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

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

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

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

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

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.

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?

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

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

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?

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.

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

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.

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

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

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

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

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

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?

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?

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

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

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 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.

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?

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?

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

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?

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

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.

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

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

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

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

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

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.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?