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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

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.

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.

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

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?

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?

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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

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

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 find the chosen number from the grid using the clues?

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?

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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.

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.

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

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.

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

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

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?

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?

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

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

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.

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

How many models can you find which obey these rules?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?