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For younger learners

  • Early Years Foundation Stage

The Art of Deduction

Creating convincing arguments or "proofs", to show that statements are always true, is a key mathematical skill. The problems in this feature offer you the chance to explore geometrical properties, make conjectures and create proofs to show that these are always true.

Many of the problems in this feature include proof sorting activities which challenge you to rearrange statements in order to recreate clear, rigorous proofs.  

Plus magazine has a selection of interesting articles exploring proofs in which pictures play an important role.

Pentakite

Age 14 to 18
Challenge Level Yellow star
Given a regular pentagon, can you find the distance between two non-adjacent vertices?

Quad in Quad

Age 14 to 18
Challenge Level Yellow starYellow star
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

Kite in a Square

Age 14 to 18
Challenge Level Yellow starYellow star
Can you make sense of the three methods to work out what fraction of the total area is shaded?

The Converse of Pythagoras

Age 14 to 18
Challenge Level Yellow starYellow star
Can you prove that triangles are right-angled when $a^2+b^2=c^2$?

To Swim or to Run?

Age 16 to 18
Challenge Level Yellow starYellow star
The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?


We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.

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Making Sense of Statistics

This collection of problems has been put together to help you to explore and understand important ideas in statistics.

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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