Operations & Algebraic Thinking

Number Patterns

Generating and describing a number pattern from a given rule.

Intermediate15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Factors & Multiples

Following a Rule

A number pattern is a sequence of numbers generated by repeating the same rule over and over. Once the rule is known, the next several numbers in the pattern — and useful facts about every number in it — can be found without needing to see the whole sequence written out.

Definition — Pattern Rule

An instruction describing exactly how to get from one term in a sequence to the next, such as 'add 6' or 'multiply by 2.' Applying the rule repeatedly, starting from the first term, generates the entire pattern.

Given a starting number and a rule, a pattern is built one step at a time by applying the rule to the most recent term. Patterns can also reveal extra features — like every term always being even, or every term always ending in the same digit — beyond just the list of numbers itself.

Worked Example — Generating a Pattern from a Rule

Generate the first five terms of a pattern that starts at 3 and follows the rule 'add 5.' Start at 3, then repeatedly add 5: 3, 8, 13, 18, 23. Those are the first five terms.

Worked Example — Describing a Feature of a Pattern

A pattern starts at 2 and follows the rule 'multiply by 2': 2, 4, 8, 16, 32. What do you notice about every term? Every term in this pattern is an even number, since doubling any whole number always produces an even result.

Tip

Write out at least five or six terms of a pattern before trying to describe a feature of it — a feature that looks true for the first two or three terms sometimes breaks later in the sequence.

Common Mistakes

Applying the rule to the starting number itself instead of to the most recently generated term, producing an incorrect sequence.
After the first term, always apply the rule to the term that came immediately before, not back to the original starting number each time.
Confusing an addition rule with a multiplication rule, such as reading 'multiply by 2' as 'add 2.'
Read the rule carefully and apply the exact operation it names — addition and multiplication rules can produce very different-looking patterns from the same starting number.

Key Takeaways

A number pattern is generated by repeatedly applying the same rule, starting from a given number.
Each new term is found by applying the rule to the most recently generated term.
A pattern can have features, like every term being even, that go beyond just its list of numbers.

Summary

Number patterns apply a consistent rule to generate a predictable sequence. The next unit returns to place value, extending it to much larger, multi-digit numbers.

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