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 

Age 11 to 18
This article by Colin Foster presents the idea of mathematical etudes as a way to develop fluency without tedium.

Almost One 

Age 11 to 14
Challenge Level
Choose some fractions and add them together. Can you get close to 1?

Triangles in Circles 

Age 11 to 14
Challenge Level
Can you find triangles on a 9-point circle? Can you work out their angles?

Cyclic Quadrilaterals 

Age 11 to 16
Challenge Level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

The Simple Life 

Age 11 to 14
Challenge Level
The answer is $5x+8y$... What was the question?