These tasks, chosen from our 2022 summer challenges, are particularly suitable for the start of term, when you are getting to know your students.

We hope that students working on these problems will enjoy discovering that algebra can be a versatile tool for solving a range of problems.

Students are invited to explore a variety of problems and are then challenged to construct convincing arguments to explain what they have discovered.

These problems offer students the chance to investigate geometrical properties, make conjectures and create convincing mathematical proofs.

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

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

Challenge Level

This feature introduces students to the world of networks and graph theory and their applications.

The activities in this feature offer a variety of playful contexts in which students are required to plan ahead and analyse the outcomes.

The problems in this feature will give students 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.

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

This feature offers students some interesting problems that introduce them to number theory, where they are able to apply some standard algebraic techniques and pictorial representations.

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

This feature is intended to help students understand how probability can help them make better choices.

Challenge Level

We share a model for reflecting on what makes a good mathematician

Challenge Level

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

Challenge Level

How do we write numbers in different forms?

Challenge Level

How can Cuisenaire rods be used to develop visualising and reasoning?

Challenge Level

Problems designed to inspire students to explore and provoke a need to explain

Challenge Level

The problems in this feature encourage students to consider inverses and working backwards to solve problems.

Challenge Level

Encouraging students to reflect on their own and others' solutions

Challenge Level

Using different representations helps students to think mathematically.

Challenge Level

Advice and problems to help your students become more resilient.

Challenge Level

Developing fluency, provoking reasoning.

Challenge Level

Invite your students to be playful with this selection of numerical tasks.

Challenge Level

In this feature, we offer a selection of rich problems about area for use in all secondary classrooms.

Challenge Level

Short problems ideal for revision and assessment

Challenge Level

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

There's more room to manoeuvre than you might initially imagine!

See some Number Patterns problems from Wild Maths and make your classroom more creative.

Challenge Level

Try a selection of problems from Cambridge University's epiSTEMe project

A selection of resources from the Cambridge Mathematics Education Project

Challenge Level

Using NRICH tasks to enrich your students' mathematical experience

Challenge your students to push the boundaries!

Challenge Level

What maths can your students discover on dotty grids?

Challenge Level

A chance for students to use statistical skills to answer some interesting questions.

These problems are designed to help students develop an appreciation for the importance of place value and powers.

Challenge Level

These tasks will support your students' understanding of positive and negative numbers.

Challenge Level

These resources are designed to introduce students to complex numbers in an exploratory way.

Challenge Level

Challenge your students to develop their visualisation skills by working on these tasks

Challenge Level

This collection offers resources for teaching perimeter, area, volume, and finally integration.

Challenge Level

These classroom resources aim to help students reason with numbers.

These classroom resources aim to help students think about geometrical reasoning.

Challenge Level

These problems are designed to help Stage 3, 4 and 5 students to handle data and work with statistics.

Challenge Level

Read about Steve Hewson's research project on exceptional mathematicians.

These problems introduce number sequences and representations, and summation of series.

Challenge Level

Teacher resources on working systematically at secondary level

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.