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

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

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

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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?

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

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

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

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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.

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

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

Number problems at primary level that require careful consideration.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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.

Can you make square numbers by adding two prime numbers together?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do 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?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?