The hardest 11+ maths topics and how to tackle them
The 11+ maths paper covers the full KS2 national curriculum, but a handful of topics produce far more wrong answers than the rest. They're the ones that ask children to hold two ideas in their head at once: A method and a reason for using it.
This guide walks through the topics that come up again and again as sticking points, with worked examples you can sit down and do with your child tonight. It's written for parents who don't necessarily want to teach the maths from scratch, but do want to know what to look for when something isn't clicking.
Why some 11+ topics are harder than others
The hardest 11+ maths topics tend to share three features. They build on top of an earlier idea (so a shaky foundation shows up later), they need a child to choose a method rather than apply a fixed recipe, and they appear inside word problems where the maths is hidden by the wording.
If your child gets every question right in a textbook chapter on fractions but trips up on a mixed paper, that's normal. Topic-by-topic practice is easier than mixed practice, and 11+ papers are deliberately mixed. The fix isn't more practice of the same topic, it's mixed practice where the child has to identify what kind of question they're looking at before solving it.
When your child gets a question wrong, ask them to talk you through what they did before you correct anything. Half the time you'll find the maths was fine and they read the question wrong. That's a different fix.
Fractions: One of the biggest sticking points
Fractions are among the most commonly missed topics at 11+. Adding and subtracting fractions with different denominators, ordering mixed numbers, and converting between mixed numbers and improper fractions all show up regularly.
The core issue is that fractions break the rule children learnt for whole numbers: A bigger number on the bottom means a smaller value. One-eighth is smaller than one-quarter, even though 8 is bigger than 4. Until that flip is internalised, every fractions question is a guess.
Worked example: Adding fractions with different denominators
Solve 2/3 + 1/4.
Step 1: Find a common denominator. The smallest number that both 3 and 4 divide into is 12.
Step 2: Convert each fraction. 2/3 = 8/12 (multiply top and bottom by 4). 1/4 = 3/12 (multiply top and bottom by 3).
Step 3: Add the numerators only. 8/12 + 3/12 = 11/12.
Step 4: Check whether the answer can be simplified. 11 and 12 share no common factor other than 1, so 11/12 is the final answer.
The most common mistake here is adding both the tops and the bottoms: 2/3 + 1/4 = 3/7. If your child writes that, the foundation isn't in place yet. Go back to a visual model (paper strips or fraction bars) before doing any more written practice.
Ratio and proportion: Word problems in disguise
Ratio questions at 11+ tend to be wrapped in real-world contexts: Sharing sweets, mixing paint, splitting prize money. The maths is straightforward once you've spotted the ratio. The hard part is spotting it.
The method is the same every time. Add the parts of the ratio to get the total number of shares, divide the total quantity by that number to find what one share is worth, then multiply back up to find each person's amount.
Worked example: Sharing in a ratio
Anya and Kwame share £45 in the ratio 4:5. How much does each receive?
Step 1: Add the parts. 4 + 5 = 9 shares in total.
Step 2: Find one share. £45 divided by 9 = £5.
Step 3: Multiply back. Anya gets 4 x £5 = £20. Kwame gets 5 x £5 = £25.
Step 4: Check the total. £20 + £25 = £45. Correct.
The check at the end is the bit children skip and shouldn't. It catches almost every arithmetic slip before they move on.
Order of operations (BIDMAS)
BIDMAS (brackets, indices, division and multiplication, addition and subtraction) is one of the topics where a child can know the rule and still get the answer wrong. The reason is that division and multiplication share a tier, as do addition and subtraction. Children often treat BIDMAS as a strict left-to-right list, so they do division before multiplication even when the multiplication comes first.
The rule is: When two operations are on the same tier, work left to right. So 12 divided by 3 multiplied by 2 isn't 12 / 6 = 2. It's 12 / 3 = 4, then 4 x 2 = 8.
Worked example: BIDMAS in a single expression
Calculate 3 + 4 x (5 - 2)² / 6.
Step 1: Brackets first. (5 - 2) = 3.
