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For younger learners

  • Early Years Foundation Stage

Time to Be Irrational!

Time to be irrational!

This feature invites you to explore some of the more interesting properties of irrational numbers, and see how they crop up in algebra and geometry. Spend some time being irrational, and see what you discover!

Irrational Constructions 
Age 16 to 18
Challenge Level Yellow star

What questions does the spiral construction prompt you to ask?

Staircase Sequences 
Age 16 to 18
Challenge Level Yellow star

Can you make sense of these unusual fraction sequences?

Irrational Roots 
Age 16 to 18
Challenge Level Yellow star

You're used to working with quadratics with integer roots, but what about when the roots are irrational?

Nested Surds 
Age 16 to 18
Challenge Level Yellow starYellow starYellow star

Can you find values that make these surd statements true?

Related

  • The Root of the Problem
  • Indices and Surds
  • Sequences and Series

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The Value of Working Systematically

These problems are best solved using systematic approaches.

Integration as Area

These problems invite you to explore integration as area, and use area integrals to solve problems.

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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