This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

How would you count the number of fingers in these pictures?

What can you say about the angles on opposite vertices of any cyclic quadrilateral? Working on the building blocks will give you insights that may help you to explain what is special about them.

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .

Explore the properties of matrix transformations with these 10 stimulating questions.

Marcus, Kathryn, Philippa and Ellie all used fantastic proportional reasoning as they worked on this problem.

Spreadsheets, trial and improvement, and simultaneous equations were just some of the approaches used to solve this problem.

We really liked the way Alex approached the solution to this problem, using a mixture of numerical and pure methods.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

Members of the NRICH team are beginning to write blogs and this very short article is designed to put the reasoning behind this move in context.

NRICH website full of rich tasks and guidance. We want teachers to use what we have to offer having a real sense of what we mean by rich tasks and what that might imply about classroom practice.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?