The most obvious patterns are not always the ones we should be looking for.

In this lesson, students will explore a situation in which a simple pattern of numbers develops. However, this simple pattern does not continue beyond the 5th term, and it turns out that something more complicated is going on.

The purpose of the lesson is to encourage students to avoid making quick assumptions about number sequences and instead to look carefully at the details, exploring the mathematical structure that underlies the numbers.

Why teach this?

Attending to deep structure, rather than superficial patterns, is essential for tackling difficult mathematical problems.

Key curriculum links

• Make and test conjectures about the generalisations that underlie patterns and relationships
• Look for proofs or counter-examples

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