11+ Maths: 12 Worked Examples
· 9 min read
Twelve worked 11+ maths examples across the topics that separate strong candidates — fractions, ratio, percentages, area and multi-step word problems.
Why practise 11+ maths with worked examples?
Most 11+ maths marks are lost not because a child cannot do the arithmetic, but because they do not recognise what a question is asking or skip a step under time pressure. Worked examples fix both problems. By following a clear, repeatable method on each question type, a child builds the habit of setting work out properly — which both reduces careless errors and earns method marks where papers award them. The examples below cover the topics that most often separate strong candidates from the rest: fractions and percentages, ratio, area and volume, and multi-step word problems. Work through each one untimed first, writing every step down, and only add time pressure once the method is automatic. These are the same topics covered in our complete list of 11+ maths topics; use that guide to map the full curriculum, then drill the methods here. For how to fold these into timed practice, see our guide to using practice papers well.
Fractions, decimals and percentages
Example 1 — Fraction of an amount: What is 3/4 of 60? Method: divide by the denominator, then multiply by the numerator. 60 divided by 4 is 15; 15 multiplied by 3 is 45. Answer: 45. Example 2 — Decimal to fraction: Write 0.35 as a fraction in its simplest form. Method: 0.35 is 35 hundredths, so 35/100; divide top and bottom by 5 to get 7/20. Answer: 7/20. Example 3 — Percentage of an amount: Find 15% of 80. Method: build it from easy chunks — 10% of 80 is 8, and 5% is half of that, 4; add them to get 12. Answer: 12. The thread through all three is that fractions, decimals and percentages are three ways of writing the same idea, and strong candidates convert fluently between them. Encourage your child to learn the common equivalents by heart (1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%, 3/4 = 0.75 = 75%) because instant recall of these saves precious seconds on every paper.
Ratio and proportion
Example 4 — Sharing in a ratio: Share £48 between two children in the ratio 3:5. Method: add the parts (3 + 5 = 8), divide the total by the number of parts (£48 divided by 8 = £6 per part), then multiply out: 3 parts is £18 and 5 parts is £30. Check they add back to £48. Answer: £18 and £30. Example 5 — Scaling a recipe: A recipe for 4 people uses 200g of flour. How much for 6 people? Method: find the amount per person (200g divided by 4 = 50g), then multiply by the new number (50g times 6 = 300g). Answer: 300g. Example 6 — Unit cost: If 5 pens cost £2.00, how much do 8 pens cost? Method: find the cost of one (200p divided by 5 = 40p), then multiply (40p times 8 = 320p = £3.20). Answer: £3.20. The reliable technique across all ratio and proportion questions is to find the value of one part or one unit first, then scale up. Children who try to jump straight to the answer tend to slip; the 'find one, then multiply' habit is almost foolproof.
Area, perimeter and volume
Example 7 — Rectangle: A rectangle is 8cm long and 5cm wide. Find its area and perimeter. Method: area is length times width (8 times 5 = 40 square cm); perimeter is the distance all the way round, 2 times (8 + 5) = 26cm. Note the units — area is in square cm, perimeter in cm — because mixing them up is a classic lost mark. Example 8 — Triangle: Find the area of a triangle with base 10cm and height 6cm. Method: area of a triangle is half the base times the height, so (10 times 6) divided by 2 = 30 square cm. Example 9 — Cuboid volume: Find the volume of a box 4cm by 3cm by 2cm. Method: volume is length times width times height (4 times 3 times 2 = 24 cubic cm). The recurring trap in this topic is units and formulae confusion, so drill your child to write the formula first, substitute the numbers, then state the answer with the correct unit (cm, square cm, or cubic cm). Getting into that three-line habit prevents most of the errors examiners see.
Multi-step word problems
Example 10 — Time: A train leaves at 09:45 and arrives at 11:20. How long is the journey? Method: count up from 09:45 to 10:45 (one hour), then 10:45 to 11:20 (35 minutes), giving 1 hour 35 minutes. Counting up in chunks is far safer than subtracting times. Example 11 — Money: Sarah has £20 and buys 3 books costing £4.50 each. How much change does she get? Method: find the total spent (3 times £4.50 = £13.50), then subtract from £20 to get £6.50. Answer: £6.50. Example 12 — Fractions in context: A class has 30 children and 2/5 are boys. How many girls are there? Method: find the boys (30 divided by 5 = 6, times 2 = 12 boys), then subtract from the total (30 minus 12 = 18 girls). Answer: 18. Multi-step problems are where careful candidates pull ahead, because each one hides two or three operations. Teach your child to underline what the question actually asks for, jot the steps in order, and check that the final answer makes sense in context before moving on.
How do I help when my child gets stuck?
When your child cannot start a question, resist the urge to show the answer — it teaches nothing and dents confidence. Instead, ask three questions in order: what is the question actually asking for, what information have we been given, and which single small step could we take first. Most stuck moments dissolve once a child names the goal and takes one concrete step. If they are still stuck, work the question together while narrating your own thinking out loud, then immediately give them a very similar question to do alone so the method sticks. Keep sessions short and frequent rather than long and exhausting; fifteen focused minutes a day beats a draining hour once a week. And track which topics recur as sticking points so you can target them, rather than re-covering ground your child already knows. If you would like the difficulty to adjust automatically to your child's level — easing off where they are confident and reinforcing where they struggle — our free diagnostic at grammarprep.uk/onboarding gives a starting benchmark across all four 11+ subjects, and the adaptive engine takes over from there. Pair this maths practice with the verbal reasoning worked examples to keep all four subjects moving together.