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.
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Mathematical etudes
This article by Colin Foster presents the idea of mathematical etudes as a way to develop fluency without tedium.
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Almost one
Age
11 to 14
Challenge level
Choose some fractions and add them together. Can you get close to 1?
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Triangles in circles
Age
11 to 14
Challenge level
Can you find triangles on a 9-point circle? Can you work out their angles?
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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?
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The simple life
Age
11 to 14
Challenge level
The answer is $5x+8y$... What was the question?
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Enriching the secondary curriculum
Age
11 to 16
Challenge level
Using NRICH tasks to enrich your students' mathematical experience
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Featuring our short problems
Age
11 to 16
Challenge level
Short problems ideal for revision and assessment