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.
article
Mathematical etudes
This article by Colin Foster presents the idea of mathematical etudes as a way to develop fluency without tedium.
problem
Almost one
Age
11 to 14
Challenge level
Choose some fractions and add them together. Can you get close to 1?
problem
Triangles in circles
Age
11 to 14
Challenge level
Can you find triangles on a 9-point circle? Can you work out their angles?
problem
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?
problem
The simple life
Age
11 to 14
Challenge level
The answer is $5x+8y$... What was the question?