20 Hinge Questions for Primary Maths: Spot the Misconception Before You Move On

A hinge question is one multiple-choice question asked at the exact moment a lesson turns — where everything after it depends on the class understanding what came before. The term comes from Dylan Wiliam: the lesson "hinges" on the answer. Every pupil answers at once, usually on a mini-whiteboard, and the pattern tells you in thirty seconds whether to move on or fix one misconception.

The trick is in the wrong answers: each distractor is a real misconception, so a wrong answer tells you what to do next. All 20 below work that way — every option is labelled with the thinking behind it, plus what to do next.

How to use a hinge question mid-lesson

Ask it before you move on, not at the end of the lesson. The routine takes about two minutes: show the question, have everyone answer at once (mini-whiteboards, or fingers for A, B, C, D — no hands up), then scan for the pattern. Which wrong answer is winning? That names the misconception. Then act: one wrong answer dominating, re-teach it now; answers split everywhere, go back a step. Never grade a hinge question — once it counts, pupils guess safely instead of showing what they think.

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Place value — Questions 1–2

Q1. Which of these numbers has 4 tens?

• A. 14 — sees the 4 but ignores its place
• B. 40
• C. 104 — same error: the 4 is in the ones place
• D. 400 — reads the 4 as the biggest digit

Answer: B — 40. The 4 in 40 is in the tens place; in 14 and 104 it is in the ones, in 400 in the hundreds.

If A or C wins: build them with tens rods and ones cubes.

Q2. What is 300 + 40 + 7?

• A. 374 — writes the parts in the order they sound, 7 before 4
• B. 437 — swaps the hundreds and tens
• C. 347
• D. 3047 — writes the parts side by side instead of adding them into places

Answer: C — 347. 3 hundreds, 4 tens and 7 ones make 347.

If D wins: use a three-column chart — each part lands in its own column.

Addition and subtraction — Questions 3–4

Q3. What is 47 + 28?

• A. 65 — added 7 + 8 = 15, then forgot to carry the 1
• B. 75
• C. 715 — wrote the full 15 in the ones column instead of carrying
• D. 615 — added the columns separately and joined them: 6 and 15

Answer: B — 75. 7 + 8 = 15, write 5 and carry 1; then 4 + 2 + 1 = 7.

If A wins: re-teach carrying with base-10 blocks — ten ones become one ten. If C or D wins, model it one column at a time.

Q4. What is 100 − 37?

• A. 63
• B. 73 — borrowed across the zero but didn't reduce the tens column
• C. 67 — subtracted 3 instead of 7 (100 − 30 = 70, then 70 − 3)
• D. 37 — repeated the number being subtracted

Answer: A — 63. Borrow 1 hundred: 10 − 7 = 3 and 9 − 3 = 6.

If B wins: re-teach borrowing across zero with a hundred square — a full worked example is worth it here.

Multiplication and division — Questions 5–7

Q5. What is 6 × 7?

• A. 48 — answered 6 × 8, the next fact in the table
• B. 36 — answered 6 × 6, the previous fact
• C. 13 — added instead of multiplying
• D. 42

Answer: D — 42. Six sevens are 42.

If A or B wins: practise the 7 times table in order, then mixed.

Q6. What is 23 × 4?

• A. 82 — did 3 × 4 = 12, wrote 2, and forgot to carry the 1
• B. 92
• C. 812 — multiplied each digit separately and joined the answers: 8 and 12
• D. 46 — doubled 23 instead of multiplying by 4

Answer: B — 92. Partition: 20 × 4 = 80 and 3 × 4 = 12; 80 + 12 = 92.

If C wins: write out partitioning: two multiplications, then add.

Q7. What is 48 ÷ 6?

• A. 6 — divided 48 by 8, swapping the divisor and the answer
• B. 8
• C. 7 — used 6 × 7 = 42, the nearest fact below
• D. 42 — subtracted 6 from 48 instead of dividing

Answer: B — 8. Six eights are 48, so 48 ÷ 6 = 8.

If A wins: practise the link — "6 × ? = 48" is the same question.

Fractions — Questions 8–10

Q8. Which fraction is bigger, 3/4 or 5/8?

