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Mathematical Etudes
Almost One
Triangles in Circles
Cyclic Quadrilaterals
The Simple Life
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
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 14Challenge Level 
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 14Challenge Level
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 16Challenge Level
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 14Challenge Level
Age 11 to 14
Challenge Level
The answer is $5x+8y$... What was the question?