's degree and GCSEs at grade 4 (C) or above in English, maths and science. During the course, your provider checks your fundamental maths — through subject-knowledge audits, assignments and your teaching placements — in its own way. The maths you need is the National Curriculum for Key Stages 1 and 2, and the ability to explain it to a child.
The curriculum topics are: number and place value; the four operations; fractions (decimals in Year 4, decimals and percentages in Year 5); measurement; geometry; and statistics (Years 2–6). Two topics are Year 6 only: ratio and proportion, and algebra. Two fluency targets matter most: children should know their number bonds to 20 by the end of Year 2, and their multiplication tables to 12 × 12 by the end of Year 4. As a trainee, you should be fluent in both — and in the reasoning behind them.
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Revision notes — the six areas that catch trainees out
1. Place value and the four operations
Place value is the foundation of everything else. The most common trainee error is with decimals: 3.7 × 10 = 37, not 3.70 and not 37.0 — multiplying by 10 moves every digit one place to the left. Dividing by 10 moves every digit one place to the right: 47 ÷ 10 = 4.7. If you find yourself "adding a zero", stop and think in terms of place value instead — "adding a zero" fails the moment decimals appear.
For written methods, know the standard column methods for addition, subtraction, multiplication and division, and know when a mental method is faster. A trainee who can only do column multiplication will be slow; a trainee who can only do mental maths will make errors on large numbers. You need both.
2. Fractions, decimals and percentages
Fractions, decimals and percentages are the same idea in three forms, and the exam-style questions test whether you can move between them. Learn these equivalences by heart: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%.
The classic error is adding fractions by adding the tops and the bottoms: 1/3 + 1/4 is not 2/7. You need a common denominator: 1/3 = 4/12 and 1/4 = 3/12, so 1/3 + 1/4 = 7/12. The other classic error is with decimal multiplication: 0.5 × 0.2 = 0.1, not 1.0 — multiplying two numbers less than 1 gives a smaller number, and the decimal point moves two places in total (one for each factor).
3. Measurement and conversion
Know the metric units and their conversions: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1,000 g, 1 litre = 1,000 ml. The common error is converting in the wrong direction: 2.5 litres is 2,500 ml, not 250 ml — litres are bigger than millilitres, so the number gets bigger when you convert down. Always ask: "Is the unit I'm converting to bigger or smaller? Should the number get bigger or smaller?"
4. Geometry — area and perimeter
Area and perimeter are confused more often than any other pair in primary maths. Area is the space inside a shape, measured in square units (cm²). Perimeter is the distance around the edge, measured in ordinary units (cm). For a rectangle 8 cm by 5 cm: area = 8 × 5 = 40 cm², and perimeter = 2 × (8 + 5) = 26 cm. If your answer for an area has no "squared" unit, it is wrong.
5. Statistics — mean, median, mode, range
For a set of numbers: the mean is the total divided by how many numbers there are; the median is the middle value when the numbers are in order; the mode is the most common value; the range is the largest minus the smallest. For 4, 7, 9, 12: the total is 32, so the mean is 32 ÷ 4 = 8. The median is the middle of 7 and 9, which is 8. There is no mode (no value repeats), and the range is 12 − 4 = 8. Note that the mean, median and range can all be 8 for the same data — that is a coincidence, not a rule.
6. Ratio, proportion and algebra (Year 6 only)
Ratio and algebra appear only in Year 6, but trainees are still expected to know them. A ratio of 2:3 shared between 25 means 5 parts in total (2 + 3), so each part is worth 25 ÷ 5 = 5, giving 10 and 15. For algebra, the key skill is reading a formula: if the cost of hiring a hall is £20 plus £5 per hour, then the cost for h hours is 20 + 5h. Substituting h = 4 gives 20 + 20 = £40.
Self-test — 10 questions with answers
Q1. What is 3.7 × 10?
A. 3.70
B. 37
C. 370
D. 0.37
Answer: B — 37. Multiplying by 10 moves every digit one place to the left: 3.7 becomes 37. Option A is the same number written differently (3.70 = 3.7) — multiplying by 10 must make the number bigger.
Q2. What is 15% of 240?
A. 24
B. 30
C. 36
D. 48
Answer: C — 36. 10% of 240 is 24, and 5% is half of that, 12. 24 + 12 = 36. Or: 15 × 240 ÷ 100 = 3,600 ÷ 100 = 36.
Q3. What is 1/3 + 1/4?
A. 2/7
B. 7/12
C. 1/7
D. 2/12
Answer: B — 7/12. Use a common denominator of 12: 1/3 = 4/12 and 1/4 = 3/12, so 4/12 + 3/12 = 7/12. Option A is the classic error — adding the numerators and the denominators.
Q4. What is 0.5 × 0.2?
