Magical Numbers – Lesson 3: The Golden Ratio

Description

Meet the number that the Fibonacci ratios were approaching.

This lesson introduces the golden ratio through geometry and proportion before moving carefully into its algebraic properties.

Learners explore:

• what it means for rectangles to have the same proportions;
• comparing long-side : short-side ratios;
• the defining self-similarity of a golden rectangle;
• the golden ratio φ ≈ 1.618;
• the identity φ² = φ + 1;
• using that identity to simplify higher powers of φ.

The standalone printable handout contains diagrams, worked examples, learner prompts, explanations for younger learners, grown-up guidance and answers/discussion.

Suitable for learners aged 10 and over. The final algebraic section is a natural extension for learners ready for it.

This is Lesson 3 of the six-part Beyond Curriculum: Magical Numbers course.

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