• A. 3/4
• B. 5/8 — compares the numbers as whole numbers: 5 > 3 and 8 > 4
• C. They are equal — assumes two fractions with different numbers are the same size
• D. You can't tell — has no strategy for comparing fractions

Answer: A — 3/4. Convert to eighths: 3/4 = 6/8, bigger than 5/8.

If B wins: go back to fraction strips — same wholes, different numbers of pieces. Bigger pieces beat more pieces.

Q9. What is 1/2 + 1/4?

• A. 2/6 — added tops and bottoms: 1 + 1 = 2, 2 + 4 = 6
• B. 1/2 — added the numerators, kept a denominator (2/4), then simplified
• C. 3/4
• D. 2/8 — added the numerators but multiplied the denominators

Answer: C — 3/4. Common denominator first: 1/2 = 2/4, and 2/4 + 1/4 = 3/4.

If A wins: use a bar model: adding denominators shrinks the pieces, not the total.

Q10. What is 3/5 of 20?

• A. 15 — divided 20 by 4 instead of 5, then multiplied by 3
• B. 12
• C. 4 — divided by 5 but forgot to multiply by 3
• D. 60 — multiplied 20 by 3 but forgot to divide by 5

Answer: B — 12. Divide by 5 first (20 ÷ 5 = 4), then multiply by 3 (4 × 3 = 12).

If C or D wins: re-teach the two steps: "divide first, then multiply".

Decimals — Questions 11–12

Q11. Which is bigger, 0.6 or 0.59?

• A. 0.6
• B. 0.59 — thinks the longer number is bigger, because 59 > 6
• C. They are equal — thinks the digits 6 and 9 balance out
• D. 0.69 — joined the digits together instead of comparing

Answer: A — 0.6. Write both with two decimal places: 0.60 beats 0.59.

If B wins: use a hundred square: 0.6 covers 60 squares, 0.59 covers 59.

Q12. What is 1.4 + 0.25?

• A. 1.29 — lined up the right-hand digits and added 4 + 25 = 29
• B. 1.39 — treated the decimals as whole numbers: 14 + 25 = 39
• C. 3.9 — read 0.25 as 2.5
• D. 1.65

Answer: D — 1.65. Line up the decimal points: 1.40 + 0.25 = 1.65.

If A wins: re-teach column addition with decimal points aligned.

Measurement — Questions 13–14

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Q13. A pencil is 15 cm long — how long in millimetres?

• A. 150 mm
• B. 15 mm — kept the same number and just changed the unit
• C. 1.5 mm — divided by 10 instead of multiplying
• D. 1500 mm — multiplied by 100 instead of 10

Answer: A — 150 mm. There are 10 mm in 1 cm, so 15 × 10 = 150 mm.

If B wins: measure real objects in both units.

Q14. A rectangle is 5 cm by 3 cm. What is its perimeter?

• A. 15 cm — calculated the area (5 × 3) instead of the perimeter
• B. 8 cm — added 5 + 3 once, counting only two sides
• C. 16 cm
• D. 30 cm — doubled the area instead of adding the sides

Answer: C — 16 cm. The distance around: 5 + 3 + 5 + 3 = 16 cm.

If A or D wins: walk around the shape with a finger, or measure a real rectangle with string, first.

Shape — Questions 15–16

Q15. Which shape has 4 equal sides and 4 right angles?

• A. Rectangle — has 4 right angles, but only opposite sides are equal
• B. Rhombus — has 4 equal sides, but its angles are not right angles
• C. Triangle — has 3 sides, not 4
• D. Square

Answer: D — Square. The only shape here with all four sides equal and all four angles right angles.

If A wins: compare a square with a long rectangle.

Q16. A triangle has angles 90°, 45° and 45°. What type is it?

• A. Right-angled isosceles
• B. Equilateral — all three angles would have to be equal (60° each)
• C. Scalene — all three angles would have to be different
• D. Obtuse — would need an angle bigger than 90°

Answer: A — Right-angled isosceles. The 90° angle makes it right-angled; the two equal 45° angles make it isosceles.

If B wins: re-teach that "equilateral" means all sides and all angles equal.

Time — Questions 17–18

Q17. What time is 2:45?