A. 1.0
B. 0.7
C. 0.25
D. 0.1
Answer: D — 0.1. 0.5 is a half and 0.2 is a fifth, so 0.5 × 0.2 = 1/2 × 1/5 = 1/10 = 0.1. Multiplying two numbers smaller than 1 gives a smaller number — if your answer is bigger than either factor, it is wrong.
Q5. A rectangle is 8 cm long and 5 cm wide. What is its area and its perimeter?
A. Area 40 cm², perimeter 26 cm
B. Area 26 cm², perimeter 40 cm
C. Area 40 cm, perimeter 26 cm²
D. Area 13 cm², perimeter 40 cm
Answer: A — Area 40 cm², perimeter 26 cm. Area = 8 × 5 = 40 cm². Perimeter = 2 × (8 + 5) = 26 cm. Option C swaps the units: area is always in square units.
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Q6. How many millilitres are in 2.5 litres?
A. 25 ml
B. 250 ml
C. 2,500 ml
D. 25,000 ml
Answer: C — 2,500 ml. 1 litre = 1,000 ml, so 2.5 × 1,000 = 2,500 ml. Millilitres are smaller than litres, so the number must get bigger — that rules out A and B immediately.
Q7. What is the mean of 4, 7, 9 and 12?
A. 7
B. 8
C. 9
D. 32
Answer: B — 8. The total is 4 + 7 + 9 + 12 = 32, and there are 4 numbers, so the mean is 32 ÷ 4 = 8. Option D is the total, not the mean — the most common error.
Q8. What is 3/4 of 28?
A. 7
B. 14
C. 21
D. 24
Answer: C — 21. A quarter of 28 is 7, so three quarters is 3 × 7 = 21. Or: 28 ÷ 4 × 3 = 21.
Q9. £25 is shared in the ratio 2:3. How much does each person get?
A. £10 and £15
B. £12.50 and £12.50
C. £5 and £20
D. £8 and £17
Answer: A — £10 and £15. The ratio has 2 + 3 = 5 parts, so each part is worth £25 ÷ 5 = £5. The first person gets 2 × £5 = £10 and the second gets 3 × £5 = £15.
Q10. A class has 30 children. Two fifths of them are girls. How many boys are there?
A. 12
B. 18
C. 20
D. 15
Answer: B — 18. Two fifths of 30 is 30 ÷ 5 × 2 = 12 girls. So there are 30 − 12 = 18 boys. The trap is option A: 12 is the number of girls, not the number of boys — always re-read the question after calculating.
Answer key
1 B · 2 C · 3 B · 4 D · 5 A · 6 C · 7 B · 8 C · 9 A · 10 B
Score guide — what your score means
- 9–10 — Strong. Your subject knowledge is solid. Spend your time on pedagogy instead: how to explain these ideas to children, and how to spot and correct their errors.
- 7–8 — Good, with gaps. Re-read the explanations for the questions you missed — especially the fraction and decimal questions (Q3, Q4), which are the ones that most often expose a shaky understanding.
- 5–6 — Developing. Work through the revision notes topic by topic, and practise the fluency targets: number bonds to 20 and tables to 12 × 12, until they are automatic.
- 0–4 — Starting out. Start with place value and the four operations, then move to fractions. Do not skip ahead to ratio and algebra until the foundations are secure.
What to do next
- For literacy: the companion article is PGCE Literacy Revision for Primary Trainees.
- For fees and funding: see QTS and PGCE Fees UK 2027.
- For statistics practice: the statistics notes for TLT, ECT, PST and JEST cover mean, median, mode and range with more worked examples.
- Official sources: Get Into Teaching for entry requirements, and the National Curriculum primary mathematics programmes of study for the full curriculum.
Frequently asked questions
Is there a national PGCE numeracy test I need to pass?
No. The national skills tests were abolished in 2019. Your training provider assures your fundamental maths by the end of the course, through its own audits, assignments and placements. Ask your provider how they check it — the method varies, but the maths itself is the same.
What GCSE grades do I need for primary teaching?
GCSE grade 4 (C) or above in English, maths and science, plus a bachelor's degree. If you do not have the GCSEs, most providers accept an equivalency test — check with the provider you are applying to.
What is the difference between the mean, median and mode?
The mean is the total divided by how many numbers there are. The median is the middle value when the numbers are in order. The mode is the most common value. A data set can have all three, or only some of them — and they can coincidentally be the same number, as in Q7.
Do I need to know ratio and algebra?
Yes, even though they are Year 6 only in the National Curriculum. As a trainee you are expected to know the whole primary curriculum, including the Year 6 content — and to be able to teach it.
Where can I find more maths practice?
The statistics notes on this site cover data handling in depth, and the National Curriculum document linked above lists every topic you are expected to know. For structured revision, work through the curriculum year by year, testing yourself on each topic before moving on.
All questions and worked examples here are original MissMono study material. GOV.UK and the National Curriculum are Crown copyright material; this page is not affiliated with or endorsed by the Department for Education.