# Mathematical Etudes and Purposeful Practice

### Mathematical Etudes and Purposeful Practice

In music, an etude is a piece designed to develop a particular skill while avoiding the tedium of practising without purpose. In this feature, Colin Foster introduces *mathematical etudes*; tasks for the mathematics classroom that give students opportunities to practise specific skills in a rewarding and rich context.

This article by Colin Foster presents the idea of mathematical etudes as a way to develop fluency without tedium.

##### Age 11 to 14

Challenge Level

Choose some fractions and add them together. Can you get close to 1?

##### Age 11 to 14

Challenge Level

Can you find triangles on a 9-point circle? Can you work out their angles?

##### Age 11 to 16

Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

##### Age 11 to 14

Challenge Level

The answer is $5x+8y$... What was the question?