In this feature you will be challenged to derive elegant and efficient solutions to problems which, at first sight, might seem very difficult.

We hope that these problems will help you appreciate that algebra can be a versatile tool for solving a range of problems.

This feature will introduce the symbols $\implies$ and $\iff$ and challenge you to reason logically and create true statements using these symbols.

In this feature you are invited to explore a variety of problems, and are then asked to construct convincing arguments to explain what you have discovered.

The problems in this feature offer you the chance to explore geometrical properties, and then challenge you to create clear, rigorous proofs.

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.

The problems in this feature challenge you to create convincing arguments or "proofs", and to identify where the logic breaks down in some "dodgy proofs".

The problems in this feature offer you the chance to identify number patterns, make conjectures and create convincing mathematical proofs.

The problems in this feature will encourage you to explore the impact that your lifestyle choices have on the environment.

The problems in this feature will allow you to explore the impact of lifestyle choices and help you gain a better understanding of the contributors to global emissions.

The resources in this feature introduce you to the world of networks and graph theory.

The resources in this feature have been designed to give you an introduction to the world of graph theory and networks, and to their applications.

Challenge Level

This collection of activities offers you a variety of playful contexts in which you will be challenged to plan ahead and analyse the outcomes.

This collection of activities offers you a variety of playful contexts in which you will be challenged to plan ahead and analyse the outcomes.

The problems in this feature will give you the chance to investigate the properties of numbers in a variety of contexts.

Enter the world of modular arithmetic and discover the secrets of public key cryptography.

This feature introduces you to number theory, a rich source of interesting problems which can lead to surprising results.

Number theory is a rich source of interesting problems which can lead to surprising results.

A chance to consider the equations of straight line graphs before moving on to consider the properties of quadratics and cubics.

Curve sketching can be a very useful tool when you are solving equations or inequalities.

Challenge Level

Probability can help you make better choices and challenge commonly-held misconceptions.

Challenge Level

The problems in this feature challenge you to explore different ways of arriving at a solution

Challenge Level

What makes a good mathematician? This feature will help you to build your mathematical muscles.

Challenge Level

A chance to compare numbers expressed in different ways, and to use these different representations in calculations.

Challenge Level

Use Cuisenaire rods to help you visualise patterns and relationships with numbers

Challenge Level

Explore these problems and explain the mathematical ideas you discover!

Challenge Level

Working backwards can help you to make great leaps forwards!

Challenge Level

These problems can be represented in many different ways!

Challenge Level

Find out about Complex Numbers and their applications.

Challenge Level

These problems will make you say "I wonder what happens if...?"

Challenge Level

If you know the output, how can you work out the input?

What if we could find the square root of negative numbers?

Challenge Level

We hope you enjoy being mathematically playful with these puzzling problems.

Challenge Level

This feature explores problems connected with area and integration

Challenge Level

These problems invite you to think about area in unusual ways.

Challenge Level

Resources to help you think about calculus and transformations

Challenge Level

Some mathematical results can be proved beautifully with just a simple diagram...

Challenge Level

These resources explore probability in medicine and the law.

Challenge Level

Explore how to use statistics and probability to make informed decisions

Challenge Level

These CMEP resources explore the use of trigonometric identities and other trig features

Challenge Level

Problems to help you get started with higher mathematics courses

Challenge Level

Be playful with graphs and networks, and see what theorems you can discover!

Challenge Level

Be playful with polygons. What patterns can you find?

Challenge Level

These resources from CMEP explore some aspects of differentiation and integration

In this feature, explore what happens to functions when you transform their graphs

Challenge Level

This CMEP feature explores the properties of circles and triangles

Challenge Level

Explore some shape problems and make some discoveries!

Challenge Level

Try some of our CMEP resources around the theme of logarithms.

Challenge Level

Explore and sketch curves with different properties.

Challenge Level

Try our new CMEP tasks to help you to think functionally!

Challenge Level

Who would have thought that addition could be so intriguing?

Challenge Level

Try some of our CMEP resources around the theme of quadratics.

Challenge Level

This feature introduces some topics from Decision Mathematics

Challenge Level

You can get a great feel for functions by sketching their graphs or using graph plotting software...

Challenge Level

What advanced mathematics can you do on a dotty grid?

What stories do complicated data sets tell us? How can we present the information clearly?

By exploring these problems you'll gain a greater appreciation of the importance of place value.

When numbers are raised to different powers, there are lots of properties you can explore.

Challenge Level

Learn about vectors and how to use them to solve problems

Challenge Level

What are complex numbers, and how can we represent them?

Challenge Level

Creating mental images is a powerful way to solve maths problems.

Challenge Level

Working on these problems will offer you insights into how areas and perimeters are related.

Challenge Level

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

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.

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

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