Find out about Magic Squares in this article written for students. Why are they magic?!

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these three-digit numbers to the nearest 100?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

An investigation that gives you the opportunity to make and justify predictions.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Can you find the chosen number from the grid using the clues?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you replace the letters with numbers? Is there only one solution in each case?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

This challenge is about finding the difference between numbers which have the same tens digit.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Have a go at balancing this equation. Can you find different ways of doing it?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

What two-digit numbers can you make with these two dice? What can't you make?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Can you work out some different ways to balance this equation?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

What happens when you round these numbers to the nearest whole number?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Can you find all the different ways of lining up these Cuisenaire rods?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Find out what a "fault-free" rectangle is and try to make some of your own.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?