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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 link

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 One link

Almost One live

Stage: 3 Challenge Level: Challenge Level:1

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

Triangles in Circles link

Triangles in Circles live

Stage: 3 Challenge Level: Challenge Level:1

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

Cyclic Quadrilaterals link

Cyclic Quadrilaterals live

Stage: 3 Challenge Level: Challenge Level:1

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

The Simple Life link

The Simple Life live

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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