Number substitution (words as sums) questions appear in almost every GL-style verbal-reasoning paper, and they reward children who have a fixed, unhurried routine. Letters stand for numbers, and your child has to swap each letter for its value and work out a coded sum. Like every VR type, these stop being hard the moment the method becomes automatic — so here is exactly how to teach it, a full worked example, the traps that quietly cost marks, and how to build the skill using free practice.
What the question actually looks like
A typical question gives a short key such as "If A = 3, B = 6, C = 2, D = 8" and then asks your child to find the value of an expression like A × B − C, or to work out which answer letter matches the result. In a GL paper this sits inside a tightly timed test — around a minute a question, multiple-choice with answers on a separate OMR sheet, and no calculator — so mental accuracy under a little pressure is the real test, not clever arithmetic.
Papers usually include three to five of these per test. Each one is worth the same single mark as any other question, which is precisely why a reliable technique here is such high-value preparation: these are marks a well-drilled child should almost never drop.
The fixed five-step method
Teach this order every single time, until it runs on autopilot:
- Read the whole expression first. Notice the operations and any brackets before touching a number.
- Write each value above its letter. Physically pencil the number over the letter — A × B − C becomes 3 × 6 − 2 written out in full. Transcription, not maths, is where most marks die.
- Apply BIDMAS. Brackets, then Indices, then Division and Multiplication (left to right), then Addition and Subtraction (left to right).
- Work left to right within each stage. This stops silly slips when two operations share a level.
- Match to the answer options and check. Re-read the question to be sure you answered what was asked.
A full worked example
Using the key A = 3, B = 6, C = 2, find A × B − C.
- Substitute: 3 × 6 − 2.
- BIDMAS says multiply before subtracting: 3 × 6 = 18.
- Now subtract: 18 − 2 = 16.
The wrong answer here is 12 — that comes from working strictly left to right and doing 3 × 6 as if it were 3, then a jumble. The classic slip, though, is subtracting first: reading "6 − 2 = 4" and then "3 × 4 = 12". Both give 12, and 12 will very often be one of the tempting multiple-choice options placed there deliberately. BIDMAS is what separates 16 from the trap.
A harder Year 6 version
Now try a bracketed one to see the difficulty step up. Using A = 4, B = 5, C = 2, D = 3, find (A + B) × C − D.
- Substitute: (4 + 5) × 2 − 3.
- Brackets first: 4 + 5 = 9.
- Then multiply: 9 × 2 = 18.
- Then subtract: 18 − 3 = 15.
A Year 4 or 5 child meets the simple two-letter version; by Year 6 the examiner adds brackets, a division, or an extra term to test whether BIDMAS is genuinely secure. Practising both side by side builds a realistic sense of how the same skill scales up in a real paper.
The traps that cost marks
Almost every dropped mark on this question type comes from one of a small handful of errors. Drill your child to watch for each:
- Skipping BIDMAS and working blindly left to right — the single biggest cause of wrong answers.
- Grabbing a neighbouring letter's value — reading B's number for C because the key is cramped. Writing values above the letters fixes this.
- Sign slips with subtraction, especially where an answer could dip below zero.
- Answering the wrong thing — the last line sometimes asks "which letter equals this total?" not "what is the total?".
- Mis-shading the OMR sheet — the right sum, the wrong bubble. Always check the answer line matches the question number.
A quick BIDMAS reference
Keep this order visible while your child practises until it is memorised:
| Order | Stands for | Rule |
|---|---|---|
| 1 | Brackets | Do everything inside first |
| 2 | Indices | Powers and roots |
| 3 | Division / Multiplication | Left to right |
| 4 | Addition / Subtraction | Left to right |
How to practise this type
Little and often wins: five questions of this type daily for a week beats fifty crammed into one sitting. Our free verbal-reasoning worksheets are organised by exact question type, so you can drill number substitution on its own until the method is automatic. The Arena's VR mode gives instant feedback with XP for motivation, and you can chase a high score on the live leaderboard once accuracy is solid. When the type feels easy in isolation, fold it back into full timed mock papers so pacing develops alongside precision, and browse the revision hub to keep the wider syllabus ticking over. For the full landscape of question styles, see the 21 VR types overview.
Frequently asked questions
Is a calculator allowed?
No. GL-style 11+ papers are done entirely by hand, so all substitution and arithmetic must be mental or jotted in the margin. That is why fast, accurate BIDMAS is worth practising for its own sake.
How many of these appear in a test?
Typically three to five per verbal-reasoning paper, each worth one mark. Exact counts vary by region and year, so treat that as a guide rather than a fixed figure — but it is enough that reliable technique here noticeably lifts a score.
Does substitution appear in maths papers too?
Yes. The same "swap a letter for a number, then follow BIDMAS" skill underpins early algebra in the maths paper, so mastering it here pays off twice. Your child is really learning substitution, a core Year 5 to 6 idea, dressed up as a reasoning puzzle.