Loading...CAT4 Number Series Practice: Questions, Examples and Strategies
Learn how CAT4 Number Series questions work, which numerical rules pupils need to recognise, how to solve them systematically and how to practise without encouraging guessing.
What is CAT4 Number Series?
CAT4 Number Series is one of the two subtests within the Quantitative Reasoning battery. Pupils are shown a sequence of numbers and must identify the rule that determines which number should come next.
What the task requires
- Detecting numerical patterns
- Tracking repeated or alternating operations
- Using differences, ratios and familiar number relationships
- Holding several terms in working memory
- Testing whether a proposed rule fits the whole sequence
- Rejecting distractors that fit only part of the pattern
What it is not
- A test of memorising one fixed list of sequences
- A standard school arithmetic exercise
- A task solved reliably from only the final two terms
- A subtest where the first plausible rule must be correct
- A complete measure of a pupil’s mathematical attainment
- The only quantitative evidence in a CAT4 profile
Six common CAT4 Number Series rule families
The difficulty comes from identifying which relationship remains consistent across the complete sequence. At higher levels, more than one rule may operate at the same time.
Constant addition or subtraction
The same number is added or subtracted each time. The first useful check is the difference between neighbouring terms.
Example: 5, 9, 13, 17 …
Multiplication or division
Each term is created by multiplying or dividing the previous term by the same value.
Example: 3, 6, 12, 24 …
Alternating operations
Two operations repeat in turn. Pupils may need to separate odd-position and even-position transitions.
Example: 4, 8, 10, 20, 22 …
Increasing or decreasing differences
The amount added or subtracted changes systematically, such as increasing by one on every step.
Example: 2, 5, 9, 14, 20 …
Interleaved sequences
Two independent patterns occupy alternating positions. Comparing every second term may reveal the structure.
Example: 2, 10, 4, 20, 6, 30 …
Familiar number patterns
Sequences may use squares, cubes, doubling, halving or another familiar relationship, especially at higher levels.
Example: 1, 4, 9, 16, 25 …
A worked CAT4 Number Series example
Question
Step-by-step solution
The difference between each pair of neighbouring terms is three:
4 + 3 = 7
7 + 3 = 10
10 + 3 = 13
The rule is therefore “add three each time”. The next term is:
13 + 3 = 16
This is an original illustrative example created to explain the reasoning method. It is not a copied or live CAT4 item.
A four-step strategy for CAT4 Number Series
The same routine can be adapted across simple and difficult sequences. It reduces impulsive guessing and helps pupils explain their reasoning.
Compare neighbouring terms
Calculate or estimate the differences. If the values grow quickly, also consider multiplication or division.
Look for repetition, alternation or changing gaps
If one rule does not fit, check whether two operations alternate, the difference changes systematically or two sequences are interleaved.
State the rule precisely
Describe the rule before selecting an answer: for example, “add three, then double” rather than “the numbers get bigger”.
Test and predict
Apply the rule across the complete sequence. Only then use it to calculate the next term and compare it with the options.
Common CAT4 Number Series mistakes
Most errors are not random. Identifying the error type tells parents and tutors what the pupil should practise next.
Using only the final two terms
A rule may fit one transition by coincidence. It must explain every transition in the sequence.
Assuming constant addition
Not every series uses the same gap. Check multiplication, alternation and increasing differences.
Missing two interleaved patterns
If adjacent transitions look inconsistent, compare the first, third and fifth terms separately from the second, fourth and sixth.
Correct rule, inaccurate arithmetic
Pupils may identify the pattern but make a calculation error when applying it to the final term.
Choosing the first plausible option
Distractors may represent common arithmetic slips or a rule that works for only part of the sequence.
Rushing before the method is secure
Early timing can reward guesswork. Accuracy and explanation should come before speed.
How parents and tutors should use Number Series practice
Effective practice
- Begin with a small number of untimed questions
- Ask the pupil to explain the rule aloud
- Check that the rule works across every term
- Record whether mistakes are strategic or arithmetic
- Mix rule families after each is understood separately
- Add short timed sets gradually
Practice to avoid
- Repeating the same memorised sequences
- Giving the operation before the pupil has reasoned
- Completing long sets without reviewing mistakes
- Using materials intended for a much older pupil
- Judging progress from one short sample score
- Treating speed as more important than method
How Number Series difficulty changes by CAT4 level
The format remains broadly recognisable, but the complexity of the rules, distractors and numerical values increases with age.
| School stage | Likely emphasis | Useful preparation |
|---|---|---|
| Years 4–5 | Clear addition, subtraction, multiplication and simple alternating patterns | Use short untimed sets and ask the pupil to describe each gap. |
| Years 6–7 | Changing differences, interleaving and combinations of familiar operations | Teach pupils to compare every second term and test rules systematically. |
| Years 8–9 | Less obvious relationships and distractors based on partial rules | Mix rule families and practise rejecting answers that fit only part of the sequence. |
| Years 10–11 | Multi-step operations, closer alternatives and greater pacing demands | Use realistic Level F/G mixed practice after the method is secure. |
Number Series compared with Number Analogies
Number Series
Pupils identify a rule operating through a sequence and use it to predict the next term.
Main demand: tracking change over several positions.
Number Analogies
Pupils identify a relationship in one group of numbers and transfer it to another group.
Main demand: applying the same transformation consistently.
CAT4 Number Series questions answered
What is CAT4 Number Series?
What does CAT4 Number Series measure?
What kinds of rules appear in Number Series questions?
How should a child practise CAT4 Number Series?
What should a pupil do when no single rule seems to work?
Should children memorise CAT4 Number Series questions?
Is Number Series the same as Number Analogies?
Should Number Series practice be timed?
Does one weak Number Series result determine the CAT4 score?
What is the best first step?
Practise CAT4 Number Series using a reliable method
Begin with the free sample, identify which rule families are unfamiliar and introduce timing only after the pupil can explain and check the pattern accurately.