---
title: "Generating a pattern from a rule"
description: "Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur"
canonical: https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy
source: https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy.md
retrieved: 2026-09-02
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Generating a pattern from a rule

Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

Subject: Mathematics · Area: Multiplication & Division · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy

## Ready when they can

- Given 'start at 1, add 3', generate terms and notice they alternate odd/even
- Given a shape pattern, predict the next three terms and describe the rule
- Explain why starting at 2 and adding 4 always gives even numbers

## Lesson: Building a pattern from a rule

A pattern rule tells you two things: where to start, and what to do every time. If the rule is 'start at 1, add 3,' you begin at 1, then add 3 again and again: 1, 4, 7, 10, 13. The step does not have to be adding. 'Start at 3, multiply by 2' gives 3, 6, 12, 24, 48.

*(drawing: Look closely: 1 is odd, 4 is even, 7 is odd, 10 is even, 13 is odd. Every other number flips between odd and even.)*

**Example.** Zara makes a shape pattern: circle, square, circle, square, circle. The rule is 'circle, then square, repeat.' The next three shapes are square, circle, square. Some patterns repeat a longer group, like circle, circle, square. Find the group that keeps coming back, then carry it on.

Patterns often hide a surprise the rule never mentions. In 1, 4, 7, 10, 13 the numbers flip odd, even, odd, even. That happens because the step, 3, is odd, and adding an odd number always swaps odd for even. When the step is even the flip never happens: start at 2 and add 4 and every number stays even, because even plus even is even.

**Recap.** A rule sets the start and the step, and once you build the pattern, watch for surprises hiding inside it, like numbers that keep flipping between odd and even.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Patterns in Times Tables](https://lightmysky.com/learn/mathematics/patterns-in-times-tables-mt_w6MxaaoMXZ)

## Opens up

- [Number Pattern Relationships](https://lightmysky.com/learn/mathematics/number-pattern-relationships-mt_fxPtngwUfz)
- [Linear number sequences](https://lightmysky.com/learn/mathematics/linear-number-sequences-mt_hBZwbst0ow)
- [Reasoning with Equivalences](https://lightmysky.com/learn/mathematics/reasoning-with-equivalences-mt_jCy07DyBNU)