CogAT Number Series Guide: Patterns, Strategies and Practice

Of the three sections in the CogAT Quantitative Battery, number series questions are the ones that most children find simultaneously the most familiar and the most confusing. Every child has worked with number patterns in maths class. But the patterns in the CogAT Quantitative Battery are designed to be non-routine — they require genuine reasoning, not just arithmetic — and children who encounter them without preparation are often surprised by how different they feel from classroom maths.

This guide covers the most common number series patterns, the strategies that work, and how to practise effectively at home.

What number series questions look like

A number series question presents a sequence of numbers that follows a specific rule, then asks the student to identify what comes next (or what is missing from the middle). A simple example:

3, 6, 9, 12, ___   Answer: 15 (add 3 each time)

Harder questions involve multiple rules operating simultaneously, non-constant differences, or alternating sequences:

2, 3, 5, 8, 12, ___   Answer: 17 (differences increase by 1: +1, +2, +3, +4, +5)

The eight most common pattern types

1. Constant addition or subtraction

The simplest type — add or subtract the same number each time. 4, 7, 10, 13, ___ (add 3). Virtually all children can handle this; the challenge is recognising it quickly when it's embedded in a more complex-looking sequence.

2. Constant multiplication or division

Each term is multiplied or divided by the same number. 2, 4, 8, 16, ___ (multiply by 2). These "geometric sequences" appear from Grade 3 upward and require children to think multiplicatively rather than additively — a shift that takes practice.

3. Increasing or decreasing differences

The differences between consecutive terms themselves change in a pattern. 1, 2, 4, 7, 11, ___ — the differences are 1, 2, 3, 4, so the next difference is 5, giving 16. This is the pattern type that trips up the most children because it requires working at two levels simultaneously: the sequence itself, and the sequence of differences.

4. Alternating sequences

Two interleaved sequences that alternate: 1, 10, 2, 20, 3, 30, ___. The odd positions follow one rule (add 1) and the even positions follow another (add 10). The strategy is to look at every other term rather than consecutive terms.

5. Square and cube numbers

At higher grade levels: 1, 4, 9, 16, 25, ___ (perfect squares — 6² = 36). Children who haven't memorised square and cube numbers struggle to recognise these patterns quickly.

6. Fibonacci-style sequences

Each term is the sum of the two preceding terms: 1, 1, 2, 3, 5, 8, ___. These appear at Grade 4 and above. The key insight is that you're adding the two terms before, not applying a fixed rule to each term independently.

7. Combined operations

The rule alternates between two operations: 2, 4, 3, 6, 5, 10, ___ (multiply by 2, then subtract 1, alternating). These require careful tracking of position within the sequence.

8. Fraction and decimal sequences

At Grade 5 and above: 0.1, 0.3, 0.5, 0.7, ___ or ½, 1, 1½, 2, ___. The pattern logic is identical to whole-number sequences — it's the number form that requires familiarity.

Common mistakes to practise away

Applying the rule to the wrong term. In alternating sequences, children often apply the pattern they've identified to the next consecutive term rather than to the next term in the same sub-sequence. Slowing down to identify the type of sequence before applying a rule prevents this.

Stopping after finding the first pattern. Some sequences require checking whether the pattern holds across all terms before committing to an answer. A child who identifies "+3" from the first two terms and assumes it applies throughout can be tripped up by a sequence where the rule changes.

Arithmetic errors under time pressure. Number series questions are timed, and rushing through the arithmetic step introduces calculation errors even when the reasoning is correct. Building speed with mental maths — not just pattern recognition — improves accuracy on these questions.

How to practise at home

Number series practice is one of the easiest types to do conversationally, without any materials at all. At dinner or in the car: "I'm thinking of a number sequence: 3, 6, 12, 24. What comes next? What's the rule?" Starting with simple rules and progressively introducing the pattern types above builds both the recognition skills and the arithmetic fluency the test requires.

For children who struggle with the increasing-difference type, practise writing out the differences explicitly: write the sequence on paper, then write the gap between each pair of numbers below it, then write the gap between those gaps. Seeing the levels of pattern laid out visually makes the structure clear in a way that mentally tracking it often doesn't.