# 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.

### Mathematical Etudes

##### Stage: 3, 4 and 5

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

### Almost Onelive

##### Stage: 3 Challenge Level:

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

### Triangles in Circleslive

##### Stage: 3 Challenge Level:

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

##### Stage: 3 Challenge Level:

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

### The Simple Lifelive

##### Stage: 3 Challenge Level:

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