This complete printable course begins with the Fibonacci sequence and gradually connects number patterns to geometry, ratios, infinite decimals, continued fractions and numerical curiosities.

The complete course includes:

• Lesson 1: The Fibonacci sequence;
• Lesson 2: Fibonacci rectangles and spirals;
• Lesson 3: The golden ratio;
• Lesson 4: Numbers that go on forever;
• Lesson 5: Infinite fractions;
• Lesson 6: Other magical numbers;
• six standalone teaching handouts with worked examples and grown-up guidance;
• answers and discussion for every lesson;
• the complete Magical Numbers Exercises booklet with practice, reasoning, investigations and challenges.

The resources are designed for flexible use: follow the website alongside the printables, use the handouts independently, or print individual lessons as needed.

Suitable for learners aged 10 and over. Some later algebraic sections can be treated as optional extension material.

☕ Free to download

This resource is completely free. If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

This is the complete six-part Beyond Curriculum: Magical Numbers course from Sumthing Else.

The exercises are designed to reinforce the ideas from the lesson handouts while also giving learners opportunities to reason, investigate and go further.

The booklet includes practice on:

• the Fibonacci sequence;
• Fibonacci rectangles and spirals;
• the golden ratio;
• terminating, repeating and irrational decimals;
• continued fractions and approximations;
• other magical-number investigations.

Each lesson section includes a mixture of warm-up questions, core practice, reasoning, investigation and challenge tasks. Answers and discussion are collected at the end, with clickable navigation in the digital PDF.

Suitable for learners aged 10 and over.

Use this booklet alongside the Magical Numbers course or as additional independent practice.

☕ Free to download

This resource is completely free. If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.

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.

☕ Free to download

This resource is completely free. If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi.