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?