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Maths: question types and approaches
The same mathematical knowledge can appear in many disguises. These examples show how to identify the quantity you need, select a method and check the result.
Choose a topic below. Each worked example is deliberately small so the method is easy to follow; exam questions may combine more features or steps. These are original teaching examples, not copied test questions.
Question type 1
Number and calculation
Skill and approach: Use place value, number facts and accurate operations.
Try the idea: Calculate 4.8 ÷ 10.
See the worked explanation
0.48. Dividing by ten makes each digit’s value one tenth as large. It does not mean removing a zero.
Watch for: Estimate whether the answer should be larger or smaller.
Question type 2
Fractions, decimals and percentages
Skill and approach: Connect equivalent amounts and distinguish a part from the whole.
Try the idea: Three eighths of 96 counters are blue. How many are not blue?
See the worked explanation
60. One eighth is 12; three eighths is 36. Subtract the blue counters: 96 − 36 = 60. Alternatively, find five eighths.
Watch for: Read whether the question asks for the selected part or what remains.
Question type 3
Ratio and proportion
Skill and approach: Identify equal-sized parts and scale them consistently.
Try the idea: Red and green beads are in the ratio 2:3. There are 40 beads. How many are green?
See the worked explanation
24. There are five ratio parts altogether. Each part contains 40 ÷ 5 = 8 beads, so green beads number 3 × 8.
Watch for: The ratio 2:3 does not mean two thirds of all the beads are red.
Question type 4
Measures, scales and time
Skill and approach: Identify units and interval sizes before calculating.
Try the idea: A journey starts at 09:45 and lasts 1 hour 35 minutes. When does it finish?
See the worked explanation
11:20. Add one hour to get 10:45, then 15 minutes to 11:00 and the remaining 20 minutes.
Watch for: For scales, count spaces between labels, not the marks themselves.
Question type 5
Shape, angles and coordinates
Skill and approach: Use geometric properties and distinguish different measurements.
Try the idea: A triangle has angles of 48° and 67°. Find its third angle.
See the worked explanation
65°. The known angles total 115°; subtract from 180°. Check: 48 + 67 + 65 = 180.
Watch for: For coordinates, read across first, then up or down.
Question type 6
Data and multi-step problems
Skill and approach: Read labels, select relevant information and link calculations.
Try the idea: A table shows 18 visitors on Monday and 27 on Tuesday. Each pays £4. What is the total income?
See the worked explanation
£180. Add the visitors first: 18 + 27 = 45. Multiply the total by £4. Check by calculating each day separately: £72 + £108.
Watch for: A correct calculation can answer the wrong question; reread the final instruction.
Helping at home
Ask “What are we finding?” before “Which calculation?”. A diagram or a short written plan can make multi-step problems clearer. Review the method as well as the final number.
Which types should we practise?
Use the target school’s current admissions guidance and familiarisation material to choose the relevant formats. This guide describes common question families, not a syllabus for every school. Check the test instructions about timing and whether children may return to earlier questions.
Further reading: Exam Papers Plus — Maths guidance and GL Assessment’s official familiarisation guidance. These links offer additional background; our explanations and worked examples are independently written.
A clearer next step for your child
Our 11+ tuition gives children time to explore unfamiliar questions and explain their thinking. Mock exams provide an opportunity to practise working through a paper in an exam setting.
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