Teaching mathematics

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# Week 3: Developing understanding of proportion and ratio

## Introduction

The Mona Lisa, a portrait by the Renaissance painter Leonardo da Vinci, is said to be the best known, most visited and the most written about artwork in the world.

The proportions within this world-famous painting contain a special relationship, known as the golden ratio.

The golden ratio, or phi, is 1:1.618 and has been coined ‘golden’ because it is said to be aesthetically pleasing. Many artists and architects use this proportional relationship in their work.

Another of da Vinci’s most famous works is his Vitruvian man. The full title of this work is Le proporzioni del corpo umano secondo Vitruvio, which translates to The proportions of the human body according to Vitruvius.

Ratio and proportion played a crucial role in both of these important works of art, and the golden ratio can be found throughout the human body.

Figure 1 Leonardo da Vinci with some of his masterpieces

This is just one example of the application of proportional reasoning. This week explores how ratio and proportion relates to many other real-life contexts. You will consider how learners develop proportional reasoning and solve problems relating to ratio and proportion. You will also look at common mistakes and misconceptions which arise, and discuss how you might address these in your teaching.

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