Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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

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

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?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

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

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.

This task follows on from Build it Up and takes the ideas into three dimensions!

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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

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

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Are these statements relating to odd and even numbers always true, sometimes true or never true?

These tasks give learners chance to generalise, which involves identifying an underlying structure.

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

It starts quite simple but great opportunities for number discoveries and patterns!

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

Nim-7 game for an adult and child. Who will be the one to take the last counter?

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

Got It game for an adult and child. How can you play so that you know you will always win?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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.

Can you work out how to win this game of Nim? Does it matter if you go first or second?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?