Description
Explore a different kind of infinity: fractions nested inside fractions.
Learners meet continued fractions through accessible recursive examples and see how finite truncations give increasingly accurate rational approximations.
This lesson explores:
- reading and building nested fractions;
- continued fractions for the golden ratio;
- successive Fibonacci-ratio approximations;
- continued-fraction approximations to √2;
- comparing the accuracy of different approximations;
- solving a repeating continued fraction using algebra.
The printable handout includes worked examples, learner tasks, visual structure, grown-up guidance and answers/discussion. It is designed to stand alone as well as complement the website lesson.
Suitable for learners aged 10 and over; the algebraic challenge is optional extension material.
This is Lesson 5 of the six-part Beyond Curriculum: Magical Numbers course.
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