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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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.