My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

This problem is designed to help children to learn, and to use, the two and three times tables.

Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Can you use the information to find out which cards I have used?

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Can you place these quantities in order from smallest to largest?

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

Invent a scoring system for a 'guess the weight' competition.

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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

Use the differences to find the solution to this Sudoku.

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Can you draw the shape that is being described by these cards?

Some children have been doing different tasks. Can you see who was the winner?

Design your own scoring system and play Trumps with these Olympic Sport cards.

Can you spot circles, spirals and other types of curves in these photos?

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

A random ramble for teachers through some resources that might add a little life to a statistics class.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

How many legs do each of these creatures have? How many pairs is that?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Can you rank these quantities in order? You may need to find out extra information or perform some experiments to justify your rankings.

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

Can you lay out the pictures of the drinks in the way described by the clue cards?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?

Is it really greener to go on the bus, or to buy local?

How many generations would link an evolutionist to a very distant ancestor?

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits

A pair of Sudoku puzzles that together lead to a complete solution.

Four small numbers give the clue to the contents of the four surrounding cells.

This Sudoku, based on differences. Using the one clue number can you find the solution?

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .