Letters stand for numbers. Do the sum, then turn the answer back into a letter. That last step is the one children forget, and forgetting it costs the whole mark.
This is one of the applied verbal reasoning types: there is a rule, it can be taught in a session, and a child who has it improves immediately.
What the question asks
You are given letters with number values, then a calculation written in letters, and five lettered options. For example: if A = 3, B = 4, C = 12, D = 7 and E = 1, what is A times B?
Three steps, and the third is the one
- Substitute. Write the number above each letter in the calculation.
- Calculate. Normal arithmetic, normal order of operations.
- Convert back. Find which letter has that value, and answer with the letter.
Write the values down rather than holding them in your head. With five letters in play, a child trying to remember them all will drop one.
A worked example
Using A = 3, B = 4, C = 12, D = 7, E = 1:
| Question | Substituted | Answer | As a letter |
|---|---|---|---|
| A × B | 3 × 4 | 12 | C |
| D − A | 7 − 3 | 4 | B |
| C ÷ A | 12 ÷ 3 | 4 | B |
| A + B | 3 + 4 | 7 | D |
Note the second and third rows give the same answer by different routes. That is deliberate in real papers, and it is why the final conversion matters: 4 is not the answer, B is.
Where the marks go
- Answering with the number. The options are letters. If 12 is not offered, a child who worked out 12 has nothing.
- Not writing the values down. Five letters is more than most children hold reliably.
- Ignoring order of operations. Multiplication and division come before addition and subtraction, exactly as in maths.
- Panicking at an answer with no letter. Recheck the arithmetic: in a well-set question the answer always has a letter.
See our guide to letter and number codes and our guide to verbal reasoning.
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The answer is a letter, not a number
I find it useful to split verbal reasoning into applied topics and language topics. Coded calculations sit squarely in the applied family: there is a rule, it can be taught, and once a child has it they improve fast.
The one thing that costs marks here is not the arithmetic. It is finishing. A child substitutes correctly, calculates correctly, arrives at twelve, and then looks at five lettered options wondering what went wrong. The answer was C.
So I drill the three steps as three steps, out loud. Substitute, calculate, convert back. The third one has to feel as compulsory as the other two, because on its own it is the difference between a mark and nothing.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
What are letter-coded calculations in the 11+?
Letters are given number values, a calculation is written using the letters, and the answer must be given as a letter. So you substitute the numbers, do the arithmetic, then convert the result back into whichever letter holds that value.
What do children get wrong on coded calculations?
They answer with the number. The options are letters, so a child who correctly works out 12 but does not convert it back to C has nothing to choose. It is the third step, and it is the one that gets dropped.
Do order of operations rules apply?
Yes, exactly as in ordinary maths. Multiplication and division come before addition and subtraction, so a calculation must not simply be worked left to right.
What if the answer does not match any letter?
Recheck the arithmetic, because in a well-set question the result always corresponds to one of the given letters. An answer with no letter is a signal that something has gone wrong earlier.
Are coded calculations worth practising?
Yes, they are among the best value in verbal reasoning. This is an applied type with a teachable rule, so a child shown a reliable method improves straight away, unlike the vocabulary-based types which take months of reading.