• A. Quarter past 2 — that is 2:15, not 2:45
• B. Quarter to 3
• C. Half past 2 — that is 2:30, not 2:45
• D. Quarter to 2 — that is 1:45, not 2:45

Answer: B — Quarter to 3. At 2:45, 15 minutes remain until 3 o'clock.

If A wins: practise "past" and "to" on a clock face.

Q18. A film starts at 3:20 pm and lasts 1 hour 50 minutes. When does it end?

• A. 4:70 pm — added hours and minutes separately (3 + 1 = 4, 20 + 50 = 70) without converting
• B. 5:10 pm
• C. 4:50 pm — treated 50 minutes as half an hour
• D. 6:10 pm — added an extra hour

Answer: B — 5:10 pm. 3:20 + 1 hour = 4:20; 4:20 + 50 minutes = 5:10.

If A wins: minutes never pass 59 — 70 minutes is 1 hour 10 minutes. Show it on a number line.

Mixed — Questions 19–20

Q19. A book costs £4.50. You pay with £5. How much change?

• A. £1.50 — subtracted pounds and pence separately: 5 − 4 = 1, and kept the 50p
• B. 5p — gave 50p as 5p — wrong place
• C. 50p
• D. £4.50 — repeated the price instead of working out the change

Answer: C — 50p. £5.00 − £4.50 = £0.50, which is 50p.

If A wins: count up from £4.50 to £5.00 on a number line, or use real coins.

Q20. Which calculation equals 6 × 4?

• A. 6 + 4 — added instead of multiplying (10, not 24)
• B. 6 − 4 — subtracted instead of multiplying (2, not 24)
• C. 6 ÷ 4 — divided instead of multiplying (1.5, not 24)
• D. 4 × 6 — multiplication can be done in either order

Answer: D — 4 × 6. Multiplication is commutative: 6 × 4 and 4 × 6 both equal 24.

If A, B or C wins: show the same numbers with each sign and compare the answers.

How to read the answers — the 30-second decision

• Almost everyone right: the idea is secure — move on.
• One wrong answer wins: one misconception — re-teach that idea now.
• Answers split everywhere: the idea isn't secure — go back a step.
• Most right, a few on one wrong answer: move on and help that small group later.

Keep a one-line note after each lesson: the question, the winning wrong answer, and what you did. After a few weeks, you will have a map of your class's misconceptions. For a matching end-of-lesson check, see our Exit Ticket Questions for Science Lessons.

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Frequently asked questions

What is a hinge question?

One multiple-choice question, asked where everything after it depends on the class understanding what came before — the lesson "hinges" on the answer. The term is Dylan Wiliam's. Every pupil answers at once, and the pattern decides: move on, re-explain, or fix one misconception.

How is a hinge question different from a normal quiz question?

A normal question checks whether pupils know the answer. A hinge question checks how they think: each wrong option matches a specific misconception, so the wrong answer tells you what to teach next — asked mid-lesson, while there is still time to change the teaching.

How many hinge questions should I ask in a lesson?

Usually one or two — one at each point where the lesson genuinely turns. Each costs about two minutes, so choose the step everything else depends on.

Should I grade hinge questions?

No. Once it counts towards a mark, pupils answer safely instead of honestly. Keep hinge questions ungraded; use them to plan your next five minutes, not your mark book.

Do hinge questions work for subjects other than maths?

Yes — anywhere a misconception can be a wrong option: science, grammar, history. Maths is the easiest place to start because misconceptions are so predictable. Our Exit Ticket Questions for Science Lessons applies the same idea at the end of a lesson.

What to do next

1. Pick one question for tomorrow's lesson — the one matching the step your class is about to take.
2. Prepare mini-whiteboards (or A–D cards) so every pupil answers at once.
3. Ask it, scan the answers, and act on the pattern: move on, re-teach one idea, or go back a step.
4. Note the winning wrong answer in one line — your misconception map for the class.
5. Read Edutopia's quick formative assessments for more two-minute checks.

All 20 questions are original MissMono teaching material, except Q8, which follows the canonical worked example. The hinge-question technique is Dylan Wiliam's; this page is not affiliated with or endorsed by him.