Write the jumps underneath: number sequences
The Short Answer
A number sequence gives a run of numbers and asks what comes next. Write the jump between each pair of numbers underneath, then look at the row of jumps. If they are all the same, add one more. If they are not, ask what the jumps themselves are doing. The arithmetic is never the difficulty — choosing which of the rules you are looking at is.
What is a number sequence question?
Your child is given a run of numbers and asked what comes next. Sometimes the missing number is in the middle rather than at the end.
None of the arithmetic will surprise them. The difficulty is entirely in working out which rule they are looking at, and doing it quickly.
Jumps underneath
The method has not changed since Year 4 and does not need to.
Write the jump between each pair of numbers underneath the sequence.
Look at the row of jumps. Are they all the same? If so, add one more jump to the last number.
If they are not the same, ask what the jumps themselves are doing.
If that leads nowhere, work through the other rules in order.
Writing the jumps down is faster than not writing them down. Not safer — faster. It costs a few seconds and it saves the guessing that eats a minute.
The five rules
| Rule | What it looks like | Example |
|---|---|---|
| Same jump | The jumps are all equal | 4, 7, 10, 13 |
| Multiply or divide | The numbers double, treble or halve | 3, 6, 12, 24 |
| Add the two before | Each number is the sum of the previous two | 1, 1, 2, 3, 5 |
| The jump grows | The jumps form their own sequence | 2, 3, 5, 8, 12 |
| Two taking turns | Jumps swing between large positive and negative | 5, 20, 6, 18, 7, 16 |
The last one is worth knowing by its signature. When the jumps make no sense at all — swinging from plus fifteen to minus fourteen — that is not a hard sequence. It is two easy ones interleaved.
Can you show me a worked example?
Where do pupils lose marks?
Not writing the jumps down and guessing a rule from the first two numbers.
Committing on two examples. Two jumps of plus three could be a constant jump or the start of something growing.
Missing the interleaved case and trying to force one rule onto numbers that are following two.
Arithmetic slips near the end. By the fifth number the working is long, and a subtraction done in the head is where the answer usually goes wrong.
Try it yourself
Write the jumps underneath before deciding anything. If the jumps make no sense, look at whether two sequences are taking turns.
- 4, 7, 10, 13, ?
- 3, 6, 12, 24, ?
- 1, 1, 2, 3, 5, ?
- 2, 3, 5, 8, 12, ?
- 5, 20, 6, 18, 7, 16, ?
- 16. The jumps are 3, 3, 3 — a constant jump, so add one more.
- 48. The jumps are 3, 6, 12, which are growing, and growing by doubling. Easier to see as multiplication: each number is twice the one before.
- 8. The jumps are 0, 1, 1, 2, which looks like chaos until you notice each number is the sum of the two before it: 3 plus 5 is 8.
- 17. The jumps are 1, 2, 3, 4 — the jump itself is growing by one each time, so the next jump is 5. 12 plus 5 is 17.
- 8. The jumps are 15, −14, 12, −11, 9, which alternate wildly, and that is the signal. Two sequences are taking turns: 5, 6, 7 going up by one, and 20, 18, 16 going down by two. The next number belongs to the first sequence, so it is 8.
How much practice does this type need at home?
Three short sessions a week, and the drill that helps most is not sequences at all — it is quick mental subtraction. Children who are slow at finding the gap between 47 and 61 are slow at this type, whatever they know about rules.
Beyond that, ask your child to make a sequence for you and tell you the rule afterwards. Building one requires choosing a rule and applying it consistently, which is the same knowledge the question tests, and it is considerably more fun than continuing somebody else's.
Free: a Verbal Reasoning workbook
Questions across the Verbal Reasoning question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why write the jumps down rather than work them out mentally?
Because it is faster, not safer. Writing four jumps costs a few seconds; guessing at a rule and finding out at the fourth number that it is wrong costs far more, and by then the working is muddled. Once the jumps are on the page the rule is usually visible without any thinking at all, which is exactly what you want when the clock is running.
What do I do when the jumps look like nonsense?
Suspect two sequences taking turns. Jumps that swing between large positive and large negative numbers almost always mean the sequence is really two sequences interleaved — look at the first, third and fifth numbers as one run, and the second, fourth and sixth as another. Each will have a simple rule of its own.
How does my child tell a growing jump from multiplication?
Write the jumps and then the jumps between the jumps. If the second row is constant, the jump is growing by a fixed amount. If the original numbers double or treble, multiplication is simpler to spot directly — 3, 6, 12, 24 announces itself. Where both readings work, choose the simpler one, because papers are set with one intended rule.
Are these different from the letter sequences in verbal reasoning?
They share a shape — find the rule, continue it — but numbers can grow and multiply in ways letters cannot, so there are more rules to distinguish. The habit that carries across is the same: write the gaps down before deciding, and never commit to a rule on the strength of two examples.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
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