Step 2: Indices. 3² = 9. The expression becomes 3 + 4 x 9 / 6.
Step 3: Division and multiplication, left to right. 4 x 9 = 36. Then 36 / 6 = 6. The expression becomes 3 + 6.
Step 4: Addition. 3 + 6 = 9.
Final answer: 9.
A common error is doing 4 x 9 / 6 as 4 x (9/6), which gives 6 the slow way and works here, but breaks when the numbers don't divide neatly. Stick to strict left-to-right within a tier.
Early algebra: Substitution and simple equations
11+ algebra is usually limited to substitution (working out the value of an expression when you're told what the letters stand for) and one-step or two-step equations. It's not as hard as the word algebra suggests, but children often freeze at the sight of a letter where a number should be.
The key mental shift: A letter is just a placeholder for a number you don't know yet. Wherever you see x, you can write the number in pencil and treat the question normally.
Worked example: Substitution and a two-step equation
Substitution: If x = 4 and y = 7, find the value of 3x + 2y.
Replace each letter. 3(4) + 2(7) = 12 + 14 = 26.
Two-step equation: Solve 3x + 5 = 20.
Step 1: Undo the addition. Subtract 5 from both sides. 3x = 15.
Step 2: Undo the multiplication. Divide both sides by 3. x = 5.
Step 3: Check. 3(5) + 5 = 20. Correct.
When practising, write the check every time, even if it feels obvious. It catches sign errors, which are among the most common slips in early algebra.
Worded multi-step problems
Multi-step word problems are where everything else gets tested at once. The child has to read carefully, identify the operations, perform them in the right order, and check that the answer makes sense in context. Any weakness in the underlying topic gets exposed.
The most useful skill is underlining or jotting down what they know before they start calculating. Most wrong answers on word problems come from misreading the question, not from getting the maths wrong.
Worked example: A two-step word problem
A baker uses 250g of flour for one loaf. She wants to bake 6 loaves and has 1.5kg of flour. How much extra flour does she need?
Step 1: What does the question ask? The extra flour needed, in the same units (grams or kilograms).
Step 2: Work out flour required. 250g x 6 = 1,500g.
Step 3: Convert to matching units. 1.5kg = 1,500g.
Step 4: Compare. 1,500g - 1,500g = 0. She has exactly enough and doesn't need any extra.
The answer here is zero, which children find unsettling. Examiners write questions like this on purpose because guessing won't help, the child has to do the working. Reassure them that zero is a valid answer when the question has that outcome.
Geometry and measurement: Area, perimeter, volume
Geometry questions are usually less conceptually difficult, but they have the highest rate of unit errors. A perimeter answer left in cm² instead of cm, an area in cm instead of cm², or a volume confused with surface area. These all lose marks even when the calculation is correct.
The simplest fix is to write the units down before doing any maths. If your child writes "perimeter = ___ cm" at the start, they're far less likely to forget at the end.
The formula they need to know cold by exam day: Rectangle area = length x width. Triangle area = (base x height) / 2. Rectangle perimeter = 2 x (length + width). Cuboid volume = length x width x height. That's most of what comes up at 11+.
How to spot where your child is stuck
| What you see | What it usually means | What to do |
|---|---|---|
| Gets fractions right one day, wrong the next | Pattern-matches rather than understands the method | Use a visual model (paper strips, fraction bars) and rebuild from there |
| Word problems are blank, even on familiar topics | Reading comprehension, not the maths, is the blocker | Read the question together and ask what they think it's asking before any calculation |
| Long sequences of mental arithmetic produce small errors | Working memory overload, not weakness in the topic | Encourage writing each step down, even short ones |
| BIDMAS questions wrong despite knowing the rule | Misreading the same-tier left-to-right rule | Practise 10 mixed expressions with the rule visible, then 10 without |
| Geometry answers correct but with wrong units | Forgetting to track units through the calculation | Write the unit at the start of every answer, not the end |
Mark practice papers together but don't correct as you go. Let your child finish the paper, then walk back through wrong answers and ask them what they were thinking. The reasoning matters more than the right answer.
