Most 11+ maths is mental arithmetic against the clock. A typical GL Assessment maths paper asks around 50 questions in 50 minutes — roughly a minute each — with no calculator and answers marked A to E on a separate OMR sheet. There is simply no time for long, formal working on every question. The children who score highest are not the ones who write the most; they are the ones who calculate in their heads with a few quick jottings and move on. This guide sets out the mental-maths techniques that genuinely double a child's speed, with worked examples you can practise tonight.
Why mental maths decides the 11+
Speed and accuracy carry equal weight in a tightly timed paper. A child who knows every method but works slowly will leave questions blank at the end — and blanks score zero. Because GL papers are age-standardised, raw marks are converted into a Standard Age Score (SAS, roughly 69 to 141, with 100 the average and many grammar schools looking for around 111 and above), so every extra question answered correctly nudges that score upward. The goal is not just getting it right but getting it right fast enough to reach the end. Building fluency now is the single highest-value thing you can do, and it pairs neatly with timed practice on our mock papers and free maths worksheets.
The foundations: tables and square numbers
Every mental shortcut rests on two things being automatic. First, times tables to 12 × 12 — not negotiable. By the start of Year 5, each fact should surface in under two seconds, because every hesitation costs time on dozens of questions. Second, the square numbers, which examiners lean on constantly in area, sequence and factor questions.
- Square numbers to 15: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
- Handy extras: 16² = 256, 20² = 400, 25² = 625.
- Cube numbers: 1, 8, 27, 64, 125 — these appear in volume and pattern questions.
If tables and squares are shaky, fix them first: five focused minutes a day beats one long weekly session, because retrieval practice little-and-often is what moves facts into instant recall.
Core speed techniques with worked examples
These are the workhorses. Teach one at a time, practise it until it is automatic, then add the next.
Doubling and halving
To multiply by 4, double and double again: 17 × 4 → 34 → 68. To multiply by 5, halve then times by 10: 46 × 5 = 23 × 10 = 230. To divide by 5, divide by 10 then double: 90 ÷ 5 = 9 × 2 = 18. To multiply by 50, times by 100 and halve: 18 × 50 = 1800 ÷ 2 = 900.
Compensation (round and adjust)
For addition near a round number: 368 + 197 = 368 + 200 − 3 = 565. For subtraction: 1003 − 487 = 1003 − 500 + 13 = 516. Round the awkward number to something friendly, then correct by the small difference. This is far faster and less error-prone than column methods for many exam numbers.
Partitioning for multiplication
Break a number apart: 23 × 6 = (20 × 6) + (3 × 6) = 120 + 18 = 138. To multiply by 9, times by 10 and subtract the number: 34 × 9 = 340 − 34 = 306. To multiply by 11 (two-digit), add the digits into the middle: 45 × 11 = 4_(4+5)_5 = 495.
Fractions and percentages of an amount
Build every percentage from a few anchors, using the rule 10% = divide by 10.
- 50% = halve; 25% = divide by 4; 20% = 10% doubled; 1% = divide by 100.
- Assemble the rest: 35% of 80 = 25% (20) + 10% (8) = 28.
- Fraction of an amount: divide by the bottom, times by the top. Three-fifths of 45 = 45 ÷ 5 × 3 = 27.
A mental-maths quick-reference
Pin this near the practice desk. Each row is a shortcut a child can rehearse until it is instant.
| Task | Fast method | Example |
|---|---|---|
| × 4 | Double twice | 19 × 4 = 76 |
| × 5 | Halve, × 10 | 48 × 5 = 240 |
| × 9 | × 10 then subtract | 27 × 9 = 243 |
| × 25 | × 100 then ÷ 4 | 16 × 25 = 400 |
| ÷ 5 | ÷ 10 then double | 85 ÷ 5 = 17 |
| 10% | ÷ 10 | 10% of 70 = 7 |
| Fraction of | ÷ bottom, × top | ⅗ of 40 = 24 |
Estimation: your built-in answer checker
Because GL answers are multiple-choice A to E, a quick estimate often eliminates two or three options before you calculate exactly. If 312 × 48 is asked, round to 300 × 50 = 15,000, so any option near 5,000 or 50,000 is a trap you can ignore. Rounding to a sensible degree of accuracy, then adjusting, is both a mental technique and a safety net against silly slips. Encourage your child to glance at the answer and ask, is this roughly the size I expected? before committing.
Common traps that cost marks
Speed only helps if accuracy holds. These are the recurring ways children lose marks in a real paper:
- The switched question. The last line changes what is asked — "how much change?" not "how much did it cost?" Underline the actual question.
- Forgetting to simplify. A fraction or ratio answer left unsimplified may not match any option — always reduce to lowest terms.
- Units drift. Mixing centimetres with metres, or minutes with hours. Convert everything to one unit first.
- Place-value slips. Losing a zero when multiplying by 50 or 25 — estimate to catch it.
- Answer-sheet misalignment. On a separate OMR sheet, one skipped bubble shifts every later answer. Check the number matches every few questions.
A method for multi-step worded problems
Speed techniques handle the arithmetic; a routine handles the reading. Teach this four-step habit:
- Underline the question — what exactly is being asked, and in what units?
- List what you are given — jot the numbers and what each represents.
- Choose the operation — decide add, subtract, multiply, divide, or a fraction/percentage of an amount.
- Check the answer's size — does it match your estimate, and is it in the right units?
Practising this on realistic questions in the revision hub turns it into an automatic reflex under exam pressure.
Building speed at home
Short, daily, timed practice is the pattern that works. Five minutes of mixed mental drills every day builds far more fluency than one long weekly slog, because each session forces rapid retrieval — exactly what the exam demands. Set a target time per question (aim for under a minute, working towards 40 seconds on the easier ones) so speed and accuracy grow together. Rotate through tables, squares, percentages and the shortcuts above, and log which ones are still slow. Our free timed mock papers and topic worksheets are built for exactly this daily rhythm, and children can chase a personal best on the live leaderboard to keep motivation high.
Frequently asked questions
Is a calculator allowed in the 11+ maths paper?
No. GL Assessment maths papers are non-calculator, which is precisely why fast, reliable mental arithmetic matters so much. Everything must be done in the head or with quick jottings on the question paper.
How many questions are there and how long per question?
Formats vary by region, but a common GL maths paper is around 50 questions in 50 minutes — roughly a minute each. CSSE and some independent papers differ, so check your target school on the grammar school directory and the 11+ process guide.
When should mental-maths practice start?
Ideally in Year 4 or early Year 5, so tables and squares are fully automatic before topic revision begins. That way the child spends exam time thinking about the problem, not recalling basic facts.