Write every gap, with its sign: number sequences
The Short Answer
A number sequence gives a run of numbers and asks for a missing one. Write the gap between every pair, with its sign, before naming any rule at all. If the gaps are equal, the rule is a constant step. If they are not, look at what the gaps themselves are doing — that second row is where the harder sequences hide their pattern.
What is a number sequence question?
A run of numbers with one missing — usually at the end, sometimes in the middle — and your child has to work out the rule and supply it.
None of the arithmetic will trouble them. Identifying which rule they are looking at is the whole difficulty.
Gaps first, and check every one
The move everything else rests on:
Write the gap between every pair of numbers, with its sign, before you name any rule at all.
Not the first two. All of them. Two equal gaps could be a constant step, or the opening of a growing pattern, and there is no way to tell from two.
Once every gap is on the page, the rule is usually simply visible — and that is the point. This topic rewards a routine rather than insight, and a routine is what survives being rushed.
When the gaps themselves change
Write the sign
In 40, 33, 26, 19 the gaps are −7, not 7.
A child who writes 7 has a row of sevens in front of them and every invitation to add. Writing the minus keeps the direction on the page, and direction accounts for a good share of the errors on this topic.
A number missing from the middle
Work from the numbers either side of the gap, not from the start of the sequence.
5, ?, 17, 23. The gap from 17 to 23 is 6. The sequence is a constant step, so the gap from 5 to the missing number is also 6 — the answer is 11.
Children instinctively start at the beginning and try to work forwards through the hole. Starting from the complete pair is easier and quicker.
Where do pupils lose marks?
Naming a rule from two numbers, and being wrong at the fourth.
Dropping the sign in a descending sequence.
Stopping at the first row of gaps when the pattern is in the second.
Try it yourself
Write every gap with its sign underneath the sequence before deciding anything.
- 7, 12, 19, 28, ?
- What are the gaps in that sequence, and what are they doing?
- 3, 6, 12, 24, ?
- 40, 33, 26, 19, ?
- 5, ?, 17, 23 — find the missing number.
- 39. The gaps are +5, +7, +9 — growing by two each time — so the next gap is +11, and 28 + 11 = 39.
- 5, 7, 9. They are not equal, so this is not a constant step. Looking at what the gaps themselves do, they grow by 2 each time, which is the second row where the pattern lives.
- 48. The gaps are 3, 6, 12, which are growing by doubling — easier to see as multiplication: each number is twice the one before.
- 12. The gaps are −7 each time. Writing the sign matters here: a child who writes 7 rather than −7 can talk themselves into adding.
- 11. The gap from 17 to 23 is 6, and the sequence is a constant step, so the gap from 5 to the missing number is also 6. Working backwards from the numbers you have is the method for a gap in the middle.
How much practice does this type need at home?
Three short sessions a week, and the most useful drill 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 topic whatever they know about rules.
After that, ask your child to invent a sequence and tell you the rule afterwards. Building one means choosing a rule and applying it consistently, which is the same knowledge tested from the more enjoyable side.
Free: a Maths workbook
Questions across the Maths 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 gaps down rather than work them out mentally?
Because it is faster, not merely safer. Writing four gaps takes a few seconds; guessing a rule from the first two numbers and finding out at the fourth that it is wrong costs far more, and by then the working is muddled. Once the gaps are on the page the rule is usually visible without any thinking at all, which is exactly what you want with a clock running.
Why does the sign matter?
Because a descending sequence written without signs looks like an ascending one. In 40, 33, 26, 19 the gaps are −7, and a child who writes 7 has a row of sevens in front of them and an invitation to add. Writing −7 keeps the direction visible, and direction is what half the errors on this topic come down to.
What do I do when the gaps are not equal?
Look at what the gaps are doing, which means writing a second row of gaps underneath the first. In 7, 12, 19, 28 the gaps are 5, 7, 9 and the gaps between those are 2, 2 — constant. That tells you the next gap is 11. The pattern was never in the numbers; it was one level down.
How does my child find a number missing from the middle?
Work from the numbers either side of the gap rather than from the start. If the sequence is a constant step, find the step from a pair that is complete, then apply it backwards or forwards to the gap. Children instinctively start at the beginning and try to work forwards through the hole, which is harder than it needs to be.
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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